Filtering estimation of star sensor relative measurement reference and low frequency error calibration system

Abstract

The application discloses a star sensor relative measurement reference filtering estimation and low-frequency error calibration system, comprising: a state recursion module, which is used for extrapolating a one-step recursion installation error angle and a one-step recursion installation error angle covariance matrix of a first star sensor after calibration according to a previous time first star sensor installation error angle after calibration and the installation error angle covariance matrix; a measurement update module, which is used for calculating a first star sensor installation error angle after filtering correction and a first star sensor installation error angle after filtering correction covariance matrix according to attitude quaternion output by the star sensor at the current time and the output of the state recursion module; and a low-frequency error calibration module, which is used for calculating fitting coefficients according to installation error angles at each time. The star sensor relative measurement reference filtering estimation and low-frequency error calibration system can compensate low-frequency components of relative installation errors in real time.

Description

Technical Field

[0001] This invention belongs to the field of star sensor calibration technology, and particularly relates to a system for filtering estimation and low-frequency error calibration of a star sensor relative to a measurement reference. Background Technology

[0002] Remote sensing imaging satellites operating in geostationary orbit typically have multiple star sensors installed to achieve high-precision attitude determination. Due to limitations in ground measurement conditions, severe vibrations during launch, and thermal deformation during on-orbit operation, the installation reference of the star sensors often deviates from the theoretical calibration values. On-orbit calibration is an important method to solve this problem.

[0003] Currently, the on-orbit calibration methods for the installation reference of star sensors mainly include the calibration method for the absolute installation error between the star sensor and the load, and the calibration method for the relative installation reference between multiple star sensors.

[0004] Before launch, the absolute installation error of the star sensor can be calibrated using a theodolite with photogrammetry to establish the reference mirror. After the satellite enters orbit, the absolute installation error of the star sensor can be calibrated using landmark information or celestial information such as stars imaged by the payload. Remote sensing satellites typically have multiple star sensors installed. Due to factors such as solar and lunar interference and obstruction by satellite appendages, the star sensors usually operate alternately in orbit. To avoid fluctuations in the accuracy of onboard attitude determination caused by sensor switching, it is necessary to filter and estimate the installation reference between the various probes of the star sensor and calibrate the low-frequency errors during this period. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a system for filtering estimation and low-frequency error calibration of a star sensor relative to a measurement reference, which can compensate for the low-frequency components of relative installation errors in real time online.

[0006] To address the aforementioned technical problems, this invention discloses a system for filtering estimation and low-frequency error calibration of a star sensor relative to a measurement reference, comprising:

[0007] The state recursion module is used to determine the state based on the previous time step t. k-1 The installation error angle and covariance matrix of the installation error angle after calibration of the first star sensor are extrapolated to obtain the current time t. k The installation error angle and the covariance matrix of the installation error angle after one step of recursion after the first star sensor calibration;

[0008] The measurement update module is used to update the measurement based on the current time t. k The attitude four elements output by the first and second star sensors, and the extrapolated current time t kThe installation error angle and its covariance matrix after one-step recursion following the calibration of the first star sensor are used to calculate the current time t. k The installation error angle after filtering correction and the covariance matrix of the installation error angle after filtering correction are obtained after the first star sensor calibration.

[0009] The low-frequency error calibration module is used to update the output t of the measurement update module. k1 t k2 ... t kn The installation error angle at time t is fitted using the least squares method to obtain the fitting coefficients for the low-frequency error; where t k1 t k2 ... t kn Represents n equally spaced t k The time series is formed by arranging the data from smallest to largest.

[0010] In the aforementioned system for filtering and estimating the star sensor relative to the measurement reference and calibrating the low-frequency error, the state recursion module is used for:

[0011] Based on the previous moment t k-1 The installation error angle after the first star sensor calibration is extrapolated to obtain the current time t using the following formula. k Installation error angle after one step of recursion following the calibration of the first satellite sensor:

[0012]

[0013] θ 1R (t k / k-1 )=θ 1R (t k-1 )

[0014] ψ 1R (t k / k-1 )=ψ 1R (t k-1 )

[0015] Among them, the previous time t k-1 The installation error angles after calibration of the first satellite sensor include: θ 1R (t k-1 ) and ψ 1R (t k-1 ), θ 1R (t k-1 ) and ψ 1R (t k-1 ) represent the previous time t respectively k-1 The installation error of the first star sensor after calibration is the angle of rotation around the X, Y, and Z axes; current time t kThe installation error angle after the first satellite sensor calibration and subsequent recursive step includes: θ 1R (t k / k-1 ) and ψ 1R (t k / k-1 ), θ 1R (t k / k-1 ) and ψ 1R (t k / k-1 ) represent the current time t respectively k The installation error after the first star sensor calibration is recursively calculated in one step, with the rotation angles around the X, Y, and Z axes.

[0016] Based on the previous moment t k-1 The covariance matrix P of the installation error angle after the first star sensor is calibrated R (t k-1 The current time t can be obtained by extrapolation using the following formula. k The covariance matrix P of the installation error angle after the first star sensor calibration and subsequent recursion. R (t k / k-1 ):

[0017] P R (t k / k-1 )=m R P R (t k-1 )+Q R

[0018] Where, m R Q represents the filter factor; R The system noise array represents the installation error angle.

[0019] In the aforementioned system for filtering and estimating the star sensor relative to the measurement reference and for calibrating the low-frequency error, the installation error of the first star sensor after calibration is measured by the rotation angles around the X, Y, and Z axes. θ 1R and ψ 1R satisfy:

[0020]

[0021] in, This represents the theoretical mounting matrix of the first star sensor; This represents the mounting matrix of the first star sensor after calibration using the second star sensor as a reference; C Δ express and Error matrix between.

[0022] In the aforementioned system for filtering estimation and low-frequency error calibration of the star sensor relative to the measurement reference,

[0023]

[0024] in, σ θ and σ ψ Respectively represent and θ 1R and ψ 1R The standard deviation of the corresponding installation error angle.

[0025] In the aforementioned system for filtering estimation and low-frequency error calibration of the star sensor relative to the measurement reference, the measurement update module is used for:

[0026] Based on the current time t k The attitude four elements q output by the first star sensor ST1I (t k ), calculate the current time t k The inertial measurement information Z of the optical axis output by the first star sensor. ST1I (t k ), current time t k The first horizontal axis inertial measurement information X output by the first star sensor ST1I (t k ) and the current time t k The inertial measurement information Y on the second horizontal axis output by the first star sensor. ST1I (t k ):

[0027]

[0028]

[0029] Y ST1I (t k ) = Z ST1I (t k )×X ST1I (t k )

[0030] Where, q ST1I (t k )=[q ST1I,1 (t k ),q ST1I,2 (t k ),q ST1I,3 (t k ),q ST1I,4 (t k )] T q ST1I,1 (t k ) represents the quaternion q ST1I (t k The first component of the vector part of ) , q ST1I,2 (tk ) represents the quaternion q ST1I (t k The second component of the vector part of ) , q ST1I,3 (t k ) represents the quaternion q ST1I (t k The third component of the vector part of ) , q ST1I,4 (t k ) represents the quaternion q ST1I (t k The scalar part of );

[0031] Based on the current time t k The attitude four elements q output by the second star sensor ST2I (t k ), calculate the current time t k The inertial measurement information Z of the optical axis output by the second star sensor. ST2I (t k ), current time t k The first horizontal axis inertial measurement information X output by the second star sensor. ST2I (t k ) and the current time t k The inertial measurement information Y on the second horizontal axis output by the second star sensor. ST2I (t k ):

[0032]

[0033]

[0034] Y ST2I (t k ) = Z ST2I (t k )×X ST2I (t k )

[0035] Where, q ST2I (t k )=[q ST2I,1 (t k ),q ST2I,2 (t k ),q ST2I,3 (t k ),q ST2I,4 (t k )] T q ST2I,1 (t k ) represents the quaternion q ST2I (t k The first component of the vector part of ) , q ST2I,2 (tk ) represents the quaternion q ST2I (t k The second component of the vector part of ) , q ST2I,3 (t k ) represents the quaternion q ST2I (t k The third component of the vector part of ) , q ST2I,4 (t k ) represents the quaternion q ST2I (t k The scalar part of );

[0036] According to P R (t k / k-1 ), calculate the current time t k The filter gain coefficient matrix K R (t k ):

[0037] K R (t k ) = P R (t k / k-1 (H) R ) T inv(H R P R (t k / k-1 (H) R ) T +R R )

[0038] Among them, H R R represents the measurement error propagation matrix. R The system noise matrix represents the installation error angle; the function inv() performs the inversion operation on the input matrix.

[0039] According to X ST1I (t k ), Y ST1I (t k Z ST1I (t k ), X ST2I (t k ), Y ST2I (t k Z ST2I (t k ) and K R (t k ), calculate the current time t k Installation error angle after filtering correction following calibration of the first star sensor:

[0040]

[0041] Wherein, at the current time tk The installation error angle after filtering correction following the calibration of the first star sensor includes: θ 1R (t k ) and ψ 1R (t k ), θ 1R (t k ) and ψ 1R (t k ) represent the current time t respectively k The filtered correction values ​​of the installation error around the X, Y and Z axes after the first star sensor is calibrated;

[0042] According to P R (t k / k-1 ) and K R (t k ), calculate the current time t k The covariance matrix P of the installation error angle after the first star sensor calibration and filtering correction R (t k ):

[0043] P R (t k ) = (I 3×3 -K R (t k )H R )P R (t k / k-1 (I) 3×3 -K R (t k )H R ) T +K R (t k )R R (K R (t k )) T

[0044] Among them, I 3×3 It is a 3×3 identity matrix.

[0045] In the aforementioned system for filtering estimation and low-frequency error calibration of the star sensor relative to the measurement reference,

[0046]

[0047] in, This represents the theoretically installed unit vector of the optical axis of the first star sensor within the satellite's main system. and These represent the theoretical installation unit vectors of the first and second horizontal axes of the first star sensor within the satellite's main system. This represents the theoretically installed unit vector of the optical axis of the second star sensor within the satellite's main system. and These represent the theoretical installation unit vectors of the first and second horizontal axes of the second star sensor within the satellite's main system.

[0048] In the aforementioned system for filtering estimation and low-frequency error calibration of the star sensor relative to the measurement reference,

[0049]

[0050] Where, σ z σ represents the standard deviation of the star sensor's optical axis measurement. xy This represents the standard deviation of the star sensor's horizontal axis measurement. The function diag() expands the input n-element column vector into an n-row, n-column matrix, filling the matrix with the first element of the column vector in the first row and first column, the second element in the second row and second column, and so on, until the nth element of the column vector is filled into the nth row and nth column. The remaining elements of the matrix are filled with 0.

[0051] In the above-mentioned system for filtering estimation and low-frequency error calibration of the star sensor relative to the measurement reference, the low-frequency error calibration module calculates the fitting coefficient using the following formula:

[0052]

[0053]

[0054]

[0055] Among them, a ix express The i-th order sine coefficient of the low-frequency error fitting coefficient, b ix express The i-th order cosine coefficient of the low-frequency error fitting coefficients, a iy Represents θ 1R The i-th order sine coefficient of the low-frequency error fitting coefficient, b iy Represents θ 1R The i-th order cosine coefficient of the low-frequency error fitting coefficients, a iz Represents ψ 1R The i-th order sine coefficient of the low-frequency error fitting coefficient, b iz Represents ψ 1R The i-th order cosine coefficients of the low-frequency error fitting coefficients, i = 1, 2, ..., n; M λ This represents the transition matrix that maps the system state to the measurement state in least squares fitting; Y θ1R and Yψ1R These represent measurement information matrices around the X-axis, Y-axis, and Z-axis, respectively.

[0056] In the aforementioned system for filtering estimation and low-frequency error calibration of the star sensor relative to the measurement reference,

[0057]

[0058] Where ω represents the orbital angular velocity.

[0059] In the aforementioned system for filtering estimation and low-frequency error calibration of the star sensor relative to the measurement reference,

[0060]

[0061] Y θ1R =[θ 1R (t k1 )θ 1R (t k2 )…θ 1R (t kn )] T

[0062] Y ψ1R =[ψ 1R (t k1 )ψ 1R (t k2 )…ψ 1R (t kn )] T

[0063] in, For the reason The measurement information matrix composed of Y θ1R For θ 1R (t k1 ), θ 1R (t k2 ), ..., θ 1R (t kn The measurement information matrix composed of Y ψ1R For by ψ 1R (t k1 ), ψ 1R (t k2 ), ..., ψ 1R (t kn A measurement information matrix composed of ) Indicates t k1 t k2 、…、t kn The angle θ of the installation error around the X-axis after the first star sensor calibration. 1R (t k1 ), θ 1R (t k2), ..., θ 1R (t kn ) represents t k1 t k2 、…、t kn The angle of rotation around the Y-axis of the installation error after the first star sensor calibration, ψ. 1R (t k1 ), ψ 1R (t k2 ), ..., ψ 1R (t kn ) represents t k1 t k2 、…、t kn The angle of rotation around the Z-axis of the installation error after the first star sensor is calibrated.

[0064] The present invention has the following advantages:

[0065] This invention discloses a filtering estimation and low-frequency error calibration system for star sensors relative to a measurement reference. Addressing the on-orbit estimation problem of star sensors relative to a measurement reference on high-resolution Earth observation satellites, it uses the statistical information of the measurement accuracy of the star sensor's optical axis and horizontal axis as weights, and employs a filtering estimation method to estimate the relative installation error angle of two star sensors in real time on orbit, and estimates the low-frequency components of the relative installation error angle offline. The filtering estimation and low-frequency error calibration system for star sensors relative to a measurement reference described in this invention has both its system equations and measurement equations as steady linear systems. Its filtering estimation algorithm is easy to implement in on-board code and has reference value for similar high-precision remote sensing satellites. Attached Figure Description

[0066] Figure 1 This is a block diagram of a system for filtering estimation and low-frequency error calibration of a star sensor relative to a measurement reference, as described in an embodiment of the present invention.

[0067] Figure 2 This is a schematic diagram illustrating the change in the relative installation error angle of the first star sensor, with the second star sensor as a reference, in an embodiment of the present invention.

[0068] Figure 3 This is a schematic diagram of the filtering estimation result of the relative installation error angle of the first star sensor, based on the second star sensor, in an embodiment of the present invention.

[0069] Figure 4 This is a schematic diagram of the fitting result of the relative installation error angle of the first star sensor, with the second star sensor as a reference, in an embodiment of the present invention.

[0070] Figure 5 This is a schematic diagram of the fitting result of the relative installation error angle of the first star sensor, with the second star sensor as a reference, in an embodiment of the present invention.

[0071] Figure 6 This is a schematic diagram showing the changes in the optical axis angle and horizontal axis angle between the first star sensor and the second star sensor after calibration and compensation in an embodiment of the present invention. Detailed Implementation

[0072] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments disclosed in the present invention will be described in further detail below with reference to the accompanying drawings.

[0073] Reference Figure 1 In this embodiment, the filtering estimation and low-frequency error calibration system for the star sensor relative to the measurement reference includes:

[0074] The state recursion module is used to determine the state based on the previous time step t. k-1 The installation error angle and covariance matrix of the installation error angle after calibration of the first star sensor are extrapolated to obtain the current time t. k The installation error angle and its covariance matrix after one-step recursion following the calibration of the first star sensor.

[0075] In this embodiment, the specific workflow of the state recursion module is as follows:

[0076] Based on the previous moment t k-1 The installation error angle after the first star sensor calibration is extrapolated to obtain the current time t using the following formula. k Installation error angle after one step of recursion following the calibration of the first satellite sensor:

[0077]

[0078] θ 1R (t k / k-1 )=θ 1R (t k-1 )

[0079] ψ 1R (t k / k-1 )=ψ 1R (t k-1 )

[0080] Among them, the previous time t k-1 The installation error angles after calibration of the first satellite sensor include: θ 1R (t k-1 ) and ψ 1R (t k-1 ), θ 1R (t k-1 ) and ψ 1R (t k-1 ) represent the previous time t respectively k-1The installation error of the first star sensor after calibration is the angle of rotation around the X, Y, and Z axes; current time t k The installation error angle after the first satellite sensor calibration and subsequent recursive step includes: θ 1R (t k / k-1 ) and ψ 1R (t k / k-1 ), θ 1R (t k / k-1 ) and ψ 1R (t k / k-1 ) represent the current time t respectively k The installation error after the first star sensor calibration is recursively calculated in one step, with the rotation angles around the X, Y, and Z axes.

[0081] Based on the previous moment t k-1 The covariance matrix P of the installation error angle after the first star sensor is calibrated R (t k-1 The current time t can be obtained by extrapolation using the following formula. k The covariance matrix P of the installation error angle after the first star sensor calibration and subsequent recursion. R (t k / k-1 ):

[0082] P R (t k / k-1 )=m R P R (t k-1 )+Q R

[0083] Where, m R Q represents the filter factor; R The system noise array represents the installation error angle.

[0084] Preferably, the installation error of the first star sensor after calibration is the rotation angle around the X-axis, Y-axis, and Z-axis. θ 1R and ψ 1R satisfy:

[0085]

[0086] in, This represents the theoretical mounting matrix of the first star sensor; This represents the mounting matrix of the first star sensor after calibration using the second star sensor as a reference; C Δ express and Error matrix between.

[0087] Preferred,

[0088]

[0089] in, σ θ and σ ψ Respectively represent and θ 1R and ψ 1R The standard deviation of the corresponding installation error angle.

[0090] The measurement update module is used to update the measurement based on the current time t. k The attitude four elements output by the first and second star sensors, and the extrapolated current time t k The installation error angle and its covariance matrix after one-step recursion following the calibration of the first star sensor are used to calculate the current time t. k The installation error angle after filtering correction and the covariance matrix of the first star sensor after calibration.

[0091] In this embodiment, the specific workflow of the measurement update module is as follows:

[0092] Based on the current time t k The attitude four elements q output by the first star sensor ST1I (t k ), calculate the current time t k The inertial measurement information Z of the optical axis output by the first star sensor. ST1I (t k ), current time t k The first horizontal axis inertial measurement information X output by the first star sensor ST1I (t k ) and the current time t k The inertial measurement information Y on the second horizontal axis output by the first star sensor. ST1I (t k ):

[0093]

[0094]

[0095] Y ST1I (t k ) = Z ST1I (t k )×X ST1I (t k )

[0096] Where, q ST1I (t k )=[q ST1I,1 (t k ),q ST1I,2 (tk ),q ST1I,3 (t k ),q ST1I,4 (t k )] T q ST1I,1 (t k ) represents the quaternion q ST1I (t k The first component of the vector part of ) , q ST1I,2 (t k ) represents the quaternion q ST1I (t k The second component of the vector part of ) , q ST1I,3 (t k ) represents the quaternion q ST1I (t k The third component of the vector part of ) , q ST1I,4 (t k ) represents the quaternion q ST1I (t k The scalar part of ).

[0097] Based on the current time t k The attitude four elements q output by the second star sensor ST2I (t k ), calculate the current time t k The inertial measurement information Z of the optical axis output by the second star sensor. ST2I (t k ), current time t k The first horizontal axis inertial measurement information X output by the second star sensor. ST2I (t k ) and the current time t k The inertial measurement information Y on the second horizontal axis output by the second star sensor. ST2I (t k ):

[0098]

[0099]

[0100] Y ST2I (t k ) = Z ST2I (t k )×X ST2I (t k )

[0101] Where, q ST2I (t k )=[q ST2I,1 (t k ),q ST2I,2 (tk ),q ST2I,3 (t k ),q ST2I,4 (t k )] T q ST2I,1 (t k ) represents the quaternion q ST2I (t k The first component of the vector part of ) , q ST2I,2 (t k ) represents the quaternion q ST2I (t k The second component of the vector part of ) , q ST2I,3 (t k ) represents the quaternion q ST2I (t k The third component of the vector part of ) , q ST2I,4 (t k ) represents the quaternion q ST2I (t k The scalar part of ).

[0102] According to P R (t k / k-1 ), calculate the current time t k The filter gain coefficient matrix K R (t k ):

[0103] K R (t k ) = P R (t k / k-1 (H) R ) T inv(H R P R (t k / k-1 (H) R ) T +R R )

[0104] Among them, H R R represents the measurement error propagation matrix. R The system noise matrix represents the installation error angle; the function inv() represents the inversion operation of the input matrix.

[0105] According to X ST1I (t k ), Y ST1I (t k Z ST1I (t k ), X ST2I (t k ), Y ST2I (t kZ ST2I (t k ) and K R (t k ), calculate the current time t k Installation error angle after filtering correction following calibration of the first star sensor:

[0106]

[0107] Wherein, at the current time t k The installation error angle after filtering correction following the calibration of the first star sensor includes: θ 1R (t k ) and ψ 1R (t k ), θ 1R (t k ) and ψ 1R (t k ) represent the current time t respectively k The installation error after calibration of the first star sensor is corrected by filtering around the X, Y, and Z axes.

[0108] According to P R (t k / k-1 ) and K R (t k ), calculate the current time t k The covariance matrix P of the installation error angle after the first star sensor calibration and filtering correction R (t k ):

[0109] P R (t k ) = (I 3×3 -K R (t k )H R )P R (t k / k-1 (I) 3×3 -K R (t k )H R ) T +K R (t k )R R (K R (t k )) T

[0110] Among them, I 3×3 It is a 3×3 identity matrix.

[0111] Preferred,

[0112]

[0113] in, This represents the theoretically installed unit vector of the optical axis of the first star sensor within the satellite's main system. and These represent the theoretical installation unit vectors of the first and second horizontal axes of the first star sensor within the satellite's main system. This represents the theoretically installed unit vector of the optical axis of the second star sensor within the satellite's main system. and These represent the theoretical installation unit vectors of the first and second horizontal axes of the second star sensor within the satellite's main system.

[0114] Preferred,

[0115]

[0116] Where, σ z σ represents the standard deviation of the star sensor's optical axis measurement. xy This represents the standard deviation of the star sensor's horizontal axis measurement. The function diag() expands the input n-element column vector into an n-row, n-column matrix, filling the matrix with the first element of the column vector in the first row and first column, the second element in the second row and second column, and so on, until the nth element of the column vector is filled into the nth row and nth column. The remaining elements of the matrix are filled with 0.

[0117] The low-frequency error calibration module is used to update the output t of the measurement update module. k1 t k2 ... t kn The installation error angle at time t is fitted using the least squares method to obtain the fitting coefficients for the low-frequency error; where t k1 t k2 ... t kn Represents n equally spaced t k The time series is formed by arranging the data from smallest to largest.

[0118] In this embodiment, the low-frequency error calibration module can calculate the fitting coefficient using the following formula:

[0119]

[0120]

[0121]

[0122] Among them, a ix express The i-th order sine coefficient of the low-frequency error fitting coefficient, b ix express The i-th order cosine coefficient of the low-frequency error fitting coefficients, a iy Represents θ 1R The i-th order sine coefficient of the low-frequency error fitting coefficient, b iy Represents θ 1R The i-th order cosine coefficient of the low-frequency error fitting coefficients, a iz Represents ψ 1R The i-th order sine coefficient of the low-frequency error fitting coefficient, b iz Represents ψ 1R The i-th order cosine coefficients of the low-frequency error fitting coefficients, i = 1, 2, ..., n; M λ This represents the transition matrix that maps the system state to the measurement state in least squares fitting; Y θ1R and Y ψ1R These represent measurement information matrices around the X-axis, Y-axis, and Z-axis, respectively.

[0123] Preferred,

[0124]

[0125] Where ω represents the orbital angular velocity.

[0126] Preferred,

[0127]

[0128] Y θ1R =[θ 1R (t k1 )θ 1R (t k2 )…θ 1R (t kn )] T

[0129] Y ψ1R =[ψ 1R (t k1 )ψ 1R (t k2 )…ψ 1R (t kn )] T

[0130] in, For the reason The measurement information matrix composed of Y θ1R For θ 1R (t k1 ), θ 1R (t k2 ), ..., θ1R (t kn The measurement information matrix composed of Y ψ1R For by ψ 1R (t k1 ), ψ 1R (t k2 ), ..., ψ 1R (t kn A measurement information matrix composed of ) Indicates t k1 t k2 、…、t kn The angle θ of the installation error around the X-axis after the first star sensor calibration. 1R (t k1 ), θ 1R (t k2 ), ..., θ 1R (t kn ) represents t k1 t k2 、…、t kn The angle of rotation around the Y-axis of the installation error after the first star sensor calibration, ψ. 1R (t k1 ), ψ 1R (t k2 ), ..., ψ 1R (t kn ) represents t k1 t k2 、…、t kn The angle of rotation around the Z-axis of the installation error after the first star sensor is calibrated.

[0131] To verify the effectiveness of the present invention, a mathematical simulation method was used to verify the filtering estimation and low-frequency error calibration system of the star sensor relative to the measurement reference. Figure 2 The variation of the relative installation error angle of the first star sensor is shown with the second star sensor as a reference. Figure 3 The result is a filtered estimate of the relative installation error angle of the first star sensor, with the second star sensor as the reference. Figure 4 The fitting result is the relative installation error angle of the first star sensor, with the second star sensor as the reference. Figure 5 This describes the changes in the optical axis angle and horizontal axis angle between the first and second star sensors before calibration. Figure 6 To calibrate and compensate for the changes in the optical axis angle and transverse axis angle between the first and second star sensors, simulation results show that the system described in this invention can effectively calibrate and compensate for the low-frequency error of the star sensor mounting reference.

[0132] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0133] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A system for filtering estimation and low-frequency error calibration of a star sensor relative to a measurement reference, characterized in that, include: The state recursion module is used to determine the state based on the previous time step t. k-1 The installation error angle and covariance matrix of the installation error angle after calibration of the first star sensor are extrapolated to obtain the current time t. k The installation error angle and the covariance matrix of the installation error angle after one step of recursion after the first star sensor calibration; The measurement update module is used to update the measurement based on the current time t. k The attitude four elements output by the first and second star sensors, and the extrapolated current time t k The installation error angle and its covariance matrix after one-step recursion following the calibration of the first star sensor are used to calculate the current time t. k The installation error angle after filtering correction and the covariance matrix of the installation error angle after filtering correction are obtained after the first star sensor calibration. The low-frequency error calibration module is used to update the output t of the measurement update module. k1 t k2 ... t kn The installation error angle at time t is fitted using the least squares method to obtain the fitting coefficients for the low-frequency error; where t k1 t k2 ... t kn Represents n equally spaced t k The time series is formed by arranging the data from smallest to largest.

2. The system for filtering estimation and low-frequency error calibration of a star sensor relative to a measurement reference according to claim 1, characterized in that, The state recursion module is used for: Based on the previous moment t k-1 The installation error angle after the first star sensor calibration is extrapolated to obtain the current time t using the following formula. k Installation error angle after one step of recursion following the calibration of the first satellite sensor: i 1R (t k / k-1 )=θ 1R (t k-1 ) ψ 1R (t k / k-1 )=ψ 1R (t k-1 ) Among them, the previous time t k-1 The installation error angles after calibration of the first satellite sensor include: θ 1R (t k-1 ) and ψ 1R (t k-1 ), θ 1R (t k-1 ) and ψ 1R (t k-1 ) represent the previous time t respectively k-1 The installation error of the first star sensor after calibration is the angle of rotation around the X, Y, and Z axes; current time t k The installation error angle after the first satellite sensor calibration and subsequent recursive step includes: θ 1R (t k / k-1 ) and ψ 1R (t k / k-1 ), θ 1R (t k / k-1 ) and ψ 1R (t k / k-1 ) represent the current time t respectively k The installation error after the first star sensor calibration is recursively calculated in one step, with the rotation angles around the X, Y, and Z axes. Based on the previous moment t k-1 The covariance matrix P of the installation error angle after the first star sensor is calibrated R (t k-1 The current time t can be obtained by extrapolation using the following formula. k The covariance matrix P of the installation error angle after the first star sensor calibration and subsequent recursion. R (t k / k-1 ): P R (t k / k-1 )=m R P R (t k-1 )+Q R Where, m R Q represents the filter factor; R The system noise array represents the installation error angle.

3. The system for filtering estimation and low-frequency error calibration of a star sensor relative to a measurement reference according to claim 2, characterized in that, The installation error of the first star sensor after calibration, around the X, Y, and Z axes, is a rotation angle. θ 1R and ψ 1R satisfy: in, This represents the theoretical mounting matrix of the first star sensor; This represents the mounting matrix of the first star sensor after calibration using the second star sensor as a reference; C Δ express and Error matrix between.

4. The system for filtering estimation and low-frequency error calibration of a star sensor relative to a measurement reference according to claim 2, characterized in that, in, σ θ and σ ψ Respectively represent and θ 1R and ψ 1R The standard deviation of the corresponding installation error angle.

5. The system for filtering estimation and low-frequency error calibration of a star sensor relative to a measurement reference according to claim 2, characterized in that, The measurement update module is used for: Based on the current time t k The attitude four elements q output by the first star sensor ST1I (t k ), calculate the current time t k The inertial measurement information Z of the optical axis output by the first star sensor. ST1I (t k ), current time t k The first horizontal axis inertial measurement information X output by the first star sensor ST1I (t k ) and the current time t k The inertial measurement information Y on the second horizontal axis output by the first star sensor. ST1I (t k ): Y ST1I (t k )=Z ST1I (t k )×X ST1I (t k ) Where, q ST1I (t k )=[q ST1I,1 (t k ),q ST1I,2 (t k ),q ST1I,3 (t k ),q ST1I,4 (t k )] T q ST1I,1 (t k ) represents the quaternion q ST1I (t k The first component of the vector part of ) , q ST1I,2 (t k ) represents the quaternion q ST1I (t k The second component of the vector part of ) , q ST1I,3 (t k ) represents the quaternion q ST1I (t k The third component of the vector part of ) , q ST1I,4 (t k ) represents the quaternion q ST1I (t k The scalar part of ); Based on the current time t k The attitude four elements q output by the second star sensor ST2I (t k ), calculate the current time t k The inertial measurement information Z of the optical axis output by the second star sensor. ST2I (t k ), current time t k The first horizontal axis inertial measurement information X output by the second star sensor. ST2I (t k ) and the current time t k The inertial measurement information Y on the second horizontal axis output by the second star sensor. ST2I (t k ): Y ST2I (t k )=Z ST2I (t k )×X ST2I (t k ) Where, q ST2I (t k )=[q ST2I,1 (t k ),q ST2I,2 (t k ),q ST2I,3 (t k ),q ST2I,4 (t k )] T q ST2I,1 (t k ) represents the quaternion q ST2I (t k The first component of the vector part of ) , q ST2I,2 (t k ) represents the quaternion q ST2I (t k The second component of the vector part of ) , q ST2I,3 (t k ) represents the quaternion q ST2I (t k The third component of the vector part of ) , q ST2I,4 (t k ) represents the quaternion q ST2I (t k The scalar part of ); According to P R (t k / k-1 ), calculate the current time t k The filter gain coefficient matrix K R (t k ): K R (t k )=P R (t k / k-1 )(H R ) T inv(H R P R (t k / k-1 )(H R ) T +R R ) Among them, H R R represents the measurement error propagation matrix. R The system noise matrix represents the installation error angle; the function inv() performs the inversion operation on the input matrix. According to X ST1I (t k ), Y ST1I (t k Z ST1I (t k ), X ST2I (t k ), Y ST2I (t k Z ST2I (t k ) and K R (t k ), calculate the current time t k Installation error angle after filtering correction following calibration of the first star sensor: Wherein, at the current time t k The installation error angle after filtering correction following the calibration of the first star sensor includes: θ 1R (t k ) and ψ 1R (t k ), θ 1R (t k ) and ψ 1R (t k ) represent the current time t respectively k The filtered correction values ​​of the installation error around the X, Y and Z axes after the first star sensor is calibrated; According to P R (t k / k-1 ) and K R (t k ), calculate the current time t k The covariance matrix P of the installation error angle after the first star sensor calibration and filtering correction R (t k ): P R (t k )=(I 3×3 -K R (t k )H R )P R (t k / k-1 )(I 3×3 -K R (t k )H R ) T +K R (t k )R R (K R (t k )) T Among them, I 3×3 It is a 3×3 identity matrix.

6. The system for filtering estimation and low-frequency error calibration of a star sensor relative to a measurement reference according to claim 5, characterized in that, in, This represents the theoretically installed unit vector of the optical axis of the first star sensor within the satellite's main system. and These represent the theoretical installation unit vectors of the first and second horizontal axes of the first star sensor within the satellite's main system. This represents the theoretically installed unit vector of the optical axis of the second star sensor within the satellite's main system. and These represent the theoretical installation unit vectors of the first and second horizontal axes of the second star sensor within the satellite's main system.

7. The system for filtering estimation and low-frequency error calibration of a star sensor relative to a measurement reference according to claim 5, characterized in that, Where, σ z σ represents the standard deviation of the star sensor's optical axis measurement. xy This represents the standard deviation of the star sensor's horizontal axis measurement. The function diag() expands the input n-element column vector into an n-row, n-column matrix, filling the matrix with the first element of the column vector in the first row and first column, the second element in the second row and second column, and so on, until the nth element of the column vector is filled into the nth row and nth column. The remaining elements of the matrix are filled with 0.

8. The system for filtering estimation and low-frequency error calibration of a star sensor relative to a measurement reference according to claim 5, characterized in that, The low-frequency error calibration module calculates the fitting coefficients using the following formula: Among them, a ix express The i-th order sine coefficient of the low-frequency error fitting coefficient, b ix express The i-th order cosine coefficient of the low-frequency error fitting coefficients, a iy Represents θ 1R The i-th order sine coefficient of the low-frequency error fitting coefficient, b iy Represents θ 1R The i-th order cosine coefficient of the low-frequency error fitting coefficients, a iz Represents ψ 1R The i-th order sine coefficient of the low-frequency error fitting coefficient, b iz Represents ψ 1R The i-th order cosine coefficients of the low-frequency error fitting coefficients, i = 1, 2, ..., n; M λ This represents the transition matrix that maps the system state to the measurement state in least squares fitting; Y θ1R and Y ψ1R These represent measurement information matrices around the X-axis, Y-axis, and Z-axis, respectively.

9. The system for filtering estimation and low-frequency error calibration of a star sensor relative to a measurement reference according to claim 8, characterized in that, Where ω represents the orbital angular velocity.

10. The system for filtering estimation and low-frequency error calibration of a star sensor relative to a measurement reference according to claim 8, characterized in that, Y θ1R =[θ 1R (t k1 )i 1R (t k2 )…θ 1R (t kn )] T Y ψ1R =[ψ 1R (t k1 )ψ 1R (t k2 )…ψ 1R (t kn )] T in, For the reason The measurement information matrix composed of Y θ1R For θ 1R (t k1 ), θ 1R (t k2 ), ..., θ 1R (t kn The measurement information matrix composed of Y ψ1R For by ψ 1R (t k1 ), ψ 1R (t k2 ), ..., ψ 1R (t kn A measurement information matrix composed of ) Indicates t k1 t k2 、…、t kn The angle θ of the installation error around the X-axis after the first star sensor calibration. 1R (t k1 ), θ 1R (t k2 ), ..., θ 1R (t kn ) represents t k1 t k2 、…、t kn The angle of rotation around the Y-axis of the installation error after the first star sensor calibration, ψ. 1R (t k1 ), ψ 1R (t k2 ), ..., ψ 1R (t kn ) represents t k1 t k2 、…、t kn The angle of rotation around the Z-axis of the installation error after the first star sensor is calibrated.

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