CN106568462A - Multi-probe star sensor fusion attitude testing method - Google Patents

Abstract

A multi-probe star sensor fusion attitude test method, starting from the error characteristics of the star sensor, decomposing and classifying and drawing up the corresponding attitude test method, solves a kind of multi-probe star sensor fusion attitude test without rules to follow. Sensor fusion applications at the system level provide guidance. The system error test method and cycle error test method described in the present invention can explore the boundary of the fusion attitude determination capability of the star sensor, and further provide constraints for star sensor support, whole star thermal control, and mechanical structure design, which is beneficial to High-precision satellite program implementation.

Description

A multi-probe star sensor fusion attitude test method

technical field

The invention relates to the technical field of star sensors, in particular to a multi-probe star sensor fusion attitude test method, which is suitable for the star sensor test of fusion and attitude determination based on the information of multiple probes, and can be used for the fusion of star sensors at the system level. The application provides guidance and can also be applied to the non-information fusion quasar sensor test.

Background technique

The star sensor is a high-precision optical attitude sensor widely used in spacecraft attitude measurement. It takes the star as the measurement target, images the star on the photoelectric converter through the optical system, extracts the star point and recognizes the star map, and combines The star catalog determines the direction of the star sensor optical axis vector in the inertial coordinate system, and then completes the attitude measurement.

Most traditional star sensors have an integrated structure, that is, the optical probe corresponds to the processing circuit one by one, and the processing circuit only calculates the inertial attitude of the corresponding probe. In the actual application environment, the spacecraft selects the number of star sensors according to different requirements, and designs the corresponding installation orientation, and then performs system-level attitude determination in the attitude and orbit control system (AOCS, Attitude Orbit Control System) (Reference [1]: Jie Li, Yiqing Chen. Constant-gaininformation filter for attitude determination of precision pointing spacecraft. 47th International Astronautical Congress, 1996; Reference [2]: Liu Yiwu, Chen Yiqing. Star sensor measurement model and its application in satellite attitude determination system Applications in. Acta Astronautica Sinica, 2003). The system-level fusion attitude determination algorithm is usually related to the star sensor performance index and installation orientation.

In order to improve the dynamic performance and accuracy index of the star sensor and enhance the reliability of the product, research institutes have started to develop a multi-probe information fusion quasar sensor, that is, a single processing circuit can process multiple probe information and a single probe information can be used for multiple processing In the processing circuit, the information of each probe can be fused in combination with the installation orientation of each probe, so as to provide a higher-precision attitude measurement, such as the HYDRA star sensor developed by the French SODERN company (references: L.Blarre, N. Perrimon. New Multiple Head Star Sensor (HYDRA) description and development status: a highly autonomous, accurate and very robust system to pave the way for gyroless very accurate AOCS systems. AIAA Guidance, Navigation, and Control Conference and Exhibit. 2005). The method of attitude measurement using information fusion indirectly expands the combined field of view of the star sensor and increases the number of available stars. In addition, the star sensor can independently complete the functions of installation accuracy calibration between probes, low-frequency error estimation, and precession and aberration compensation, thereby improving the accuracy of attitude determination. The attitude output by it is called fusion attitude. China's second-generation three-axis stable geostationary orbit meteorological satellite uses HYDRA as the main attitude sensor. Like traditional satellites, its AOCS system level also designs a similar fusion algorithm.

To sum up, the existing AOCS use of star sensors relies on system-level information fusion, and the fusion algorithm has a certain relationship with product characteristics. The ground test did not deliberately pay attention to various errors of star sensors, or even implemented them. Relevant tests and system design have not been effectively tested. However, the development and application of information fusion quasar sensors are still in the preliminary stage. How to choose system-level fusion or star-sensor-level fusion in orbit requires a certain amount of ground testing. In addition, ground testing can explore the fusion of the quasar sensor. The capability boundary provides constraints for star sensor support, whole star thermal control, and mechanical structure design, which is conducive to the implementation of high-precision satellite solutions.

Contents of the invention

The technology of the present invention solves the problem: overcomes the deficiencies in the prior art, and provides a multi-probe star sensor fusion attitude test method, which solves the problem that the multi-probe star sensor fusion attitude test has no rules to follow, and can be used for spacecraft How to choose system-level fusion or sensor-level fusion in orbit provides a reference.

Technical solution of the present invention: a multi-probe star sensor fusion attitude testing method, comprising the following steps:

(1) Go to step (2) when performing a random error test, go to step (4) when performing a systematic error test, go to step (6) when performing a periodic error test, and go to step (6) when performing a precessional aberration During testing, turn to step (7);

(2) Obtain the theoretical measurement attitude matrix C _SI of the star sensor, the optical axis noise index σ _x of the star sensor, and the horizontal axis noise index σ _z of the star sensor, and calculate the measurement attitude matrix tempC of the star sensor under the random error as

In the formula, randn(σ) means to generate Gaussian noise with a mean value of 0 and a mean square error of σ, and the value of σ is σ _x or σ _z ;

(3) Orthogonal normalization is performed on the star sensor measurement attitude matrix tempC under random error, and the actual measurement attitude matrix of the star sensor is obtained in, for line 1 of the for line 2 of the for In line 3 of , norm is the vector L2 norm normalization function, and × is the vector cross product operator

Go to step (9);

(4) Obtain the equivalent installation deviations Δx, Δy, Δz of the star sensor in the body coordinate system of the installed satellite, and calculate the star sensor installation deviation matrix ΔC _SB as

ΔC _SB ＝R _y (Δy)·R _x (Δx)·R _z (Δz)

Among them, R _x (υ) is the direction cosine array when rotating angle υ around the X axis in the satellite body coordinate system, R _y (υ) is the direction cosine array when rotating angle υ around the Y axis in the satellite body coordinate system, R _z (υ) is the direction cosine matrix when rotating the angle υ around the Z axis in the satellite body coordinate system;

(5) Obtain the theoretical installation matrix C _SB of the star sensor and the inertial attitude matrix C _BI of the satellite, and calculate the actual measurement attitude matrix of the current star sensor for

Go to step (9);

(6) Receive the rotation axis selection instruction sent from the outside, and select the rotation axis to obtain the star sensor interference amplitude A _ST and the star sensor interference period T _ST . When the selected rotation axis is the optical axis, calculate the The star sensor measurement error matrix ΔC _X is

When the selected rotation axis is the horizontal axis, the calculated star sensor measurement error matrix ΔC _Z under the influence of interference is:

Then, according to the star sensor measurement error matrix and the theoretical measurement attitude matrix C _SI , calculate the actual measurement attitude matrix of the current star sensor for

or

Go to step (9);

Wherein, t is the measurement time of the star sensor; the rotation axis selection command includes the optical axis or the horizontal axis; the rotation axis includes the optical axis and the horizontal axis;

(7) When obtaining the current epoch, then calculate the precession compensation matrix C _PR of the star sensor as

Among them, ζ _A , θ _A , ε, ψ, Δε are the description parameters of precession;

(8) Obtain the theoretical measurement attitude matrix C _SI of the star sensor, and calculate the actual measurement attitude matrix of the current star sensor for

Go to step (9);

(9) Calculate the actual measurement attitude matrix of the current star sensor corresponding quaternion Then obtain the quaternion q _SI actually measured and output by the star sensor, and calculate the error quaternion for

In the formula, is the conjugate quaternion of q _SI , is a quaternion multiplication operator;

Then according to the error quaternion Calculate the three-axis equivalent attitude error e _x , e _y , e _z of the current star sensor as

In the formula, Indicates the error quaternion The i-th component of , i=1, 2, 3.

Compared with the prior art, the present invention has the following advantages:

(1) On the basis of comprehensive analysis of star sensor error characteristics, the test method of the present invention solves the problem that a class of multi-probe star sensor fusion attitude test has no rules to follow. Compared with the prior art, it is more conducive to understanding the various items of the product Performance;

(2) The error testing method of the present invention, compared with the prior art, is beneficial to analyze the relationship between the validity of the multi-probe star sensor attitude output and the system deviation, indirectly puts constraints on the installation deviation of the star sensor, and provides help for the design of the mechanical structure of the whole star ;

(3) The error testing method of the present invention, compared with the prior art, can better analyze the relationship between the accuracy of the multi-probe star sensor fusion attitude determination and the periodic error. Under the premise of meeting a certain accuracy index, the star sensor can be installed indirectly Structural deformation puts forward constraints to provide reference for the design of the mechanical structure and thermal control of the whole star;

(4) Compared with the prior art, the error testing method of the present invention can be more conducive to mining various performance indicators of products, and has a guiding effect on the fusion selection of on-orbit sensor level/system level.

Description of drawings

Fig. 1 is the constitution diagram of testing system of the present invention;

Fig. 2 is the test main flowchart of the present invention;

Fig. 3 is a flowchart of each test mode of the present invention.

detailed description

Aiming at the deficiencies in the prior art, the invention proposes a multi-probe star sensor fusion attitude testing method. Taking the HYDRA star sensor test developed by French SODERN company as an example below, the specific implementation of the method of the present invention is described in detail in conjunction with the accompanying drawings, including the following steps:

(1) Connect the star sensor ground test system as shown in Figure 1. The system consists of ground test equipment and spaceborne equipment. The ground test equipment is a dynamics computer and EGSE (Electrical Ground Support Equipment), and the spaceborne equipment includes a star sensor (including processing circuit Electronic Unit and optical probe Optical Head) and AOCS, wherein the dynamics computer runs the items described in the present invention Test program (i.e. the formula algorithm described in step 2 below).

(2) According to the test purpose, set the star sensor test mode, and the dynamic computer selects the corresponding test sub-process according to the test mode. Figure 2 is a block diagram of the main test process. When carrying out random error test, turn to step (2a), when carrying out systematic error test, turn to step (2b), when carrying out periodic error test, turn to step (2c), when carrying out precession aberration test, Turning to step (2d), Fig. 3 is a sub-flow diagram of each test program.

(2a) Random error test sub-process: obtain the theoretical measurement attitude matrix C _SI of the star sensor, the optical axis noise index σ _x of the star sensor, and the horizontal axis noise index σ _z of the star sensor, and calculate the star sensor measurement under random error The attitude matrix tempC is

In the formula, randn(σ) means to generate Gaussian noise with a mean value of 0 and a mean square error of σ, and the value of σ is σ _x or σ _z ;

Orthogonal normalization is performed on the star sensor measurement attitude matrix tempC under the random error, and the actual measurement attitude matrix of the star sensor is obtained in, for line 1 of the for line 2 of the for In line 3 of , norm is the vector L2 norm normalization function, and × is the vector cross product operator

Go to step (3);

(2b) System error test sub-process: Obtain the equivalent installation deviations Δx, Δy, Δz of the star sensor in the body coordinate system of the installed satellite, and calculate the star sensor installation deviation matrix ΔC _SB as

ΔC _SB ＝R _y (Δy)·R _x (Δx)·R _z (Δz)

Among them, R _x (υ) is the direction cosine array when rotating angle υ around the X axis in the satellite body coordinate system, R _y (υ) is the direction cosine array when rotating angle υ around the Y axis in the satellite body coordinate system, R _z (υ) is the direction cosine matrix when rotating the angle υ around the Z axis in the satellite body coordinate system;

Obtain the theoretical installation matrix C _SB of the star sensor and the inertial attitude matrix C _BI of the satellite, and calculate the actual measurement attitude matrix of the current star sensor for

Go to step (3);

(2c) Periodic error test sub-process: Receive the rotation axis selection command sent from the outside, and select the rotation axis, and obtain the star sensor interference amplitude A _ST and star sensor interference period T _ST , when the selected rotation axis is the optical axis , the star sensor measurement error matrix ΔC _X under the influence of interference is calculated as

When the selected rotation axis is the horizontal axis, the calculated star sensor measurement error matrix ΔC _Z under the influence of interference is:

Then calculate the actual measurement attitude matrix of the current star sensor according to the star sensor measurement error matrix ΔC _X or ΔC _Z and the theoretical measurement attitude matrix C _SI for

or

Go to step (3);

Wherein, t is the measurement time of the star sensor; the rotation axis selection command includes the optical axis or the horizontal axis; the rotation axis includes the optical axis and the horizontal axis;

(2d) Precession aberration test sub-process: when obtaining the current epoch, then calculate the precession compensation matrix C _PR of the star sensor as

Among them, ζ _A , θ _A , ε, ψ, and Δε are precession description parameters, which are only related to epoch time. For specific calculations, please refer to the literature (Liu Lin. Spacecraft Orbit Theory. National Defense University Press);

Obtain the theoretical measurement attitude matrix C _SI of the star sensor, and calculate the actual measurement attitude matrix of the current star sensor for

Go to step (3);

(3) Calculate the actual measurement attitude matrix of the current star sensor corresponding quaternion And stimulate EGSE, then obtain the quaternion q _SI actually measured by the star sensor, and calculate the error quaternion for

In the formula, is the conjugate quaternion of q _SI , is a quaternion multiplication operator;

Then according to the error quaternion Calculate the three-axis equivalent attitude error e _x , e _y , e _z of the current star sensor as

In the formula, Indicates the error quaternion The i-th component of , i=1, 2, 3.

Parts not described in detail in the present invention belong to the well-known technology in the art.

Claims (1)

1. a multi-probe star sensor fusion attitude testing method is characterized in that comprising the steps: (1) Go to step (2) when performing a random error test, go to step (4) when performing a systematic error test, go to step (6) when performing a periodic error test, and go to step (6) when performing a precessional aberration During testing, turn to step (7); (2) Obtain the theoretical measurement attitude matrix C _SI of the star sensor, the optical axis noise index σ _x of the star sensor, and the horizontal axis noise index σ _z of the star sensor, and calculate the measurement attitude matrix tempC of the star sensor under the random error as $\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; +</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; )</span>\end{array}\right]$ In the formula, randn(σ) means to generate Gaussian noise with a mean value of 0 and a mean square error of σ, and the value of σ is σ _x or σ _z ; (3) Orthogonal normalization is performed on the star sensor measurement attitude matrix tempC under random error, and the actual measurement attitude matrix of the star sensor is obtained in, for line 1 of the for line 2 of the for In line 3 of , norm is the vector L2 norm normalization function, and × is the vector cross product operator $\left\{\begin{array}{c}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; I</span>}}\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>\\ {\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; I</span>}}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\\ {\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; I</span>}}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; I</span>}}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&times;</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; I</span>}}\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; ;</span>$ Go to step (9); (4) Obtain the equivalent installation deviations Δx, Δy, Δz of the star sensor in the body coordinate system of the installed satellite, and calculate the star sensor installation deviation matrix ΔC _SB as ΔC _SB ＝R _y (Δy)·R _x (Δx)·R _z (Δz) Among them, R _x (υ) is the direction cosine array when rotating angle υ around the X axis in the satellite body coordinate system, R _y (υ) is the direction cosine array when rotating angle υ around the Y axis in the satellite body coordinate system, R _z (υ) is the direction cosine matrix when rotating the angle υ around the Z axis in the satellite body coordinate system; (5) Obtain the theoretical installation matrix C _SB of the star sensor and the inertial attitude matrix C _BI of the satellite, and calculate the actual measurement attitude matrix of the current star sensor for ${\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&Delta;C</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; ;</span>$ Go to step (9); (6) Receive the rotation axis selection instruction sent from the outside, and select the rotation axis to obtain the star sensor interference amplitude A _ST and the star sensor interference period T _ST . When the selected rotation axis is the optical axis, calculate the The star sensor measurement error matrix ΔC _X is ${\mathrm{<span\; class="notranslate">\; \&Delta;C</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; t</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; T</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ When the selected rotation axis is the horizontal axis, the calculated star sensor measurement error matrix ΔC _Z under the influence of interference is: ${\mathrm{<span\; class="notranslate">\; \&Delta;C</span>}}_{\mathrm{<span\; class="notranslate">\; Z</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; t</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; T</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ Then calculate the actual measurement attitude matrix of the current star sensor according to the star sensor measurement error matrix ΔC _X or ΔC _Z and the theoretical measurement attitude matrix C _SI for or Go to step (9); Wherein, t is the measurement time of the star sensor; the rotation axis selection instruction includes the optical axis or the horizontal axis; the rotation axis includes the optical axis and the horizontal axis; (7) When obtaining the current epoch, then calculate the precession compensation matrix C _PR of the star sensor as ${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; P</span>}\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&psi;</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& {\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}{\mathrm{<span\; class="notranslate">\; \&zeta;</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}\\ \mathrm{<span\; class="notranslate">\; \&psi;</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}{\mathrm{<span\; class="notranslate">\; \&zeta;</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$ Among them, ζ _A , θ _A , ε, ψ, Δε are the description parameters of precession; (8) Obtain the theoretical measurement attitude matrix C _SI of the star sensor, and calculate the actual measurement attitude matrix of the current star sensor for ${\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; P</span>}\mathrm{<span\; class="notranslate">\; R</span>}}$ Go to step (9); (9) Calculate the actual measurement attitude matrix of the current star sensor corresponding quaternion Then obtain the quaternion q _SI actually measured and output by the star sensor, and calculate the error quaternion for $\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; I</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CircleTimes;</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; I</span>}}$ In the formula, is the conjugate quaternion of q _SI , is a quaternion multiplication operator; Then according to the error quaternion Calculate the three-axis equivalent attitude error e _x , e _y , e _z of the current star sensor as ${\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ ${\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ ${\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$ In the formula, Indicates the error quaternion The i-th component of , i=1, 2, 3.