CN113405567A - Gravity satellite star sensor mounting matrix on-orbit calibration method and system - Google Patents
Gravity satellite star sensor mounting matrix on-orbit calibration method and system Download PDFInfo
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- CN113405567A CN113405567A CN202110604491.0A CN202110604491A CN113405567A CN 113405567 A CN113405567 A CN 113405567A CN 202110604491 A CN202110604491 A CN 202110604491A CN 113405567 A CN113405567 A CN 113405567A
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Abstract
The invention provides an on-orbit calibration method and system for a gravity satellite star sensor installation matrix, wherein a first relation expression is obtained by an attitude matrix, an installation error matrix and an installation matrix of a first star sensor and a second star sensor; then, calculating first attitude angular acceleration information according to an attitude matrix under a first star sensor coordinate system, and calculating second attitude angular acceleration information according to an attitude matrix under a second star sensor coordinate system; and finally, calculating the installation error attitude angle of the first star sensor and the installation error attitude angle of the second star sensor by taking the first relation as a constraint condition. The method utilizes the first relation representation obtained by the relative calibration method as the constraint condition, and combines the angular acceleration of the gravity accelerometer to carry out on-orbit calibration on the star sensor, so that the accuracy of the on-orbit calibration of the mounting matrix of the star sensor can be improved.
Description
Technical Field
The invention relates to the fields of spacecraft control, geodetic surveying, space science and the like, in particular to an in-orbit calibration method and system for a gravity satellite star sensor installation matrix.
Background
The star sensor (star sensor for short) is an important component in a gravity measurement satellite system, and is used for determining the attitude of a gravity satellite relative to an inertial space, providing coordinate conversion information for a non-conservative force measurement result of an accelerometer and providing high-precision three-axis attitude determination information for the gravity satellite by combining with orbit parameters. The star sensor is a sensitive device for measuring the attitude by taking a fixed star as a reference object, the attitude information of the star sensor is from the pointing direction of a direction vector of star light of the fixed star in an inertial reference coordinate system and the pointing direction of the direction vector of the star light of the fixed star in a measurement coordinate system of the star sensor, and the attitude measurement precision can reach the level of angular seconds. In practical application, however, the installation error of the star sensor can reach the angle grading, and the measurement error caused by the installation error is higher than the random measurement error of the star sensor. Although the error of the star sensor mounting matrix is calibrated on the ground before the satellite is launched, the star sensor needs to be used on the orbit for a long time, and the factors such as component aging, working environment change, star body launching impact and the like cause the change of the mounting matrix, so that an on-orbit calibration method of the star sensor mounting matrix is urgently needed to ensure the stable measurement accuracy of the star sensor so as to realize the calibration of the mounting matrix of the star sensor with higher accuracy.
Disclosure of Invention
The invention aims to provide an on-orbit calibration method and system for a gravity satellite star sensor mounting matrix, which can improve the calibration precision of the star sensor mounting matrix.
In order to achieve the purpose, the invention provides the following scheme:
an in-orbit calibration method for a gravity satellite star sensor mounting matrix comprises the following steps:
obtaining a first relational representation:
wherein B is the ratio of the first star sensor attitude matrix to the second star sensor attitude matrix,
is a mounting error matrix of the first star sensor,
is a mounting matrix of the first star sensor,
is a mounting error matrix of the second star sensor,
the star sensor is an installation matrix of the second star sensor;
calculating a first attitude angular acceleration of the first star sensor under the coordinate system of the first star sensor according to the attitude matrix of the first star sensor under the coordinate system of the first star sensor;
calculating a second attitude angular acceleration of the second star sensor under the coordinate system of the second star sensor according to the attitude matrix of the second star sensor under the coordinate system of the second star sensor;
acquiring an angular acceleration value measured by a gravity satellite accelerometer;
expressed as constraints in terms of a first relationship, respectively
And
calculating the installation error attitude angle of the first star sensor
And the installation error attitude angle of the second star sensor
Wherein the content of the first and second substances,
for the first attitude angular acceleration to be the first attitude angular acceleration,
for the second attitude angular acceleration to be the first attitude angular acceleration,
the angular acceleration value measured for the gravity satellite accelerometer.
Optionally, the calculating a first attitude angular acceleration of the first star sensor in the self coordinate system according to the attitude matrix of the first star sensor in the self coordinate system specifically includes:
coordinate conversion is carried out on the attitude matrix of the second star sensor under the coordinate system of the second star sensor, and the attitude matrix of the second star sensor taking the coordinate system of the first star sensor as a reference coordinate system is obtained and recorded as an attitude conversion matrix;
fusing the attitude transformation matrix with an attitude matrix of the first star sensor under a coordinate system of the first star sensor to obtain a fusion matrix;
and calculating the first attitude angular acceleration according to the fusion matrix.
Optionally, the calculating a second attitude angular acceleration of the second star sensor in the self coordinate system according to the attitude matrix of the second star sensor in the self coordinate system specifically includes:
coordinate conversion is carried out on the attitude matrix of the first star sensor under the coordinate system of the first star sensor, and the attitude matrix of the first star sensor taking the coordinate system of the second star sensor as a reference coordinate system is obtained and recorded as an attitude conversion matrix;
fusing the attitude transformation matrix with an attitude matrix of the second star sensor under a coordinate system of the second star sensor to obtain a fusion matrix;
and calculating a second attitude angular acceleration according to the fusion matrix.
Optionally, before the obtaining the first relational representation, the method further includes:
calculating the ratio of the first star sensor attitude matrix to the second star sensor attitude matrix, which specifically comprises the following steps:
obtaining a four-element observed value sequence q of the first star sensor1(tk) And q of the second star sensor2(tk)；
Using a formula
Calculating the mean value of the ratio of the attitude matrix sequence value of the first star sensor to the attitude matrix sequence value of the second star sensor;
taking the mean value as the ratio of the attitude matrix of the first star sensor to the attitude matrix of the first star sensor;
wherein q is1(tk) Represents tkFour-element observed quantity q of first star sensor at moment2(tk) Represents tkAnd k is 1 … n, and n is the observation quantity of the four-element observation quantity of the second star sensor at the moment.
Optionally, before obtaining the first relational representation, the method further includes:
obtaining a second relational representation:
obtaining a third relational representation:
obtaining the first relational representation according to the second relational representation and the third relational representation;
wherein R (q)1) Is an attitude matrix of the first star sensor under a self coordinate system, R (q)2) Is an attitude matrix of the second star sensor under the coordinate system of the second star sensor,
is an attitude matrix of the gravity satellite body under a self coordinate system.
In order to achieve the above object, the present invention further provides an in-orbit calibration system for a gravity satellite star sensor mounting matrix, wherein the in-orbit calibration system for the gravity satellite star sensor mounting matrix comprises:
a first relational representation acquisition module for acquiring a first relational representation:
wherein B is the ratio of the first star sensor attitude matrix to the second star sensor attitude matrix,
is a mounting error matrix of the first star sensor,
is a mounting matrix of the first star sensor,
is a mounting error matrix of the second star sensor,
the star sensor is an installation matrix of the second star sensor;
the first attitude angular acceleration calculation module is used for calculating first attitude angular acceleration of the first star sensor in the self coordinate system according to the attitude matrix of the first star sensor in the self coordinate system;
the second attitude angular acceleration calculation module is used for calculating second attitude angular acceleration of the second star sensor in the self coordinate system according to the attitude matrix of the second star sensor in the self coordinate system;
the accelerometer angular acceleration acquisition module is used for acquiring an angular acceleration value measured by a gravity satellite accelerometer;
a mounting error attitude angle calculation module for representing as constraints a first relationship, respectively based on
And
calculating the installation error attitude angle of the first star sensor
And said second starInstallation error attitude angle of sensor
Wherein the content of the first and second substances,
for the first attitude angular acceleration to be the first attitude angular acceleration,
for the second attitude angular acceleration to be the first attitude angular acceleration,
the angular acceleration value measured for the gravity satellite accelerometer.
Optionally, the first attitude angular acceleration calculation module specifically includes:
the first coordinate conversion unit is used for carrying out coordinate conversion on the attitude matrix of the second star sensor under the coordinate system of the second star sensor to obtain the attitude matrix of the second star sensor taking the coordinate system of the first star sensor as a reference coordinate system and recording the attitude matrix as the attitude conversion matrix;
the first matrix fusion unit is used for fusing the attitude transformation matrix with an attitude matrix of the first star sensor under a coordinate system of the first star sensor to obtain a fusion matrix;
and the first attitude angular acceleration calculation unit is used for calculating first attitude angular acceleration according to the fusion matrix.
Optionally, the second attitude angular acceleration calculation module specifically includes:
the second coordinate conversion unit is used for carrying out coordinate conversion on the attitude matrix of the first star sensor under the coordinate system of the first star sensor to obtain the attitude matrix of the first star sensor taking the coordinate system of the second star sensor as a reference coordinate system and recording the attitude matrix as an attitude conversion matrix;
the second matrix fusion unit is used for fusing the attitude transformation matrix with an attitude matrix of the second star sensor under a coordinate system of the second star sensor to obtain a fusion matrix;
and the second attitude angular acceleration calculation unit is used for calculating second attitude angular acceleration according to the fusion matrix.
Optionally, the gravity satellite star sensor mounting matrix on-orbit calibration system further includes:
the ratio calculation module is used for calculating the ratio of the first star sensor attitude matrix to the second star sensor attitude matrix, and specifically comprises the following steps:
an observed value sequence acquisition unit used for acquiring a four-element observed value sequence q of the first star sensor1(tk) And a four-element observed value sequence q of the second star sensor2(tk)；
A mean value calculation unit for employing a formula
Calculating the mean value of the ratio of the attitude matrix sequence value of the first star sensor to the attitude matrix sequence value of the second star sensor;
a ratio determining unit, configured to use the mean value as a ratio of the first star sensor attitude matrix to the first star sensor attitude matrix;
wherein q is1(tk) Represents tkFour-element observed quantity q of first star sensor at moment2(tk) Represents tkAnd k is 1 … n, and n is the observation quantity of the four-element observation quantity of the second star sensor at the moment.
Optionally, the gravity satellite star sensor mounting matrix on-orbit calibration system further includes:
a second relational representation obtaining module configured to obtain a second relational representation:
a third relational representation acquiring module, configured to acquire a third relational representation:
the first relation representation determining module is used for obtaining a first relation representation according to a second relation representation and a third relation representation;
wherein R (q)1) Is an attitude matrix of the first star sensor under a self coordinate system, R (q)2) Is an attitude matrix of the second star sensor under the coordinate system of the second star sensor,
is an attitude matrix of the gravity satellite body under a self coordinate system.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides an on-orbit calibration method and system for a gravity satellite star sensor installation matrix, wherein a first relation expression is obtained by an attitude matrix, an installation error matrix and an installation matrix of a first star sensor and a second star sensor; then, calculating first attitude angular acceleration information according to an attitude matrix under a first star sensor coordinate system, and calculating second attitude angular acceleration information according to an attitude matrix under a second star sensor coordinate system; and finally, calculating the installation error attitude angle of the first star sensor and the installation error attitude angle of the second star sensor by taking the first relation as a constraint condition. The method utilizes the first relation representation obtained by the relative calibration method as the constraint condition, and combines the acceleration of the star sensor and the angular acceleration of the gravity accelerometer to carry out on-orbit calibration on the star sensor, so that the on-orbit calibration precision of the mounting matrix of the star sensor can be improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of an in-orbit calibration method for a gravity satellite star sensor mounting matrix of the invention;
FIG. 2 is a schematic diagram of the module structure of the gravity satellite star sensor mounting matrix on-orbit calibration system.
Description of the symbols:
1-a first relation representation acquisition module, 2-a first attitude angular acceleration calculation module, 3-a second attitude angular acceleration calculation module, 4-an accelerometer angular acceleration acquisition module, 5-an installation error attitude angle calculation module, 6-a ratio calculation module, 7-a second relation representation acquisition module, 8-a third relation representation acquisition module and 9-a first relation representation determination module.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide an on-orbit calibration method and system for a gravity satellite star sensor mounting matrix, which take a first relation expression obtained by a relative calibration method as a constraint condition and can improve the calibration precision of the star sensor mounting matrix.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
An attitude quaternion is a hypercomplex number of four elements that can describe the rotation of one coordinate system or a vector relative to another coordinate system, i.e., the attitude of one coordinate system relative to another. The definition is as follows:
q＝[q0 q1 q2 q3]T；
the corresponding relationship between the attitude quaternion and the attitude angle (γ, θ, ψ) is:
in the selected reference coordinate system, if the attitude quaternion of one coordinate system is q, the attitude matrix of the coordinate system is:
as shown in FIG. 1, the on-orbit calibration method of the gravity satellite star sensor mounting matrix of the invention comprises the following steps:
s1: obtaining a first relational representation:
wherein B is the ratio of the first star sensor attitude matrix to the second star sensor attitude matrix,
is a mounting error matrix of the first star sensor,
is a mounting matrix of the first star sensor,
is a mounting error matrix of the second star sensor,
is the mounting matrix of the second star sensor.
S2: and calculating the first attitude angular acceleration of the first star sensor under the self coordinate system according to the attitude matrix of the first star sensor under the self coordinate system.
S3: and calculating a second attitude angular acceleration of the second star sensor under the self coordinate system according to the attitude matrix of the second star sensor under the self coordinate system.
S4: and acquiring an angular acceleration value measured by the gravity satellite accelerometer.
S5: expressed as constraints in terms of a first relationship, respectively
And
calculating the installation error attitude angle of the first star sensor
And the installation error attitude angle of the second star sensor
Wherein the content of the first and second substances,
for the first attitude angular acceleration to be the first attitude angular acceleration,
for the second attitude angular acceleration to be the first attitude angular acceleration,
the angular acceleration value measured for the gravity satellite accelerometer.
Essentially, the first relationship representation
Is a relative mounting matrix angle relative deviation relation between the first star sensor and the second star sensor, wherein, the mounting error matrix
And
can be expressed as (theta)1θ2θ3) And (beta)1β2β3)。
In addition, theoretically, the angular acceleration of the accelerometer and the angular acceleration of the star sensor should be consistent after coordinate transformation. If the star sensor has installation matrix deviation, the installation error angle is introduced as a parameter for estimation, and the attitude angle acceleration information of the star sensor is utilized
And angular acceleration data of accelerometer 1B level
Combining the star sensor installation matrix and the installation error matrix simultaneous equation, using the first relation expression as a constraint condition, and using the four-element observation data of a plurality of epochs to carry out parameter adjustment with the constraint condition to obtain the installation error angle estimation values of the first star sensor and the second star sensor, namely obtaining (theta)1θ2θ3) And (beta)1β2β3) An estimate of (d).
Further, the calculating the first attitude angular acceleration of the first star sensor in the self coordinate system according to the attitude matrix of the first star sensor in the self coordinate system specifically includes:
s21: and carrying out coordinate conversion on the attitude matrix of the second star sensor in the coordinate system of the second star sensor to obtain the attitude matrix of the second star sensor in the coordinate system of the first star sensor as a reference coordinate system, and recording the attitude matrix as an attitude conversion matrix.
S22, the attitude transformation matrix is fused with the attitude matrix of the first star sensor under the coordinate system of the first star sensor to obtain a fusion matrix
S23: and calculating the first attitude angular acceleration according to the fusion matrix.
In particular, the method is based on the fusion matrix
Calculating first attitude angular acceleration information
The method comprises the following steps:
the method according to the fusion matrix
Calculating first attitude angular acceleration information
The method specifically comprises the following steps:
according to the fusion matrix
Obtaining the fused four-element observed quantity
For the fused four-element observations
Performing CRN digital filtering:
for fusing four-element observations
The first derivative of (a).
According to
And
obtaining the attitude angular velocity omega of the first star sensorq＝[ωx,ωy,ωz]T，
For the attitude angular velocity omega of the first star sensorqPerforming CRN digital filtering:
obtaining the attitude angular acceleration of the first star sensor
Wherein, ω isxIs the component of the attitude angular velocity of the star sensor on the x axis, omegayComponent of attitude angular velocity of star sensor on y axis, omegazAnd the attitude angular velocity of the star sensor is the component of the z axis.
Preferably, the fusion matrix is acquired
And then, the observation data of the star sensor is subjected to weighted fusion by adopting a data processing method from 1A level to 1B level of the star sensor to obtain 1B level four-element observation data so as to reduce the observation noise of the star sensor.
Further, the calculating a second attitude angular acceleration of the second star sensor in the self coordinate system according to the attitude matrix of the second star sensor in the self coordinate system specifically includes:
s31: and carrying out coordinate conversion on the attitude matrix of the first star sensor under the coordinate system of the first star sensor to obtain the attitude matrix of the first star sensor taking the coordinate system of the second star sensor as a reference coordinate system, and recording the attitude matrix as an attitude conversion matrix.
S32: and fusing the attitude transformation matrix with an attitude matrix of the second star sensor under a coordinate system of the second star sensor to obtain a fusion matrix.
S33: and calculating a second attitude angular acceleration according to the fusion matrix.
Preferably, before the obtaining the first relational representation, the method further includes:
s6: calculating the ratio of the first star sensor attitude matrix to the second star sensor attitude matrix, which specifically comprises the following steps:
s61: obtaining a four-element observed value sequence q of the first star sensor1(tk) And q of the second star sensor2(tk)。
S62: using a formula
And calculating the mean value of the ratio of the attitude matrix sequence value of the first star sensor to the attitude matrix sequence value of the second star sensor.
S63: taking the mean value as a ratio of the first star sensor attitude matrix to the first star sensor attitude matrix, and then expressing the first relation as:
by calculating the mean value of the observation value sequence of the star sensor within a period of time, the sample data volume is increased, and the accuracy of obtaining the first relation representation can be improved.
Wherein q is1(tk) Represents tkFour-element observed quantity q of first star sensor at moment2(tk) Represents tkAnd k is 1 … n, and n is the observation quantity of the four-element observation quantity of the second star sensor at the moment.
Further, before obtaining the first relational representation, the method further includes:
s71: obtaining a second relational representation:
s72: obtaining a third relational representation:
s73: and obtaining the first relational representation according to the second relational representation and the third relational representation.
Wherein R (q)1) Is an attitude matrix of the first star sensor under a self coordinate system, R (q)2) Is an attitude matrix of the second star sensor under the coordinate system of the second star sensor,
is an attitude matrix of the gravity satellite body under a self coordinate system.
In order to achieve the above object, as shown in fig. 2, the present invention further provides an in-orbit calibration system for a gravity satellite star sensor mounting matrix, where the in-orbit calibration system for a gravity satellite star sensor mounting matrix comprises: the first relation represents an acquisition module 1, a first attitude angular acceleration calculation module 2, a second attitude angular acceleration calculation module 3, an accelerometer angular acceleration acquisition module 4 and a mounting error attitude angle calculation module 5.
A first relational representation obtaining module 1, configured to obtain a first relational representation:
wherein B is the ratio of the first star sensor attitude matrix to the second star sensor attitude matrix,
is a mounting error matrix of the first star sensor,
is a mounting matrix of the first star sensor,
is a mounting error matrix of the second star sensor,
is the mounting matrix of the second star sensor.
And the first attitude angular acceleration calculation module 2 is used for calculating the first attitude angular acceleration of the first star sensor in the self coordinate system according to the attitude matrix of the first star sensor in the self coordinate system.
And the second attitude angular acceleration calculation module 3 is used for calculating a second attitude angular acceleration of the second star sensor in the self coordinate system according to the attitude matrix of the second star sensor in the self coordinate system.
And the accelerometer angular acceleration acquisition module 4 is used for acquiring an angular acceleration value measured by the gravity satellite accelerometer.
A mounting error attitude angle calculation module 5 for representing as constraints a first relationship, respectively based on
And
calculating the installation error attitude angle of the first star sensor
And the installation error attitude angle of the second star sensor
Wherein the content of the first and second substances,
for the first attitude angular acceleration to be the first attitude angular acceleration,
for the second attitude angular acceleration to be the first attitude angular acceleration,
the angular acceleration value measured for the gravity satellite accelerometer.
Specifically, the first attitude angular acceleration calculation module 2 specifically includes: a first coordinate conversion unit 21, a first matrix fusion unit 22, and a first attitude angular acceleration calculation unit 23.
The first coordinate conversion unit 21 is configured to perform coordinate conversion on an attitude matrix of the second star sensor in a self coordinate system, obtain an attitude matrix of the second star sensor in a reference coordinate system based on the first star sensor coordinate system, and record the attitude matrix as an attitude conversion matrix.
And the first matrix fusion unit 22 is configured to fuse the attitude transformation matrix with an attitude matrix of the first star sensor in a coordinate system of the first star sensor to obtain a fusion matrix.
And a first attitude angular acceleration calculation unit 23, configured to calculate a first attitude angular acceleration according to the fusion matrix.
Further, the second attitude angular acceleration calculation module 3 specifically includes: a first coordinate conversion unit 31, a first matrix fusion unit 32, and a first attitude angular acceleration calculation unit 33.
And the second coordinate conversion unit 31 is configured to perform coordinate conversion on the attitude matrix of the first star sensor in the coordinate system of the first star sensor, obtain an attitude matrix of the first star sensor in a reference coordinate system based on the coordinate system of the second star sensor, and record the attitude matrix as an attitude conversion matrix.
And the second matrix fusion unit 32 is configured to fuse the attitude transformation matrix with an attitude matrix of the second star sensor in a coordinate system of the second star sensor to obtain a fusion matrix.
And a second attitude angular acceleration calculation unit 33 configured to calculate a second attitude angular acceleration according to the fusion matrix.
Further, the gravity satellite star sensor installation matrix in-orbit calibration system further comprises: and a ratio calculation module 6.
The ratio calculation module 6 is configured to calculate a ratio between the first star sensor attitude matrix and the second star sensor attitude matrix, and specifically includes:
an observed value sequence obtaining unit 61, configured to obtain a four-element observed value sequence q of the first star sensor1(tk) And a four-element observed value sequence q of the second star sensor2(tk)。
A mean value calculation unit 62 for employing the formula
And calculating the mean value of the ratio of the attitude matrix sequence value of the first star sensor to the attitude matrix sequence value of the second star sensor.
And the ratio determining unit 63 uses the average value as the ratio of the first star sensor attitude matrix to the first star sensor attitude matrix.
Wherein q is1(tk) Represents tkFour-element observed quantity q of first star sensor at moment2(tk) Represents tkAnd k is 1 … n, and n is the observation quantity of the four-element observation quantity of the second star sensor at the moment.
Further, the gravity satellite star sensor installation matrix in-orbit calibration system further comprises:
a second relational representation obtaining module 7, configured to obtain a second relational representation:
a third relational representation obtaining module 8, configured to obtain a third relational representation:
and the first relation representation determining module 9 obtains the first relation representation according to the second relation representation and the third relation representation.
Wherein R (q)1) Is an attitude matrix of the first star sensor under a self coordinate system, R (q)2) Is an attitude matrix of the second star sensor under the coordinate system of the second star sensor,
is an attitude matrix of the gravity satellite body under a self coordinate system.
Generally, two or more star sensors are installed on the gravity satellite, and the invention is suitable for the situation that the number of the star sensors is more than or equal to two.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. An in-orbit calibration method for a gravity satellite star sensor mounting matrix is characterized by comprising the following steps:
obtaining a first relational representation:
wherein B is the ratio of the first star sensor attitude matrix to the second star sensor attitude matrix,
is a mounting error matrix of the first star sensor,
is a mounting matrix of the first star sensor,
is a mounting error matrix of the second star sensor,
the star sensor is an installation matrix of the second star sensor;
calculating a first attitude angular acceleration of the first star sensor under the coordinate system of the first star sensor according to the attitude matrix of the first star sensor under the coordinate system of the first star sensor;
calculating a second attitude angular acceleration of the second star sensor under the coordinate system of the second star sensor according to the attitude matrix of the second star sensor under the coordinate system of the second star sensor;
acquiring an angular acceleration value measured by a gravity satellite accelerometer;
expressed as constraints in terms of a first relationship, respectively
And
calculating the installation error attitude angle of the first star sensor
And the installation error attitude angle of the second star sensor
Wherein the content of the first and second substances,
for the first attitude angular acceleration to be the first attitude angular acceleration,
for the second attitude angular acceleration to be the first attitude angular acceleration,
the angular acceleration value measured for the gravity satellite accelerometer.
2. The on-orbit calibration method for the gravity satellite star sensor mounting matrix according to claim 1, wherein the calculating of the first attitude angular acceleration of the first star sensor in the self coordinate system according to the attitude matrix of the first star sensor in the self coordinate system specifically comprises:
coordinate conversion is carried out on the attitude matrix of the second star sensor under the coordinate system of the second star sensor, and the attitude matrix of the second star sensor taking the coordinate system of the first star sensor as a reference coordinate system is obtained and recorded as an attitude conversion matrix;
fusing the attitude transformation matrix with an attitude matrix of the first star sensor under a coordinate system of the first star sensor to obtain a fusion matrix;
and calculating the first attitude angular acceleration according to the fusion matrix.
3. The on-orbit calibration method for the gravity satellite star sensor mounting matrix according to claim 1, wherein the calculating of the second attitude angular acceleration of the second star sensor in the self coordinate system according to the attitude matrix of the second star sensor in the self coordinate system specifically comprises:
coordinate conversion is carried out on the attitude matrix of the first star sensor under the coordinate system of the first star sensor, and the attitude matrix of the first star sensor taking the coordinate system of the second star sensor as a reference coordinate system is obtained and recorded as an attitude conversion matrix;
fusing the attitude transformation matrix with an attitude matrix of the second star sensor under a coordinate system of the second star sensor to obtain a fusion matrix;
and calculating a second attitude angular acceleration according to the fusion matrix.
4. The gravity satellite star sensor mounting matrix on-orbit calibration method according to claim 1, further comprising, before said obtaining the first relational representation:
calculating the ratio of the first star sensor attitude matrix to the second star sensor attitude matrix, which specifically comprises the following steps:
obtaining a four-element observed value sequence q of the first star sensor1(tk) And q of the second star sensor2(tk)；
Using a formula
Calculating the mean value of the ratio of the attitude matrix sequence value of the first star sensor to the attitude matrix sequence value of the second star sensor;
taking the mean value as the ratio of the attitude matrix of the first star sensor to the attitude matrix of the first star sensor;
wherein q is1(tk) Represents tkAt the first momentFour-element observed quantity q of star sensor2(tk) Represents tkAnd k is 1 … n, and n is the observation quantity of the four-element observation quantity of the second star sensor at the moment.
5. The gravity satellite star sensor mounting matrix on-orbit calibration method according to claim 1, further comprising, before obtaining the first relational representation:
obtaining a second relational representation:
obtaining a third relational representation:
obtaining the first relational representation according to the second relational representation and the third relational representation;
wherein R (q)1) Is an attitude matrix of the first star sensor under a self coordinate system, R (q)2) Is an attitude matrix of the second star sensor under the coordinate system of the second star sensor,
is an attitude matrix of the gravity satellite body under a self coordinate system.
6. An in-orbit calibration system for a gravity satellite star sensor installation matrix is characterized by comprising the following components:
a first relational representation acquisition module for acquiring a first relational representation:
wherein B is the ratio of the first star sensor attitude matrix to the second star sensor attitude matrix,
is a mounting error matrix of the first star sensor,
is a mounting matrix of the first star sensor,
is a mounting error matrix of the second star sensor,
the star sensor is an installation matrix of the second star sensor;
the first attitude angular acceleration calculation module is used for calculating first attitude angular acceleration of the first star sensor in the self coordinate system according to the attitude matrix of the first star sensor in the self coordinate system;
the second attitude angular acceleration calculation module is used for calculating second attitude angular acceleration of the second star sensor in the self coordinate system according to the attitude matrix of the second star sensor in the self coordinate system;
the accelerometer angular acceleration acquisition module is used for acquiring an angular acceleration value measured by a gravity satellite accelerometer;
a mounting error attitude angle calculation module for representing as constraints a first relationship, respectively based on
And
calculating the installation error attitude angle of the first star sensor
And the installation error attitude angle of the second star sensor
Wherein the content of the first and second substances,
for the first attitude angular acceleration to be the first attitude angular acceleration,
for the second attitude angular acceleration to be the first attitude angular acceleration,
the angular acceleration value measured for the gravity satellite accelerometer.
7. The gravity satellite star sensor mounting matrix on-orbit calibration system according to claim 6, wherein the first attitude angular acceleration calculation module specifically comprises:
the first coordinate conversion unit is used for carrying out coordinate conversion on the attitude matrix of the second star sensor under the coordinate system of the second star sensor to obtain the attitude matrix of the second star sensor taking the coordinate system of the first star sensor as a reference coordinate system and recording the attitude matrix as the attitude conversion matrix;
the first matrix fusion unit is used for fusing the attitude transformation matrix with an attitude matrix of the first star sensor under a coordinate system of the first star sensor to obtain a fusion matrix;
and the first attitude angular acceleration calculation unit is used for calculating first attitude angular acceleration according to the fusion matrix.
8. The gravity satellite star sensor mounting matrix on-orbit calibration system according to claim 6, wherein the second attitude angular acceleration calculation module specifically comprises:
the second coordinate conversion unit is used for carrying out coordinate conversion on the attitude matrix of the first star sensor under the coordinate system of the first star sensor to obtain the attitude matrix of the first star sensor taking the coordinate system of the second star sensor as a reference coordinate system and recording the attitude matrix as an attitude conversion matrix;
the second matrix fusion unit is used for fusing the attitude transformation matrix with an attitude matrix of the second star sensor under a coordinate system of the second star sensor to obtain a fusion matrix;
and the second attitude angular acceleration calculation unit is used for calculating second attitude angular acceleration according to the fusion matrix.
9. The gravity satellite star sensor mounting matrix in-orbit calibration system of claim 6, wherein the gravity satellite star sensor mounting matrix in-orbit calibration system further comprises:
the ratio calculation module is used for calculating the ratio of the first star sensor attitude matrix to the second star sensor attitude matrix, and specifically comprises the following steps:
an observed value sequence acquisition unit used for acquiring a four-element observed value sequence q of the first star sensor1(tk) And a four-element observed value sequence q of the second star sensor2(tk)；
A mean value calculation unit for employing a formula
Calculating the mean value of the ratio of the attitude matrix sequence value of the first star sensor to the attitude matrix sequence value of the second star sensor;
a ratio determining unit, configured to use the mean value as a ratio of the first star sensor attitude matrix to the first star sensor attitude matrix;
wherein q is1(tk) Represents tkFour-element observed quantity q of first star sensor at moment2(tk) Represents tkAnd k is 1 … n, and n is the observation quantity of the four-element observation quantity of the second star sensor at the moment.
10. The on-orbit calibration method for the gravity satellite star sensor mounting matrix according to claim 6, wherein the on-orbit calibration system for the gravity satellite star sensor mounting matrix further comprises:
a second relational representation obtaining module configured to obtain a second relational representation:
a third relational representation acquiring module, configured to acquire a third relational representation:
the first relation representation determining module is used for obtaining a first relation representation according to a second relation representation and a third relation representation;
wherein R (q)1) Is an attitude matrix of the first star sensor under a self coordinate system, R (q)2) Is an attitude matrix of the second star sensor under the coordinate system of the second star sensor,
is an attitude matrix of the gravity satellite body under a self coordinate system.
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