CN113218577A - Outfield measurement method for star point centroid position precision of star sensor - Google Patents
Outfield measurement method for star point centroid position precision of star sensor Download PDFInfo
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Abstract
The invention discloses an outfield measurement method for star point centroid position precision of a star sensor, which is characterized in that matched star point centroid coordinates and corresponding right ascension declination coordinates are obtained through an outfield star observation experiment of the star sensor; calculating by using the coordinates of the centroid of the star points, the optimal principal point and the focal length value to obtain a star diagonal distance measurement value; calculating by using the corresponding right ascension and declination coordinates to obtain a star diagonal distance theoretical value; then the star diagonal distance error can be obtained through calculation; theoretically deducing the relation between the star diagonal distance error and the star point centroid position error on the basis; and finally, the accuracy of the star point centroid position is obtained through calculation, and a reliable evaluation means is provided for the evaluation of the accuracy of the star point centroid position of the high-accuracy matching type star sensor and the small-field single star tracker. The error caused by simulating the star light of the fixed star by using the single-star simulator and the collimator in the laboratory is reduced, so that the measurement and the evaluation of the position precision of the star point mass center of the star sensor are more accurate.
Description
Technical Field
The invention belongs to the technical field of star sensor measurement, and particularly relates to an outfield measurement method for star point centroid position precision of a star sensor.
Background
The astronomical navigation system has the advantages of high precision, strong autonomy, no accumulated error and the like, and is favored by multi-field multi-platform navigation systems of aviation, aerospace, navigation and the like. The star sensor is a high-precision astronomical navigation attitude measurement device taking a fixed star as an observation object, and is widely applied to platforms such as satellites and ships.
The attitude measurement precision of the star sensor is generally evaluated by attitude angle precision, which is the most direct index for evaluating the attitude precision of the star sensor. The index is related to the factors such as the position accuracy of the centroid of the star point of the fixed star, the number of the fixed stars participating in calculation, the distribution characteristics of the fixed stars in the view field, the resolution of the pixel of the detector and the like, wherein the position accuracy of the centroid of the star point of the fixed star is the most important factor influencing the attitude accuracy of the star sensor. With the progress of the star sensor technology, the star sensor not only carries out a simple attitude measurement task, but also is expanded and applied to systems of pose determination of various platforms in the atmosphere, autonomous orbit determination of satellite platforms and the like. For the working mode of the small-view-field star sensor with only one star point in the view field, the evaluation of the measurement accuracy of the centroid position of the star point is particularly important.
The measurement method combining laboratory experimental measurement and theoretical evaluation can simply and conveniently realize the measurement of the star point centroid position precision of the star sensor used by the traditional satellite and airborne platform, but the laboratory method has high requirements on the performance of test equipment such as a turntable, a collimator, a single-star simulator and the like: (1) the position precision of the rotary table is generally required to be one order of magnitude higher than the precision of the star sensor to be tested, and for the very high-precision star sensor, if no matched high-precision rotary table exists, a laboratory measurement method cannot be used; (2) the focal length of a collimator tube for a laboratory is limited, so that parallel light emitted by a fixed star at infinity cannot be really simulated, and for a long-focal-length star sensor applied in some applications, extra errors are introduced in the measurement process; (3) the single-star simulator has limited spectrum range for simulating fixed stars, and can not realize the simulation of various spectrum type fixed stars.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method overcomes the defects of the existing star sensor on the precision measurement method of the star point centroid position, provides an outfield star observation experiment measurement method of the star point centroid position precision, can accurately measure the star point centroid position precision of the star sensor with some special requirements (very high precision, long focal length and various working bands), and further provides a reasonable evaluation means for the detection performance of all types of star sensors.
The technical scheme adopted by the invention for solving the technical problems is as follows: an outfield measurement method for star point centroid position accuracy of a star sensor comprises the following steps:
step (1), calibrating and obtaining initial system parameters of the star sensor in a laboratory, wherein the initial system parameters comprise a principal point and a focal length, and then building and debugging an outfield star observation experimental system at an outfield astronomical observation station under the condition of clear weather;
step (2), controlling an external field two-dimensional turntable to enable an optical axis of a star sensor on the external field two-dimensional turntable to be opposite to the zenith direction, and continuously collecting and storing star maps in a zenith area;
step (3), aiming at the shot star map, the star point extraction and star map matching functions are completed, and star point mass center coordinates of fixed stars which are successfully matched and right ascension declination information under a corresponding celestial coordinate system are stored;
calculating the theoretical star diagonal distance of the fixed star by utilizing the right ascension declination of the successfully matched fixed star;
calculating to obtain a star diagonal distance measurement value of the fixed star by using the star point centroid coordinates of the successfully matched fixed star, the initial principal point and the focal length parameter;
step (6), calculating the star diagonal distance error and the standard deviation thereof;
step (7), optimizing the initial principal point and the focal length parameter by using the results obtained in the steps (2) to (5) and taking the result of the star diagonal distance error calculated in the step (6) as a criterion, and obtaining the optimal principal point and the optimal focal length;
step (8) repeating the calculation processes of the step (3) to the step (6), and only changing the initial principal point and the focal length parameter used in the step (5) into the optimal principal point and the optimal focal length parameter obtained by resolving in the step (7);
and (9) calculating the standard deviation of the centroid position of the star point according to a conversion formula between the derived standard deviation of the centroid position of the star point and the standard deviation of the diagonal distance of the star point.
The specific method in the step (1) comprises the following steps:
in a laboratory, a conventional star sensor laboratory calibration system is built by utilizing test equipment such as an indoor two-dimensional turntable, a single-star simulator, a collimator and the like; and preliminarily calibrating the principal point coordinate (x) of the star sensor0，y0) Focal length f0Waiting for initial system parameters; under the sunny weather condition of an astronomical observation station, an outsider star observation experiment system is built by using outsider test equipment such as an outsider two-dimensional turntable, a level meter and the like.
The specific method in the step (2) comprises the following substeps:
step (2-1): leveling a base of an outfield two-dimensional turntable, electrifying the turntable and keeping a zero position, installing the star sensor on the two-dimensional turntable, and ensuring that an optical axis of the star sensor points to the zenith direction;
step (2-2): electrifying the star sensor, entering a ground detection mode, and starting ground detection software;
step (2-3): and shooting and storing the star map of the zenith area by using ground detection software.
The specific method in the step (3) comprises the following substeps:
step (3-1): for t1Extracting star points and matching star maps by n star maps continuously shot at any moment, and storing m successfully matched star maps in each star map1Centroid coordinates of individual star points
And the corresponding right ascension declination
Where j is 1, …, n and k1＝1，…，m1；
Step (3-2): for t2Time (t)2＝t1+Δt1) Continuously shooting n star maps to extract star points and match the star maps; at the moment, the star image point position of the fixed star in the view field moves a certain distance on the target surface of the detector due to the rotation of the earth, and t is obtained by calculation2A set of corresponding m of time instants2Centroid coordinates of individual star points
And declination of right ascension
Where j is 1, …, n and k2＝1，…，m2；
Step (3-3): repeating the step (3-2) for a plurality of times until tpAt a time, a set of corresponding m is obtainedpCentroid coordinates of individual star points
And declination of right ascension
Where j is 1, …, n and kp＝1，…，mp；
Step (3-4): after that, t1All fixed stars appearing in the time field of view are moved out of the field of view, p groups of data are collected in total, each group is provided with n star maps, and each star map is provided with mr(wherein, r is 1, …, p) pairs of star point centroid coordinates and right ascension declination coordinates;
step (3-5): controlling the azimuth angle of the two-dimensional rotary table to rotate 90 degrees by using the rotary table to control the computer, repeating the steps (3-1) to (3-3), and correspondingly acquiring q groups of data, wherein each group comprises n frames of star maps, and each frame of star map comprises mc(wherein, c is 1, …, q) pairs of star point centroid coordinates and right ascension declination coordinates;
step (3-6): and statistically sorting the collected star point centroid coordinates and the corresponding right ascension declination, and sharing n x (p + q) groups.
In the step (4), the theoretical star diagonal angle of the fixed star is obtained by calculating the right ascension and declination of the fixed starThe distance implementation process comprises the following steps: for convenient expression, let the right ascension and declination coordinates of two stars be (alpha)i1,δi1) And (alpha)i2,δi2) Calculating the direction vector V of the two fixed stars under the equatorial inertia system of the earthi1And Vi2The formula is as follows:
further calculating to obtain the star diagonal distance DiThe calculation formula is as follows:
in the step (5), the star diagonal distance measurement value between every two star points is calculated by using the star point centroid coordinates of the fixed stars which are successfully matched and the optimized principal point and focal length parameters, and the implementation process is as follows:
for convenient expression, the mass center coordinates of two fixed stars are respectively set as (x)s1,ys1) And (x)s2,ys2) Using the initial principal point (x) obtained in step (1)0，y0) And focal length f0Calculating the direction vector V of the two fixed stars under the measuring coordinate system of the star sensors1And Vs2The formula is as follows:
wherein the content of the first and second substances,
and then the actually measured star diagonal distance D between every two star points is obtained through calculationsThe calculation formula is as follows:
the calculation formula for calculating the star diagonal distance error in the step (6) is as follows:
ΔD＝Ds-Di
wherein DsFor actually measuring the angular separation of the stars, DiIs the theoretical diagonal moment of the star.
The standard deviation of the measurement of the star diagonal distance is as follows:
wherein Δ DkFor the kth star diagonal error, k is 1, …, and h is the total number of all the star diagonals taken.
The implementation process of the step (7) is as follows: and (5) calculating to obtain the star diagonal distance error of each group of data by using the calculation method from the step (2) to the step (5), and obtaining the optimal principal point and the focal length value by using an optimization algorithm and taking the minimum star diagonal distance error as a criterion.
The implementation process of the step (8) is as follows: repeating the calculation processes of the steps (3) to (6), and replacing the initial principal point and the focal length parameter used in the step (5) with the optimal principal point (x ') obtained by calculation in the step (7)'0，y′0) And focal length f parameters, and finally calculating the obtained star diagonal distance error and the standard deviation thereof on the basis.
The step (9) is realized by: for convenience of expression, a principal point (x'0，y′0) The coordinates of the star point and the mass center of two fixed stars as the origin of coordinates are (x)1,y1) And (x)2,y2) And if the optimal focal length is f, the star diagonal distance calculation formula is as follows:
wherein:
deducing the standard deviation sigma of the star diagonal distance without considering the focal length factorDCentroid with star pointThe relationship between the position standard deviations σ is:
wherein M ═ x1x2+y1y2+f2. The standard deviation sigma of the star point centroid position can be calculated by the above formula.
In conclusion, the method of the invention provides a method for obtaining the matched centroid coordinates of star points and the corresponding right ascension declination coordinates through an outside field star observation experiment of a star sensor; calculating by using the coordinates of the centroid of the star points, the optimal principal point and the focal length value to obtain a star diagonal distance measurement value; calculating by using the corresponding right ascension and declination coordinates to obtain a star diagonal distance theoretical value; then the star diagonal distance error can be obtained through calculation; theoretically deducing the relation between the star diagonal distance error and the star point centroid position error on the basis; and finally, the accuracy of the star point centroid position is obtained through calculation, and a reliable evaluation means is provided for the evaluation of the accuracy of the star point centroid position of the high-accuracy matching type star sensor and the small-field single star tracker.
Compared with the prior art, the invention has the advantages that:
(1) the method carries out data acquisition through an outfield star observation experiment, compared with a laboratory method, an observation object is a real fixed star sky, and the error caused by simulating fixed star starlight by using a single star simulator and a collimator in a laboratory is reduced, so that the measurement and the evaluation of the precision of the star point mass center position of the star sensor are more accurate;
(2) the star point centroid position precision measurement method of the star sensor can be used for all matched star sensors, particularly high-precision star sensors and small-field single star trackers, and provides an effective means for evaluating the imaging performance of a photoelectric imaging system.
(3) According to the star point centroid position precision measurement method of the star sensor, the calibration of the principal point, the focal length and other important parameters is realized in the process of the external field experiment, and the calculated optimal principal point and focal length value can be directly used for the star sensor.
Drawings
FIG. 1 is a block flow diagram of the method of the present invention;
FIG. 2 is a schematic diagram of an external field experiment system of a star sensor provided by the invention;
FIG. 3 is a schematic diagram of the process of collecting star maps (0 degree of orientation of the turntable) according to the present invention;
FIG. 4 is a schematic view of the process of acquiring star maps (90 degrees of turntable orientation) according to the present invention;
FIG. 5 is a computer-acquired diagram of a hunter's constellation.
In the figure: the method comprises the following steps of 1, 2, 3, 4 and 5, wherein the star sensor is a star sensor, the two-dimensional turntable is 2, the data acquisition computer is 3, and the foundation platform is 5.
Detailed Description
Embodiments of the invention are described in detail below with reference to the accompanying drawings:
the system adopted in the experiment can be shown in fig. 2, and the specific experimental process is as follows:
the first step is as follows: laboratory obtains preliminary parameter and builds external field experimental system
In a laboratory, a conventional star sensor laboratory calibration system is built by utilizing test equipment such as an indoor two-dimensional turntable, a single-star simulator, a collimator and the like; and preliminarily calibrating the principal point coordinate (x) of the star sensor0，y0) Focal length f0Waiting for initial system parameters; and (4) building and debugging an outfield star observation experiment system under the conditions of astronomical observation in the outfield and fine weather.
The second step is that: shoot star chart
The method comprises the following steps of controlling an outfield two-dimensional turntable to enable an optical axis of a star sensor on the outfield two-dimensional turntable to be opposite to the zenith direction, and continuously collecting and storing a star map of a zenith area, wherein the method comprises the following substeps:
step (2-1): leveling a base of an outfield two-dimensional turntable, electrifying the turntable and keeping a zero position, installing the star sensor on the two-dimensional turntable, and ensuring that an optical axis of the star sensor points to the zenith direction;
step (2-2): electrifying the star sensor, entering a ground detection mode, and starting ground detection software;
step (2-3): shooting and storing a star map of a zenith area by using ground detection software;
the third step: the star point extraction and star map matching are completed
The method comprises the following substeps of finishing star point extraction and star map matching functions aiming at a shot star map, and storing star point mass center coordinates of stars which are successfully matched and right ascension and declination information of right ascension under a corresponding celestial coordinate system:
step (3-1): for t1Extracting star points and matching star maps by n star maps continuously shot at any moment, and storing m successfully matched star maps in each star map1Centroid coordinates of individual star points
And the corresponding right ascension declination
Where j is 1, …, n and k1＝1，…，m1；
Step (3-2): for t2Time (t)2＝t1+Δt1) Continuously shooting n star maps to extract star points and match the star maps; at the moment, the star image point position of the fixed star in the view field moves a certain distance on the target surface of the detector due to the rotation of the earth, and t is obtained by calculation2A set of corresponding m of time instants2Centroid coordinates of individual star points
And declination of right ascension
Where j is 1, …, n and k2＝1，…，m2；
Step (3-3): repeating the step (3-2) for a plurality of times until tpAt a time, a set of corresponding m is obtainedpCentroid coordinates of individual star points
And declination of right ascension
Where j is 1, …, n and kp＝1，…，mp；
Step (3-4): after that, t1All fixed stars appearing in the time field of view are moved out of the field of view, p groups of data are collected in total, each group is provided with n star maps, and each star map is provided with mr(wherein, r is 1, …, p) pairs of star point centroid coordinates and right ascension declination coordinates;
step (3-5): controlling the azimuth angle of the two-dimensional rotary table to rotate 90 degrees by using the rotary table to control the computer, repeating the steps (3-1) to (3-3), and correspondingly acquiring q groups of data, wherein each group comprises n frames of star maps, and each frame of star map comprises mc(wherein, c is 1, …, q) pairs of star point centroid coordinates and right ascension declination coordinates;
step (3-6): and statistically sorting the collected star point centroid coordinates and the corresponding right ascension declination, and sharing n x (p + q) groups.
Step (4), calculating the theoretical star diagonal distance of the fixed star by using the right ascension declination of the fixed star successfully matched and obtained in the step (2);
the fourth step: calculating the diagonal distance of theoretical star
The theoretical star diagonal distance of the fixed star obtained by calculating the right ascension and declination of the fixed star is realized by the following steps: for convenient expression, let the right ascension and declination coordinates of two stars be (alpha)i1,δi1) And (alpha)i2,δi2) Calculating the direction vector V of the two fixed stars under the equatorial inertia system of the earthi1And Vi2The formula is as follows:
further calculating to obtain the star diagonal distance DiThe calculation formula is as follows:
the fifth step: calculating the measurement of the star-to-diagonal distance
The implementation process of calculating and obtaining the star diagonal distance measurement value between every two star points by using the star point centroid coordinates of the fixed stars successfully matched with the optimized principal point and the focal length parameters is as follows:
for convenient expression, the mass center coordinates of two fixed stars are respectively set as (x)s1,ys1) And (x)s2,ys2) Using the initial principal point (x) obtained in step (1)0，y0) And f, calculating the direction vectors V of the two fixed stars under the measuring coordinate system of the star sensors1And Vs2The formula is as follows:
wherein the content of the first and second substances,
and then the actually measured star diagonal distance D between every two star points is obtained through calculationsThe calculation formula is as follows:
and a sixth step: calculating the star-to-diagonal distance error and its standard deviation
The formula for calculating the star diagonal distance error is as follows:
ΔD＝Ds-Di
wherein DsFor actually measuring the angular separation of the stars, DiIs the theoretical diagonal moment of the star.
The standard deviation of the measurement of the star diagonal distance is as follows:
wherein Δ DkFor the kth star diagonal error, k is 1, …, and h is the total number of all the star diagonals taken.
The seventh step: principal point, focal length parameter optimization
And (5) calculating to obtain the star diagonal distance error of each group of data by using the calculation method from the step (2) to the step (5), and obtaining the optimal principal point and the focal length value by using an optimization algorithm and taking the minimum star diagonal distance error as a criterion.
Eighth step: calculating the standard deviation of the star-to-diagonal distance
Repeating the calculation processes of the steps (3) to (6), and replacing the initial principal point and the focal length parameter used in the step (5) with the optimal principal point (x ') obtained by calculation in the step (7)'0，y′0) And f' parameters of the focal length, and finally calculating the star-diagonal distance error and the standard deviation thereof.
The ninth step: calculating the standard deviation of the star point position error
For convenience of expression, a principal point (x'0，y′0) The coordinates of the star point and the mass center of two fixed stars as the origin of coordinates are (x)1,y1) And (x)2,y2) And if the optimal focal length is f, the star diagonal distance calculation formula is as follows:
wherein:
deducing the standard deviation sigma of the star diagonal distance without considering the focal length factorDThe relation between the standard deviation sigma and the star point centroid position is as follows:
wherein M ═ x1x2+y1y2+f2. The standard deviation sigma of the star point centroid position can be calculated by the above formula.
Claims (10)
1. An outfield measurement method for star point centroid position precision of a star sensor is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps that (1) initial system parameters of the star sensor are calibrated and obtained in a laboratory, the initial system parameters comprise a principal point and a focal length, and then an outfield star observation experiment system is built and debugged at an outfield astronomical observation station under the condition of clear weather;
step (2), controlling an external field two-dimensional turntable to enable an optical axis of a star sensor on the external field two-dimensional turntable to be opposite to the zenith direction, and continuously collecting and storing star maps in a zenith area;
step (3), aiming at the shot star map, the star point extraction and star map matching functions are completed, and star point mass center coordinates of fixed stars which are successfully matched and right ascension declination information under a corresponding celestial coordinate system are stored;
calculating the theoretical star diagonal distance of the fixed star by utilizing the right ascension declination of the successfully matched fixed star;
calculating to obtain a star diagonal distance measurement value of the fixed star by using the star point centroid coordinates of the successfully matched fixed star, the initial principal point and the focal length parameter;
step (6), calculating the star diagonal distance error and the standard deviation thereof;
step (7), optimizing the initial principal point and the focal length parameter by using the results obtained in the steps (2) to (5) and taking the result of the star diagonal distance error calculated in the step (6) as a criterion, and obtaining the optimal principal point and the optimal focal length;
step (8) repeating the calculation processes of the step (3) to the step (6), and only changing the initial principal point and the focal length parameter used in the step (5) into the optimal principal point and the optimal focal length parameter obtained by resolving in the step (7);
and (9) calculating the standard deviation of the centroid position of the star point according to a conversion formula between the derived standard deviation of the centroid position of the star point and the standard deviation of the diagonal distance of the star point.
2. The outfield measurement method of the accuracy of the centroid position of the star point of the star sensor according to claim 1, wherein: the specific method in the step (1) comprises the following steps: in a laboratory, a conventional star sensor laboratory calibration system is built by utilizing an indoor two-dimensional turntable, a single-star simulator and collimator test equipment; and preliminarily calibrating the principal point coordinates of the star sensor(x0，y0) Focal length f0Initial system parameters; and under the sunny weather condition of the astronomical observation station, constructing an outfield star observation experiment system by using an outfield two-dimensional turntable and a level meter outfield test device.
3. The outfield measurement method of the accuracy of the centroid position of the star point of the star sensor according to claim 1, wherein: the specific method in the step (2) is as follows:
step (2-1): leveling a base of an outfield two-dimensional turntable, electrifying the turntable and keeping a zero position, installing the star sensor on the two-dimensional turntable, and ensuring that an optical axis of the star sensor points to the zenith direction;
step (2-2): electrifying the star sensor, entering a ground detection mode, and starting ground detection software;
step (2-3): and shooting and storing the star map of the zenith area by using ground detection software.
4. The outfield measurement method of the accuracy of the centroid position of the star point of the star sensor according to claim 1, wherein: the specific method in the step (3) is as follows:
step (3-1): for t1Extracting star points and matching star maps by n star maps continuously shot at any moment, and storing m successfully matched star maps in each star map1Centroid coordinates of individual star points
And the corresponding right ascension declination
Where j is 1, …, n and k1＝1，…，m1；
Step (3-2): for t2Time (t)2＝t1+Δt1) Continuously shooting n star maps to extract star points and match the star maps; at the moment, the star image point position of the fixed star in the view field moves a certain distance on the target surface of the detector due to the rotation of the earth, and t is obtained by calculation2A set of corresponding m of time instants2Centroid coordinates of individual star points
And declination of right ascension
Where j is 1, …, n and k2＝1，…，m2；
Step (3-3): repeating the step (3-2) for a plurality of times until tpAt a time, a set of corresponding m is obtainedpCentroid coordinates of individual star points
And declination of right ascension
Where j is 1, …, n and kp＝1，…，mp；
Step (3-4): after that, t1All fixed stars appearing in the time field of view are moved out of the field of view, p groups of data are collected in total, each group is provided with n star maps, and each star map is provided with mrAnd aligning the centroid coordinate of the star point and the declination coordinate of the right ascension, wherein: r ═ l, …, p;
step (3-5): controlling the azimuth angle of the two-dimensional rotary table to rotate 90 degrees by using the rotary table to control the computer, repeating the steps (3-1) to (3-3), and correspondingly acquiring q groups of data, wherein each group comprises n frames of star maps, and each frame of star map comprises mcAnd aligning the centroid coordinate of the star point and the declination coordinate of the right ascension, wherein: c is 1, …, q;
step (3-6): and statistically sorting the collected star point centroid coordinates and the corresponding right ascension declination, and sharing n x (p + q) groups.
5. The outfield measurement method of the accuracy of the centroid position of the star point of the star sensor according to claim 1, wherein: the specific method in the step (4) comprises the following steps: for convenient expression, let the right ascension and declination coordinates of two stars be (alpha)i1,δi1) And (alpha)i2,δi2) Meter for measuringCalculating the direction vector V of the two fixed stars under the equatorial inertia system of the Earthi1And Vi2The formula is as follows:
further calculating to obtain the star diagonal distance DiThe calculation formula is as follows:
6. the outfield measurement method of the accuracy of the centroid position of the star point of the star sensor according to claim 1, wherein: the implementation process for calculating the star diagonal distance measurement value of the fixed star in the step (5) comprises the following steps:
for convenient expression, the mass center coordinates of two fixed stars are respectively set as (x)s1,ys1) And (x)s2,ys2) Using the initial principal point (x) obtained in step (1)0，y0) And focal length f0Calculating the direction vector V of the two fixed stars under the measuring coordinate system of the star sensors1And Vs2The formula is as follows:
wherein the content of the first and second substances,
and then the actually measured star diagonal distance D between every two star points is obtained through calculationsThe calculation formula is as follows:
7. the outfield measurement method of the accuracy of the centroid position of the star point of the star sensor according to claim 1, wherein: the calculation formula for calculating the star diagonal distance error in the step (6) is as follows:
ΔD＝Ds-Di
wherein DsFor actually measuring the angular separation of the stars, DiIs a theoretical star diagonal moment;
the standard deviation of the measurement of the star diagonal distance is as follows:
wherein Δ DkFor the kth star diagonal error, k is 1, …, and h is the total number of all the star diagonals taken.
8. The outfield measurement method of the accuracy of the centroid position of the star point of the star sensor according to claim 1, wherein: the implementation process of the step (7) is as follows: and (5) calculating to obtain the star diagonal distance error of each group of data by using the calculation method from the step (2) to the step (5), and obtaining the optimal principal point and the focal length value by using an optimization algorithm and taking the minimum star diagonal distance error as a criterion.
9. The outfield measurement method of the accuracy of the centroid position of the star point of the star sensor according to claim 1, wherein: the implementation process of the step (8) is as follows: repeating the calculation processes of the steps (3) to (6), and replacing the initial principal point and the focal length parameter used in the step (5) with the optimal principal point (x ') obtained by calculation in the step (7)'0，y′0) And focal length f parameters, and finally calculating the obtained star diagonal distance error and the standard deviation thereof on the basis.
10. The outfield measurement method of the accuracy of the centroid position of the star point of the star sensor according to claim 1, wherein: the step (9) is realized by:
for convenience of expression, a principal point (x'0，y′0) The coordinates of the star point and the mass center of two fixed stars as the origin of coordinates are (x)1,y1) And (x)2,y2) And if the optimal focal length is f, the star diagonal distance calculation formula is as follows:
wherein:
deducing the standard deviation sigma of the star diagonal distance without considering the focal length factorDThe relation between the standard deviation sigma and the star point centroid position is as follows:
wherein M ═ x1x2+y1y2+f2And calculating the standard deviation sigma of the star point centroid position according to the formula.
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