Satellite attitude determination method based on extended Kalman filter

Abstract

The application relates to a satellite attitude determination method based on an extended Kalman filter, which comprises the following steps: S1, constructing a system state equation based on satellite body system relative to inertial system attitude quaternion based on star sensor and fiber-optic gyroscope measurement data; S2, taking the sun guide mirror data used as a steady image system in a satellite load camera as new measurement, and combining the star sensor and fiber-optic gyroscope measurement data to form a measurement system, and constructing a measurement system measurement equation based on the attitude quaternion; S3, inputting the star sensor, fiber-optic gyroscope and sun guide mirror measurement values, constructing an extended Kalman filter by using the state equation constructed in step S1 and the measurement equation constructed in step S2, and performing optimal estimation on the satellite attitude based on an extended Kalman filter attitude determination algorithm. The beneficial effect is high accuracy of the attitude determination in the vertical direction of the sun pointing.

Description

Technical Field

[0001] This invention relates to the field of satellite attitude control technology, and specifically to a satellite attitude determination method based on extended Kalman filtering. Background Technology

[0002] A star sensor is a high-precision space attitude measurement device that uses stars as a reference frame and the starry sky as its working object.

[0003] A fiber-optic gyroscope (FOG) is a fiber optic sensor used for inertial navigation.

[0004] The Sun Guide Telescope (SGT) is one of the key technologies for attitude control of the Space Solar Telescope (SST).

[0005] A Kalman filter (KF) is an algorithm that uses the state equations of a linear system to make an optimal estimate of the system state using the system's input and output observation data. Since the observation data includes the effects of noise and interference in the system, the optimal estimation can also be viewed as a filtering process.

[0006] State equations are expressions that describe the relationship between system inputs and states. The vector ordinary differential equations satisfied by the state vectors are called the state equations of the control system. State equations are an important component of the mathematical model of a control system.

[0007] State equations, typically expressed in the form of differential or difference equations, describe how the system state changes over time. Measurement equations describe how the system state can be inferred by measuring certain physical quantities of the system. State and measurement equations together constitute the state-space model, which is the foundation for control system design and analysis.

[0008] Target observation satellites often have high requirements for attitude angle control accuracy and attitude stability. Previous attitude control research typically employed attitude determination algorithms based on star trackers (STRs) and fiber optic gyroscopes (FOGs). Because STRs and FOGs offer high measurement accuracy, they are usually mounted on observation satellites requiring high precision and stability. However, this approach has drawbacks. Optical system parameters are easily affected by temperature; parameters such as the principal point position of the star tracker and the calibration factor of the fiber optic gyroscope can influence measurement accuracy. For example, ASO-S (Advanced Space-based Solar Observatory) uses a domestically produced star tracker (STR) with a three-axis measurement accuracy of [3.5 3.5 28]″ and a fiber optic gyroscope (FOG) with an angular velocity measurement accuracy of 5e-5° / s and a constant zero-point drift better than 0.2° / h.

[0009] Because satellite optical system parameters are easily affected by temperature, such as the principal point position of the star sensor and the calibration factor of the fiber optic gyroscope, measurement accuracy can be affected. To ensure optimal performance of individual sensors, previous studies have typically considered implementing separate temperature control for the star sensor and gyroscope, or employing multi-star sensor measurement correction methods to improve the accuracy of STR triaxial measurements. Nevertheless, conventional joint attitude determination algorithms based on STR and FOG Kalman filtering still struggle to meet the attitude determination accuracy requirements of the ASO-S satellite. In particular, although the ASO-S satellite is equipped with three STRs, its unique solar observation pointing makes the STRs susceptible to the influence of Earth's atmospheric light, resulting in alternating effectiveness in orbit, making it impossible to consistently meet the correction conditions of two or more star sensors being effective simultaneously.

[0010] Chinese patent literature [1]: Wang Keyan, Jiang Weijiao, Niu Rui et al., Joint attitude determination method and satellite attitude control system based on unscented Kalman filtering, CN201910281474.0, Xi'an University of Electronic Science and Technology.

[0011] Chinese Patent Document [2]: Meng Ziyang, Liao Maoyou, You Zheng et al., A Multi-mode Attitude Determination Method for Remote Sensing Micro-nano Satellites, CN201811617702.9, Tsinghua University.

[0012] Chinese patent document [3]: Wang Feng, Chen Xueqin, Li Dongbai et al., A method for determining the agile maneuver attitude of an optical imaging satellite, CN201410213665.0, Harbin Institute of Technology.

[0013] This invention addresses the technical problem that conventional joint attitude determination algorithms based on STR and FOG Kalman filtering cannot meet the attitude determination accuracy requirements of ASO-S satellites, and makes technical improvements to the satellite attitude determination method. Summary of the Invention

[0014] The purpose of this invention is to propose a satellite attitude determination method with high accuracy in determining the attitude in the vertical direction pointing towards the sun.

[0015] To achieve the above objectives, the technical solution adopted by this invention is a satellite attitude determination method based on extended Kalman filtering, comprising the following steps:

[0016] S1. Based on the measurement data of star sensors and fiber optic gyroscopes, the system state equation is constructed based on the attitude quaternion of the satellite's own system relative to the inertial frame.

[0017] S2. The solar navigation mirror data used as an image stabilization system in the satellite payload camera is used as a new measurement quantity, and together with the measurement data of the star sensor and fiber optic gyroscope, a measurement system is formed. The measurement equation of the measurement system is constructed based on attitude quaternions.

[0018] S3. Input the measurements from the star sensor, fiber optic gyroscope, and solar navigation mirror. Using the state equation constructed in step S1 and the measurement equation constructed in step S2, construct an extended Kalman filter. Based on the attitude determination algorithm of the extended Kalman filter, perform optimal estimation of the satellite attitude.

[0019] Preferably, the four attitude elements in step S1 or S2 refer to: the coordinate system OXaYaZa rotating around the OE axis by an angle. It coincides with the coordinate system OXbYbZb, and the angles between the OE axis and the three coordinate axes OXaYaZa are: , , The attitude of coordinate system OXbYbZb relative to coordinate system OXaYaZa is expressed by... , , , Completely determined, meaning completely determined by attitude quaternions: The OE axis is the defined spatial axis, which is the same in both coordinate systems OXaYaZa and OXbYbZb. .

[0020] Preferably, in the above-described satellite attitude determination method based on extended Kalman filtering, step S1 specifically includes the following sub-steps:

[0021] S11, Definition Let q be the attitude quaternion of the satellite's system relative to the inertial frame, where: s For the standard department, q vIt is a vector part and satisfies the normalization condition. ;

[0022] S12. The kinematic equations of satellite attitude expressed in terms of attitude quaternions are as follows: ,in, The measurement error of the star sensor is represented by the covariance matrix Q. str , recorded as ω represents the satellite's attitude angular velocity relative to the inertial frame.

[0023] S13. The attitude angular velocity and constant zero-point drift measured by the fiber optic gyroscope are denoted as ωg and b, respectively. , The satellite's attitude angular velocity ω is expressed as ,in, η b The measurement error of the fiber optic gyroscope is represented by the covariance matrix Q. b , recorded as ;

[0024] S14. The attitude quaternion vector qv and the fiber optic gyroscope constant drift b are used as state variables. The system state equations are obtained. ,in, , , , , .

[0025] Preferably, in the above-described satellite attitude determination method based on extended Kalman filtering, step S2 specifically includes the following sub-steps:

[0026] S21. The Lyman-Alpha Solar Telescope, a satellite payload, is equipped with a solar navigation mirror. It uses a four-quadrant photodetector to collect solar edge signals in the azimuth and elevation directions. The four photodiodes A, B, C, and D of the solar navigation mirror generate different magnitudes of current signals due to the photoelectric effect. These signals are then amplified by a transimpedance amplifier to produce corresponding voltage signals, U1, U2, U3, and U4, respectively. The offset of the solar center from the calibrated detector focal plane center and the voltage signals satisfy the following relationship: Laboratory imaging was used to calibrate the offset and the deviation angle between the sun's azimuth and elevation directions. ;

[0027] S22. The focal length of the solar navigation mirror is denoted as f. Calculate the expression for the solar vector in the solar navigation mirror measurement system. The deviation angles α and β of the sun's azimuth and elevation directions, and the position offsets Δy and Δz, satisfy the following: , The linear measurement range of the solar navigation mirror is approximately 60″, therefore, , , Rewritten as ;

[0028] S23. Convert the inertial frame solar vector Si to the satellite's own frame Sb: ,in, Let be the attitude matrix represented by quaternions, if , ,but ,

[0029] in, Sb and Parallel, therefore The mathematical models for obtaining the solar center azimuth and elevation deviation angles α and β measured by the solar navigation mirror are as follows: , where η gt The measurement errors in azimuth and elevation are represented by the covariance matrix Q. gt , recorded as ;

[0030] S24. The attitude quaternion vector measured by the star sensor and the deviation angles α and β measured by the solar navigation mirror are the measured quantities: The measurement equation of the measurement system is obtained. ,in, , , .

[0031] Preferably, in the satellite attitude determination method based on extended Kalman filtering, the extended Kalman filter in step S3 is: with... For the state variables, the following matrix is ​​calculated from the system state equation f and the measurement equation h.

[0032] ,

[0033] ,

[0034] in, ,

[0035] ,

[0036] ,

[0037] ,

[0038] ,

[0039] ,

[0040] ,

[0041] ,

[0042] The extended Kalman filter input: star sensor attitude measurement quaternion vector. A solar navigation mirror measures the solar center deviation angles α and β, while a fiber optic gyroscope measures the attitude angular velocity. The inertial frame unit solar vector Si;

[0043] The extended Kalman filter outputs: attitude-determining quaternions Fiber optic gyroscope zero drift estimation attitude-fixed angular velocity .

[0044] Preferably, in the above-described satellite attitude determination method based on extended Kalman filtering, the attitude determination algorithm based on extended Kalman filtering in step S3 is optimized and iteratively calculated according to the following sub-steps, with T as the calculation step size:

[0045] S31, Initialization, , P0, covariance matrix Q, R, , , Quaternion standard limit q 0max Zero drift limit b max ;

[0046] S32, One-step prediction of mean square error matrix ;

[0047] S33, One-step state prediction ;

[0048] S34. Calculation of Filter Gain Matrix ;

[0049] S35, Status Update ;

[0050] S36. Estimating the mean square error ;

[0051] S37, Filter Output ;

[0052] S38, Output Limiting ;

[0053] S39, Attitude-Fixed Output , ;

[0054] S3a, Iterative Update .

[0055] The satellite attitude determination method based on extended Kalman filtering of this invention has the following advantages: It uses the data from the Sun Guide Telescope (SGT) used as an image stabilization system in the payload camera as a new measurement quantity, and combines it with the measurement data from the Star Sensor (STR) and Fiber Optic Gyroscope (FOG) to form a measurement system. An attitude determination algorithm based on the Extended Kalman Filter (EKF) is designed. Compared with the EKF algorithm that only uses STR and FOG, this attitude determination method can effectively improve the accuracy of attitude determination in the vertical direction of the sun's orientation, and better address the stability of the satellite's attitude control system under special guidance laws or special observation missions. Attached Figure Description

[0056] Figure 1 This is a schematic diagram illustrating the physical meaning of quaternion rotation.

[0057] Figure 2 This is a flowchart of a satellite attitude determination method based on extended Kalman filtering.

[0058] Figure 3 This is a schematic diagram of the measurement principle of the Solar Guide Mirror (SGT).

[0059] Figure 4 This is a schematic diagram showing the relationship between the SGT measurement values ​​of the solar navigation mirror and the solar vector. Detailed Implementation

[0060] The present invention will now be further described with reference to the embodiments and the accompanying drawings.

[0061] Example

[0062] This embodiment implements a satellite attitude determination method based on extended Kalman filtering.

[0063] Satellite optical system parameters are easily affected by temperature, such as the principal point position of the star sensor and the calibration factor of the fiber optic gyroscope, which will affect the measurement accuracy. Traditional schemes such as "star sensor + gyroscope EKF filtering" or "star sensor + low-precision attitude measurement sensor EKF filtering" are often not able to meet the attitude determination requirements of scientific satellites with special observation needs. The satellite attitude determination method in this embodiment uses the high-precision solar navigation mirror data used as an image stabilization system in the payload camera as a new measurement. This attitude determination method can effectively improve the attitude determination accuracy in the vertical direction of the sun and better solve the stability of the attitude control system of the satellite in special guidance laws or special observation tasks.

[0064] The high-precision solar navigation mirror data used in this embodiment of the satellite attitude determination method originates from satellite scientific payload information, and the high-precision attitude determination algorithm directly uses payload camera data. This approach eliminates the need for a separate attitude sensor measurement device, saving design costs.

[0065] 1. The physical meaning of rotation of attitude quaternions

[0066] Figure 1 This is a schematic diagram illustrating the physical meaning of quaternion rotation. For example... Figure 1 As shown, the coordinate system OXaYaZa rotates around the OE axis by an angle. It coincides with the coordinate system OXbYbZb, and the angle between the OE axis and the three coordinate axes OXaYaZa is... , , The orientation of coordinate system OXbYbZb relative to coordinate system OXaYaZa can be completely determined using... , , , Completely deterministic, that is, completely deterministic using quaternions:

[0067] (1)

[0068] As can be seen, the OE axis is the defined spatial axis, which is constant in both coordinate systems OXaYaZa and OXbYbZb. .

[0069] 2. This embodiment uses a high-precision attitude determination fusion algorithm scheme based on the solar navigation mirror.

[0070] Figure 2 This is a flowchart of a satellite attitude determination method based on extended Kalman filtering. (See attached flowchart.) Figure 2 As shown, this embodiment includes the following steps:

[0071] 2.1 State Equations

[0072] definition Let q be the attitude quaternion of the satellite's system relative to the inertial frame, where: s For the standard department, q v It is a vector part and satisfies the normalization condition. The kinematic equations of satellite attitude, expressed in quaternions, can be represented as:

[0073]

[0074] in, The measurement error of the star sensor (white noise, covariance matrix Q) str ), denoted as ω represents the satellite's attitude angular velocity relative to the inertial frame.

[0075] The attitude angular velocity and constant zero-point drift measured by the fiber optic gyroscope are denoted as ωg and b, respectively. , Therefore, the satellite's attitude angular velocity ω can be expressed as...

[0076]

[0077] in: η b The measurement error of the fiber optic gyroscope (white noise, covariance matrix Q) b ), denoted as .

[0078] The attitude quaternion vector qv and the constant drift b of the fiber optic gyroscope are used as state variables. The system equations are as follows:

[0079]

[0080] in, , , , .

[0081]

[0082] 2.2 Measurement Equation

[0083] Figure 3 This is a schematic diagram illustrating the measurement principle of the Solar Guide Mirror (SGT). (See attached diagram.) Figure 3 As shown, the Solar Guiding Mirror (SGT) on the Lyman-Alpha Solar Telescope utilizes a four-quadrant photodetector to collect solar edge signals in the azimuth (zg) and elevation (yg) directions. Four photodiodes A, B, C, and D generate current signals of different magnitudes due to the photoelectric effect. These signals are then amplified by a transimpedance amplifier to produce corresponding voltage signals, U1, U2, U3, and U4, respectively. The offset of the solar center relative to the calibrated detector focal plane center satisfies the following relationship with the voltage signals:

[0084]

[0085] The offset and azimuth and elevation deviation angles were calibrated using laboratory imaging (the SGT detector's measurement coordinate system is consistent with the satellite's three-axis orientation). Its measurement accuracy can reach 0.1″.

[0086] Figure 4This is a schematic diagram showing the relationship between the SGT measurements of the solar navigation mirror and the solar vector. (See attached diagram.) Figure 4 As shown, this illustrates the principle of converting solar vectors into azimuth and elevation angle deviations.

[0087] The SGT focal length is denoted as f, from which the expression for the solar vector in the SGT measurement system is calculated. for:

[0088]

[0089] The solar deviation angles α and β satisfy the following relationship with the position offsets Δy and Δz: , The SGT linear measurement range is approximately 60″ (tan(60″)≈60″). Therefore, , , Rewritten as:

[0090]

[0091] Convert the inertial frame solar vector Si to the satellite body frame Sb: .in, Let be the attitude matrix represented by quaternions, if , ,but

[0092]

[0093] in,

[0094]

[0095] Sb and Parallel, therefore

[0096]

[0097] The mathematical models for the solar center deviation angles α and β measured by SGT are as follows:

[0098]

[0099] Where, η gt The measurement error of SGT (white noise, covariance matrix Q) gt ), denoted as .

[0100] The attitude quaternion vector measured by the star sensor STR and the deviation angles α and β measured by the SGT are used as the measurement quantities: The measurement equation is as follows:

[0101]

[0102] in, , , .

[0103] 2.3 Design of Extended Kalman Filter Algorithm

[0104] by For the state variables, the following matrix is ​​calculated from the system equation f and the measurement equation h.

[0105]

[0106]

[0107] in

[0108]

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115] Filter input: STR measurement attitude quaternion vector SGT measures solar center deviation angles α and β, while FOG measures attitude angular velocity. The inertial frame unit solar vector Si.

[0116] Filter output: Attitude quaternion Gyroscope zero drift estimation attitude-fixed angular velocity .

[0117] Perform iterative calculations as follows (T is the calculation step size):

[0118] (1) Initialization: , P0, covariance matrix Q, R, , , Quaternion standard limit q 0max Zero drift limit b max .

[0119] (2) One-step prediction of the mean square error matrix:

[0120]

[0121] (3) One-step state prediction:

[0122]

[0123] (4) Calculation of filter gain matrix:

[0124]

[0125] (5) Status update:

[0126]

[0127] (6) Estimate the mean square error:

[0128]

[0129] (7) Filter output:

[0130]

[0131] (8) Output limiting:

[0132]

[0133] (9) Fixed-attitude output:

[0134] ,

[0135] (10) Iterative update:

[0136]

[0137] 3. Simulation verification of the extended Kalman filter algorithm

[0138] 3.1 Simulation Conditions

[0139] (1) Initialization

[0140] Start time: May 10, 2022, 1:40:00:00;

[0141] Simulation duration: 8000s;

[0142] Simulation step size: 0.125s.

[0143] (2) Orbital parameters

[0144]

[0145] (3) Initial values ​​of attitude parameters and sensor parameters

[0146]

[0147] (4) Actuator parameters

[0148] Maximum torque of the reaction wheel: 0.215 Nm

[0149] Reaction wheel classification: Torque wheel

[0150] Reaction wheel installation method: Four-sided oblique "pyramid" configuration

[0151] Computer DA output accuracy: <10mV

[0152] Maximum magnetic moment of the magnetic torquer: 100 Am 2

[0153] Classification of magnetic torque devices: Switched magnetic torque devices

[0154] (5) PID controller parameters

[0155]

[0156] (6) Solar Model

[0157] Julian century number starting at 12:00 on January 1, 2000: TRL

[0158] Solar orbital inclination:

[0159]

[0160] Sun's horizontal aperitoneal angle:

[0161]

[0162] True ecliptic longitude of the sun:

[0163]

[0164] J2000 inertial frame solar position unit vector:

[0165]

[0166] 3.2 EKF parameters

[0167] (1)STR+FOG+SGT

[0168]

[0169] (2)STR+FOG

[0170]

[0171] The satellite's inertia is [500, 600, 500, 0, 0, 0] kg / m 2 The moment of inertia of the reaction wheel is 0.0955 kgm. 2 .

[0172] 3.3 Simulation Results

[0173] The simulation in this embodiment lasted for 8000 seconds (approximately 1.3 times the orbital period). The first 1000 seconds were used for filter convergence. The data from 1000 seconds to 8000 seconds were statistically analyzed to calculate the angular velocity estimation accuracy and attitude angle estimation accuracy of the two attitude determination algorithms. The statistical results are shown in Table 1 below.

[0174] Table 1. Accuracy of Angular Velocity and Euler Angle Estimation

[0175] parameter STR+FOG EKF estimation accuracy STR+FOG+SGT EKF estimation accuracy <![CDATA[ω bi_x / (° / s)]]> <![CDATA[1.873e -4 ]]> <![CDATA[1.502e -4 ]]> <![CDATA[ω bi_y / (° / s)]]> <![CDATA[1.568e -4 ]]> <![CDATA[1.455e -4 ]]> <![CDATA[ω bi_z / (° / s)]]> <![CDATA[1.716e -4 ]]> <![CDATA[1.567e -4 ]]> <![CDATA[Euler_ x / ″]]> 3.2704 1.665 <![CDATA[Euler_ y / ″]]> 1.6363 0.1252 <![CDATA[Euler_ z / ″]]> 1.8710 0.0889

[0176] Simulation results of this embodiment. From the simulation verification diagrams of the STR+FOG EKF angular velocity estimation values ​​and the STR+FOG+SGT EKF angular velocity estimation values ​​of this embodiment, it can be seen that the attitude angular velocity estimation value using the SGT-based EKF attitude determination algorithm has a slightly improved accuracy compared to the conventional attitude sensor EKF algorithm. From the simulation verification diagrams of the STR+FOG EKF Euler angle estimation values ​​and the STR+FOG+SGT EKF Euler angle estimation values ​​of this embodiment, it can be seen that the attitude angle estimation value using the SGT-based EKF attitude determination algorithm has a significantly improved accuracy across all three axes compared to the conventional attitude sensor EKF algorithm; in particular, the accuracy of the attitude angle estimation in the direction perpendicular to the solar observation point is better than 0.2″ (3σ). From the schematic diagrams of the STRs used in the EKF algorithm of this embodiment and the effective STRs during the simulation, and the schematic diagram of the deviation angle curve converted from the SGT measurement values ​​in this embodiment, it can be seen that the designed PID controller has an attitude stability better than 0.8″ / 60s, meeting the performance requirements.

[0177] In this embodiment, the method 1) uses the high-precision solar navigation mirror data used as an image stabilization system in the payload camera as a new measurement quantity. This attitude determination method can effectively improve the attitude determination accuracy in non-solar observation directions and better solve the stability of the attitude control system of the satellite under special guidance laws or special observation missions.

[0178] 2) The high-precision solar navigation mirror data of the satellite payload system is applied to the integrated design of the satellite attitude determination system, which improves the stability index of satellite attitude determination, while eliminating the need for separate attitude sensor measurement equipment and saving design costs.

[0179] 3) Based on engineering practice, it provides a new approach to high-precision attitude determination, which can be referenced and inherited by satellites under development for observing the sun, and has good engineering application prospects and promotion value.

[0180] In summary, the EKF algorithm designed using STR, FOG, and SGT measurements can effectively improve the accuracy of satellite three-axis attitude angle estimation and maintain stable convergence over a long period. This embodiment demonstrates a feasible high-precision attitude determination fusion algorithm using a solar navigation mirror.

[0181] Those skilled in the art will understand that all or part of the steps of the above embodiments can be implemented by hardware or by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM).

[0182] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements and additions without departing from the principle of the present invention, and these improvements and additions should also be considered within the scope of protection of the present invention.

Claims

1. A satellite attitude determination method based on extended Kalman filtering, characterized in that... Includes the following steps: S1. Based on the measurement data of star sensors and fiber optic gyroscopes, the system state equation is constructed based on the attitude quaternion of the satellite's own system relative to the inertial frame. S2. The solar navigation mirror data used as an image stabilization system in the satellite payload camera is used as a new measurement quantity, and together with the measurement data of the star sensor and fiber optic gyroscope, a measurement system is formed. The measurement equation of the measurement system is constructed based on attitude quaternions. S3. Input the measurements from the star sensor, fiber optic gyroscope, and solar navigation mirror. Using the state equation constructed in step S1 and the measurement equation constructed in step S2, construct an extended Kalman filter. Based on the attitude determination algorithm of the extended Kalman filter, perform optimal estimation of the satellite attitude. Step S2 specifically includes the following sub-steps: S21. The Lyman-Alpha Solar Telescope, a satellite payload, is equipped with a solar navigation mirror. It uses a four-quadrant photodetector to collect solar edge signals in the azimuth and elevation directions. The four photodiodes A, B, C, and D of the solar navigation mirror generate different magnitudes of current signals due to the photoelectric effect. These signals are then amplified by a transimpedance amplifier to produce corresponding voltage signals, U1, U2, U3, and U4, respectively. The offset of the solar center from the calibrated detector focal plane center and the voltage signals satisfy the following relationship: Laboratory imaging was used to calibrate the offset and the deviation angle between the sun's azimuth and elevation directions. ; S22. The focal length of the solar navigation mirror is denoted as f. Calculate the expression for the solar vector in the solar navigation mirror measurement system. The deviation angles α and β of the sun's azimuth and elevation directions, and the position offsets Δy and Δz, satisfy the following: , The linear measurement range of the solar navigation mirror is approximately 60″, therefore, , , Rewritten as ; S23. Convert the inertial frame solar vector Si to the satellite's own frame Sb: ,in, Let be the attitude matrix represented by quaternions, if , ,but , in, Sb and Parallel, therefore The mathematical models for obtaining the solar center azimuth and elevation deviation angles α and β measured by the solar navigation mirror are as follows: , where η gt The measurement errors in azimuth and elevation are represented by the covariance matrix Q. gt , recorded as ; S24. The attitude quaternion vector measured by the star sensor and the deviation angles α and β measured by the solar navigation mirror are the measured quantities: The measurement equation of the measurement system is obtained. ,in, , , .

2. The satellite attitude determination method based on extended Kalman filtering according to claim 1, characterized in that... Step S1 or S2, the four attitude elements, refer to the angle through which the coordinate system OXaYaZa rotates around the OE axis. It coincides with the coordinate system OXbYbZb, and the angles between the OE axis and the three coordinate axes OXaYaZa are: , , The attitude of coordinate system OXbYbZb relative to coordinate system OXaYaZa is expressed by... , , , Completely determined, meaning completely determined by attitude quaternions: The OE axis is the defined spatial axis, which is the same in both coordinate systems OXaYaZa and OXbYbZb. .

3. The satellite attitude determination method based on extended Kalman filtering according to claim 2, characterized in that... Step S1 specifically includes the following sub-steps: S11, Definition Let q be the attitude quaternion of the satellite's system relative to the inertial frame, where: s For the standard department, q v It is a vector part and satisfies the normalization condition. ; S12. The kinematic equations of satellite attitude expressed in terms of attitude quaternions are as follows: ,in, The measurement error of the star sensor is represented by the covariance matrix Q. str , recorded as ω represents the satellite's attitude angular velocity relative to the inertial frame. S13. The attitude angular velocity and constant zero-point drift measured by the fiber optic gyroscope are denoted as ωg and b, respectively. , The satellite's attitude angular velocity ω is expressed as ,in, η b The measurement error of the fiber optic gyroscope is represented by the covariance matrix Q. b , recorded as ; S14. The attitude quaternion vector qv and the fiber optic gyroscope constant drift b are used as state variables. The system state equations are obtained. ,in, , , , , .

4. The satellite attitude determination method based on extended Kalman filtering according to claim 1, characterized in that... The extended Kalman filter described in step S3: For the state variables, the following matrix is ​​calculated from the system state equation f and the measurement equation h. ， ， in, , ， ， ， ， ， ， ， The extended Kalman filter input: star sensor attitude measurement quaternion vector. A solar navigation mirror measures the solar center deviation angles α and β, while a fiber optic gyroscope measures the attitude angular velocity. The inertial frame unit solar vector Si; The extended Kalman filter outputs: attitude-determining quaternions Fiber optic gyroscope zero drift estimation attitude-fixed angular velocity .

5. The satellite attitude determination method based on extended Kalman filtering according to claim 4, characterized in that, The attitude determination algorithm based on extended Kalman filtering described in step S3 is optimized and iteratively calculated according to the following sub-steps, with T as the calculation step size: S31, Initialization, , P0, covariance matrix Q, R, , , Quaternion standard limit q 0max Zero drift limit b max ; S32, One-step prediction of mean square error matrix ; S33, One-step state prediction ; S34. Calculation of Filter Gain Matrix ; S35, Status Update ; S36. Estimating the mean square error ; S37, Filter Output ; S38, Output Limiting ; S39, Attitude-Fixed Output , ; S3a, Iterative Update .

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