CN105486312B - A kind of star sensor and high frequency angular displacement sensor integrated attitude determination method and system - Google Patents
A kind of star sensor and high frequency angular displacement sensor integrated attitude determination method and system Download PDFInfo
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- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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Abstract
Its error measure model is built the present invention provides a kind of star sensor and high frequency angular displacement sensor integrated attitude determination method and system, including according to angular displacement sensor measuring principle, takes into full account various error sources existing for its observation；System measurements equation is built based on multi-star sensor information fusion result；According to satellite attitude kinematics equation and angular displacement sensor measurement model structure system state equation；Finally using two-way Kalman filtering and overall weight adjustment Models, high frequency attitude parameter optimal estimation is realized.The present invention can realize low frequency star sensor and high frequency angular displacement sensor optimal information fusion, obtain the attitude data of high-frequency high-precision, so as to lay the foundation for high-resolution optical image high-precision geometric manipulations.
Description
Technical field
The invention belongs to remote sensing satellite ground preprocessing technical field, a kind of star sensor and high frequency angular displacement are especially related to
Sensor combinations method for determining posture and system.
Background technology
High-resolution optical satellite is one of important research field of China high-resolution earth observation systems development, future
10 years China is better than 1 meter of optical satellite (abbreviation sub-meter grade optical satellite), highest space point by several spatial resolutions are launched
Resolution can even reach 0.1 meter or so.But the spatial resolution of higher is not meant to have the geometry of higher relatively smart
Degree.Since high-resolution optical satellite push-scanning image frequency is hertz up to ten thousand, and traditional star sensor determines appearance with Gyro
The posture frequency that mode exports is several hertz to tens hertz, it is difficult to meet its high-precision geometric manipulations demand.The present invention is directed to
The problem, proposes a kind of low frequency star sensor and high frequency angular displacement sensor integrated attitude determination method.In recent years, angular displacement sensor
Gradually it is mounted on a series of high-resolution optical satellites as a kind of novel gesture sensor and carries out in-orbit use, since it can
To export up to ten thousand hertz of angle increment attitude data, it is carried out optimal information fusion with low frequency star sensor can obtain high frequency
Attitude data, to meet the requirement of high-resolution optical image high-precision geometric manipulations.
The content of the invention
The present invention is difficult to meet the requirement of high-resolution optical satellite image geometric manipulations for current low frequency attitude data
Problem, there is provided one kind is based on low frequency star sensor and high frequency angular displacement sensor high accuracy integrated attitude determination technical solution.
Technical solution provided by the invention is a kind of star sensor and high frequency angular displacement sensor integrated attitude determination method, including
Following steps：
Step 1, it is as follows to build angular displacement sensor measurement model,
ωg=(1+ Δs+Λ) ω+b+ ηg
Wherein, ωgThe angular speed size obtained for angular displacement sensor measurement, Δ represent that angular displacement sensor installation misses
Difference, Λ represent angular displacement sensor scale factor error, and ω is satellite body relative to the true angular velocity of inertial space, b tables
Show angular displacement sensor drift size, ηgFor angular displacement sensor measurement noise；
Step 2, system measurements equation being built based on multi-star sensor information fusion result, realization is as follows,
Equipped with one group of orthogonal vector,Represent orthogonal vector actual value under body coordinate system,Represent
Measured value of the orthogonal vector under inertial coodinate system,Represent orthogonal vector actual value under inertial coodinate system；
It is as follows to obtain measurement equation,
Zk=HkXk+Vk
Wherein, ZkRepresent measurement vector, HkRepresent observing matrix, XkRepresent state variable,Represent quaternary number optimal estimation
Value,Represent by body to inertial system transition matrix, VkRepresent tkMoment observation noise sequence；
Step 3, system state equation is built according to satellite attitude kinematics equation and angular displacement sensor measurement model, it is real
It is now as follows,
The state of being based on is obtained according to attitude kinematics equationsSystem state equation it is as follows,
W (t)=[- 0.5 ηg ηb]T
Wherein,Represent quantity of state differential value, X (t) represents quantity of state, and F (t) represents state-transition matrix differential, W
(t) system noise sequence is represented,Represent angular velocity vector multiplication cross, I3×3Expression unit matrix, 03×3It is 0 to represent element
Matrix,Represent error quaternion vector section, Δ bTRepresent error drift；
Linearisation discretization is carried out to system above state equation to obtain,
Xk=Φk,k-1Xk-1+Γk-1Wk-1
Wherein, Xk、Xk-1Represent tkMoment, tk-1Moment state variable, Φk,k-1Represent state-transition matrix, Γk-1Represent
System noise drives battle array, Wk-1Represent system noise sequence；
Step 4, the system measurements equation and system state equation built respectively based on step 2 and step 3, using two-way card
Kalman Filtering and overall weight adjustment Models, realize high frequency attitude parameter optimal estimation.
Moreover, attitude kinematics equations represent that following attitude kinematics equations represent as follows in step 3,
Wherein,Represent the differential value of quaternary number, q and ω represent satellite body coordinate system relative to inertial coodinate system respectively
Attitude quaternion and three axis angular velocity of rotations, q=[q0 q1 q2 q3]T, ω=(ωx,ωy,ωz)。
Moreover, step 4 realize it is as follows,
(1) attitude prediction is carried out based on angle displacement measurement information
Based on angle displacement measurement information in tk-1Moment integrates following formula, obtains attitude of satellite quaternary number predicted value
Wherein,Represent tk-1Moment quaternary number optimal estimation value,Represent tk-1Moment angular speed optimal estimation value；
Angular displacement drift forecasting valuePrediction model it is as follows,
Wherein,Represent tk-1Moment angular displacement drift optimal estimation value；
For the predicted value of error covariance matrixIt is as follows to resolve model,
Wherein,Represent tk-1Moment error covariance matrix estimate, Qk-1Represent system interference variance matrix；
(2) attitude rectification is carried out based on star sensor measured value
In tkMoment, according to system measurements equation calculation observing matrix Hk, further calculate filtering gain Kk,
Wherein, Pk/k-1Represent error covariance matrix predicted value, then corresponding system state variablesFor,
Attitude of satellite quaternary number tkThe amendment updated value at momentWith the amendment updated value of angular displacement driftRespectively,
Wherein,Represent error quaternion estimate,Represent error drift amount estimate；
Error covariance matrix PkRenewal be calculated as,
Wherein, RkRepresent star sensor measuring noise square difference battle array, I represents unit matrix, HkUsing the state corrected after updating
VariableRe-start calculating；
Initial filter, inverse filtering and forward filtering are carried out according to the above process (1) (2), are based ultimately upon forward filtering
Overall weight adjustment is carried out with inverse filtering result.
The present invention also provides a kind of star sensor and high frequency angular displacement sensor integrated attitude determination system, including with lower module：
First module, it is as follows for building angular displacement sensor measurement model,
ωg=(1+ Δs+Λ) ω+b+ ηg
Wherein, ωgThe angular speed size obtained for angular displacement sensor measurement, Δ represent that angular displacement sensor installation misses
Difference, Λ represent angular displacement sensor scale factor error, and ω is satellite body relative to the true angular velocity of inertial space, b tables
Show angular displacement sensor drift size, ηgFor angular displacement sensor measurement noise；
Second module, for building system measurements equation based on multi-star sensor information fusion result, realization is as follows,
Equipped with one group of orthogonal vector,Represent orthogonal vector actual value under body coordinate system,Represent
Measured value of the orthogonal vector under inertial coodinate system,Represent orthogonal vector actual value under inertial coodinate system；
It is as follows to obtain measurement equation,
Zk=HkXk+Vk
Wherein, ZkRepresent measurement vector, HkRepresent observing matrix, XkRepresent state variable,Represent quaternary number optimal estimation
Value,Represent by body to inertial system transition matrix, VkRepresent tkMoment observation noise sequence；
3rd module, for building system mode according to satellite attitude kinematics equation and angular displacement sensor measurement model
Equation, realization is as follows,
The state of being based on is obtained according to attitude kinematics equationsSystem state equation it is as follows,
W (t)=[- 0.5 ηg ηb]T
Wherein,Represent quantity of state differential value, X (t) represents quantity of state, and F (t) represents state-transition matrix differential, W
(t) system noise sequence is represented,Represent angular velocity vector multiplication cross, I3×3Expression unit matrix, 03×3It is 0 to represent element
Matrix,Represent error quaternion vector section, Δ bTRepresent error drift；
Linearisation discretization is carried out to system above state equation to obtain,
Xk=Φk,k-1Xk-1+Γk-1Wk-1
Wherein, Xk、Xk-1Represent tkMoment, tk-1Moment state variable, Φk,k-1Represent state-transition matrix, Γk-1Represent
System noise drives battle array, Wk-1Represent system noise sequence；
4th module, for the system measurements equation built respectively based on the second module and the 3rd module and system mode side
Journey, using two-way Kalman filtering and overall weight adjustment Models, realizes high frequency attitude parameter optimal estimation.
Moreover, attitude kinematics equations represent that following attitude kinematics equations represent as follows in the 3rd module,
Wherein,Represent the differential value of quaternary number, q and ω represent satellite body coordinate system relative to inertial coodinate system respectively
Attitude quaternion and three axis angular velocity of rotations, q=[q0 q1 q2 q3]T, ω=(ωx,ωy,ωz)。
Moreover, the realization of the 4th module is as follows,
(1) attitude prediction is carried out based on angle displacement measurement information
Based on angle displacement measurement information in tk-1Moment integrates following formula, obtains attitude of satellite quaternary number predicted value
Wherein,Represent tk-1Moment quaternary number optimal estimation value,Represent tk-1Moment angular speed optimal estimation value；
Angular displacement drift forecasting valuePrediction model it is as follows,
Wherein,Represent tk-1Moment angular displacement drift optimal estimation value；
For the predicted value of error covariance matrixIt is as follows to resolve model,
Wherein,Represent tk-1Moment error covariance matrix estimate, Qk-1Represent system interference variance matrix；
(2) attitude rectification is carried out based on star sensor measured value
In tkMoment, according to system measurements equation calculation observing matrix Hk, further calculate filtering gain Kk,
Wherein, Pk/k-1Represent error covariance matrix predicted value, then corresponding system state variablesFor,
Attitude of satellite quaternary number tkThe amendment updated value at momentWith the amendment updated value of angular displacement driftRespectively,
Wherein,Represent error quaternion estimate,Represent error drift amount estimate；
Error covariance matrix PkRenewal be calculated as,
Wherein, RkRepresent star sensor measuring noise square difference battle array, I represents unit matrix, HkUsing the state corrected after updating
VariableRe-start calculating；
Initial filter, inverse filtering and forward filtering are carried out according to the above process (1) (2), are based ultimately upon forward filtering
Overall weight adjustment is carried out with inverse filtering result.
The present invention provides a kind of low frequency star sensor and high frequency angular displacement sensor integrated attitude determination technical solution, realize
The high-precision fixed appearance advantage of star sensor has complementary advantages with the output of angular displacement sensor high-frequency angle increment, by provided by the invention
Technical solution can obtain high-frequency, high-precision attitude of satellite data, be high-resolution optical satellite high-precision geometric manipulations
Lay the foundation.
Brief description of the drawings
Fig. 1 is the flow chart of the embodiment of the present invention.
Embodiment
Below in conjunction with drawings and examples the present invention will be described in detail technical solution.
Star sensor shown in Figure 1 and high frequency angular displacement sensor integrated attitude determination techniqueflow chart, below for implementation
Each step in example flow, is described in further detail the method for the present invention.
Step 1, according to angular displacement sensor operation principle, rational error measure model is built, takes into full account its measurement
Various error sources present in value.
Angular displacement sensor can directly export the angle increment data of high frequency, obtain as a kind of inertial attitude sensor
Measurement data be meant that the sampling instant compared to caused angle increment size in upper sampling instant time interval.According to upper
Principle is stated to obtain：Assuming that angular displacement sensor data sampling period is T, the three axis angular displacement observation point of satellite of a certain moment t
Wei not NX,Ny,Nz, then the three axis angular rate ω of moment t are obtainedx,ωy,ωz, specifically it is unfolded as follows：
Due to during angular displacement sensor operation on orbit existing error term include installation error, scale factor error,
Drift error and measurement noise etc., therefore the error measure model for further obtaining angular displacement sensor is as follows：
ωg=(1+ Δs+Λ) ω+b+ ηg (2)
Wherein, ωgThe angular speed size obtained for angular displacement sensor measurement, Δ represent that angular displacement sensor installation misses
Difference, Λ represent angular displacement sensor scale factor error, and ω is satellite body relative to the true angular velocity of inertial space, b tables
Show angular displacement sensor drift size, ηgFor angular displacement sensor measurement noise.It is assumed here that angular displacement sensor measurement noise
For white Gaussian noise, i.e.,σgRepresent error in measurement noise.
It is further assumed that the drift b of angular displacement sensor is sound-driving by white noise, it is expressed as：
Wherein,Represent the differential value of drift value, ηbFor angular displacement sensor and the noise of time correlation, meetσbRepresent error in drift noise.
Step 2, system measurements equation is built based on multi-star sensor information fusion result.
The present invention realizes multi-star sensor optimal information fusion, further structure based on multi-star sensor optical axis vector observation value
System measurements equation is built, detailed process is as follows：
Assuming that one group of orthogonal vector expression way under body coordinate system, inertial coodinate system is as follows：
Wherein,Represent orthogonal vector actual value under body coordinate system,Represent orthogonal vector used
Measured value under property coordinate system,Represent orthogonal vector actual value under inertial coodinate system.
It is further as follows according to measurement equation is derived by：
Zk=HkXk+Vk
Wherein, ZkRepresent measurement vector, HkRepresent observing matrix, XkRepresent state variable,Represent quaternary number optimal estimation
Value,Represent by body to inertial system transition matrix, VkRepresent tkMoment observation noise sequence, and meet：E(Vk) represent observation noise serial mean,Observation noise sequence between representing at different moments
Row covariance,Represent tjMoment observation noise matrix transposition, δkjRepresent Dick's Lay function；RkRepresent that star sensor measures to make an uproar
Sound variance matrix.
Step 3, the state side based on attitude kinematics equations and angular displacement sensor error measure model construction system
Journey.
The present invention further builds state equation according to attitude kinematics equations and angular displacement sensor measurement model, has
Body process is as follows：
Attitude kinematics equations represent as follows：
Wherein,Represent the differential value of quaternary number, q and ω represent satellite body coordinate system relative to inertial coodinate system respectively
Attitude quaternion and three axis angular velocity of rotations, q=[q0 q1 q2 q3]T, ω=(ωx,ωy,ωz)。
Further it is derived by based on stateSystem state equation：
Wherein,Represent quantity of state differential value, X (t) represents quantity of state, and F (t) represents state-transition matrix differential, W
(t) system noise sequence is represented,Represent angular velocity vector multiplication cross, I3×3Expression unit matrix, 03×3It is 0 to represent element
Matrix,Represent error quaternion vector section, Δ bTRepresent error drift, state equation derived above is continuous dynamic
System filter equation is, it is necessary to be linearized and discretization, therefore carry out linearisation discretization and obtain：
Xk=Φk,k-1Xk-1+Γk-1Wk-1 (8)
Wherein, Xk、Xk-1Represent tkMoment, tk-1Moment state variable, Φk,k-1Represent state-transition matrix, Γk-1Represent
System noise drives battle array, Wk-1Represent system noise sequence.
Step 4, the system measurements equation and system state equation built respectively based on step 2 and step 3, using two-way card
Kalman Filtering and overall weight adjustment Models, realize high frequency attitude parameter optimal estimation.
Since star sensor output frequency is several hertz to tens hertz, and angular displacement sensor output frequency reaches up to ten thousand
Hertz, the design of conventional integrated attitude determination wave filter can not meet to be actually needed.The present invention proposes a kind of double for the problem
To Kalman filtering multifrequency many attitude sensor optimal information fusion is realized with the model algorithm that overall weight adjustment is combined.
(1) attitude prediction is carried out based on angle displacement measurement information
Based on angle displacement measurement information in tk-1Moment integrates following formula, can obtain the prediction of attitude of satellite quaternary number
Value
Wherein,Represent tk-1Moment quaternary number optimal estimation value,Represent tk-1Moment angular speed optimal estimation value.
Angular displacement drift forecasting valuePrediction model it is as follows：
Wherein,Represent tk-1Moment angular displacement drift optimal estimation value.
For the predicted value of error covariance matrixIt is as follows to resolve model：
Wherein,Represent tk-1Moment error covariance matrix estimate, Qk-1Represent system interference variance matrix.
(2) attitude rectification is carried out based on star sensor measured value
In tkMoment, according to step 2 measurement equation calculating observation matrix Hk.Further calculate filtering gain Kk：
Wherein, Pk/k-1Represent error covariance matrix predicted value, then corresponding system state variablesFor：
Attitude of satellite quaternary number tkThe amendment updated value at momentWith the amendment updated value of angular displacement driftRespectively：
Wherein,Represent error quaternion estimate,Represent error drift amount estimate.
Error covariance matrix PkRenewal be calculated as：
Wherein, RkRepresent star sensor measuring noise square difference battle array, I represents unit matrix, HkUsing the state corrected after updating
VariableCalculating is re-started, the purpose for the arrangement is that making filtering that there is more preferable convergence.Correcting the attitude of satellite
After the drift of quaternary number and angular displacement, state variableNeed to be re-set as zero.
Initial filter, inverse filtering and forward filtering are carried out according to the above process, (1) to (2) is first filtering；(2)
It is inverse filtering to (1)；Finally (1) to (2) is forward filtering, and the initial value filtered every time is the result of last time filtering；Finally
Overall weight adjustment is carried out based on forward filtering and inverse filtering result.
Root symbol " f " represents forward filtering as a result, root symbol " b " represents inverse filtering as a result, root symbol " s " represents overall
Weighted adjustment as a result,
Represent tkMoment forward filtering posture optimal estimation value,Represent tkMoment inverse filtering posture is optimal to be estimated
EvaluationIt is inverse,Represent tkMoment forward and reverse filter result quaternary number error；
Represent forward and reverse quantity of state filter result error matrix,Represent to return to scalar sign, Represent tkMoment drift forward direction and inverse filtering optimal estimation value,
WithThe inverse of the forward and reverse optimal estimation value of error covariance matrix is represented respectively,Represent to arrange
The error covariance matrix estimate of weighting；
Represent forward and reverse quantity of state filter result error matrix weighted average,Represent error quaternary
Number overall weight mean vector partial results,Represent error drift overall weight average result；
Represent error quaternion overall weight as a result,Represent error drift overall weight result；
Represent tkMoment quaternary number overall weight as a result, Represent tkMoment drift value overall weight result.
When it is implemented, method provided by the present invention can realize automatic running flow based on software technology, mould can be also used
Block mode realizes corresponding system.The embodiment of the present invention also provides a kind of star sensor and high frequency angular displacement sensor integrated attitude determination
System, including with lower module：
First module, it is as follows for building angular displacement sensor measurement model,
ωg=(1+ Δs+Λ) ω+b+ ηg
Wherein, ωgThe angular speed size obtained for angular displacement sensor measurement, Δ represent that angular displacement sensor installation misses
Difference, Λ represent angular displacement sensor scale factor error, and ω is satellite body relative to the true angular velocity of inertial space, b tables
Show angular displacement sensor drift size, ηgFor angular displacement sensor measurement noise；
Second module, for building system measurements equation based on multi-star sensor information fusion result, realization is as follows,
Equipped with one group of orthogonal vector,Represent orthogonal vector actual value under body coordinate system,Represent
Measured value of the orthogonal vector under inertial coodinate system,Represent orthogonal vector actual value under inertial coodinate system；
It is as follows to obtain measurement equation,
Zk=HkXk+Vk
Wherein, ZkRepresent measurement vector, HkRepresent observing matrix, XkRepresent state variable,Represent quaternary number optimal estimation
Value,Represent by body to inertial system transition matrix, VkRepresent tkMoment observation noise sequence；
3rd module, for building system mode according to satellite attitude kinematics equation and angular displacement sensor measurement model
Equation, realization is as follows,
The state of being based on is obtained according to attitude kinematics equationsSystem state equation it is as follows,
W (t)=[- 0.5 ηg ηb]T
Wherein,Represent quantity of state differential value, X (t) represents quantity of state, and F (t) represents state-transition matrix differential, W
(t) system noise sequence is represented,Represent angular velocity vector multiplication cross, I3×3Expression unit matrix, 03×3It is 0 to represent element
Matrix,Represent error quaternion vector section, Δ bTRepresent error drift；
Linearisation discretization is carried out to system above state equation to obtain,
Xk=Φk,k-1Xk-1+Γk-1Wk-1
Wherein, Xk、Xk-1Represent tkMoment, tk-1Moment state variable, Φk,k-1Represent state-transition matrix, Γk-1Represent
System noise drives battle array, Wk-1Represent system noise sequence；
4th module, for the system measurements equation built respectively based on the second module and the 3rd module and system mode side
Journey, using two-way Kalman filtering and overall weight adjustment Models, realizes high frequency attitude parameter optimal estimation.
Each module specific implementation can be found in corresponding steps, and it will not go into details by the present invention.
Instantiation described herein is only to spirit explanation for example of the invention.The technical field of the invention
Technical staff can do various modifications or additions to described instantiation or substitute in a similar way, but
Without departing from spirit of the invention or beyond the scope of the appended claims.
Claims (6)
1. a kind of star sensor and high frequency angular displacement sensor integrated attitude determination method, it is characterised in that comprise the following steps：
Step 1, it is as follows to build angular displacement sensor measurement model,
ωg=(1+ Δs+Λ) ω+b+ ηg
Wherein, ωgThe angular speed size obtained for angular displacement sensor measurement, Δ represent angular displacement sensor installation error, Λ tables
Show angular displacement sensor scale factor error, ω is true angular velocity of the satellite body relative to inertial space, represents satellite sheet
Body coordinate system is relative to three axis angular velocity of rotations of inertial coodinate system, b expression angular displacement sensor drift sizes, ηgFor angular displacement
Sensor measurement noise；
Step 2, system measurements equation being built based on multi-star sensor information fusion result, realization is as follows,
Equipped with one group of orthogonal vector,Represent orthogonal vector actual value under body coordinate system,Represent orthogonal arrow
The measured value under inertial coodinate system is measured,Represent orthogonal vector actual value under inertial coodinate system；
It is as follows to obtain measurement equation,
Zk=HkXk+Vk
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<mi>l</mi>
<mi>b</mi>
<mn>1</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>l</mi>
<mrow>
<mi>m</mi>
<mi>i</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>A</mi>
<mrow>
<mi>b</mi>
<mi>i</mi>
</mrow>
<mi>T</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
<msubsup>
<mi>l</mi>
<mi>b</mi>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>l</mi>
<mrow>
<mi>m</mi>
<mi>i</mi>
</mrow>
<mn>3</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>A</mi>
<mrow>
<mi>b</mi>
<mi>i</mi>
</mrow>
<mi>T</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
<msubsup>
<mi>l</mi>
<mi>b</mi>
<mn>3</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mrow>
<mn>9</mn>
<mo>&times;</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
Wherein, ZkRepresent measurement vector, HkRepresent observing matrix, XkRepresent state variable,Represent quaternary number optimal estimation value,Represent by body to inertial system transition matrix, VkRepresent tkMoment observation noise sequence；
Step 3, system state equation is built according to satellite attitude kinematics equation and angular displacement sensor measurement model, realized such as
Under,
The state of being based on is obtained according to attitude kinematics equationsSystem state equation it is as follows,
<mrow>
<mover>
<mi>X</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mi>X</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>W</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mo>&lsqb;</mo>
<mover>
<mi>&omega;</mi>
<mo>^</mo>
</mover>
<mo>&times;</mo>
<mo>&rsqb;</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mn>0.5</mn>
<msub>
<mi>I</mi>
<mrow>
<mn>3</mn>
<mo>&times;</mo>
<mn>3</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mn>0</mn>
<mrow>
<mn>3</mn>
<mo>&times;</mo>
<mn>3</mn>
</mrow>
</msub>
</mtd>
<mtd>
<msub>
<mn>0</mn>
<mrow>
<mn>3</mn>
<mo>&times;</mo>
<mn>3</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
W (t)=[- 0.5 ηg ηb]T
Wherein,Represent quantity of state differential value, X (t) represents quantity of state, and F (t) represents state-transition matrix differential, and W (t) is represented
System noise sequence,Represent angular velocity vector multiplication cross, I3×3Expression unit matrix, 03×3Represent the matrix that element is 0,
Represent error quaternion vector section, Δ bTRepresent error drift, ηgFor angular displacement sensor measurement noise, ηbPassed for angular displacement
Sensor and the noise of time correlation；
Linearisation discretization is carried out to system above state equation to obtain,
Xk=Φk,k-1Xk-1+Γk-1Wk-1
Wherein, Xk、Xk-1Represent tkMoment, tk-1Moment state variable, Φk,k-1Represent state-transition matrix, Γk-1Represent system noise
Sound-driving battle array, Wk-1Represent system noise sequence；
Step 4, the system measurements equation and system state equation built respectively based on step 2 and step 3, using two-way Kalman
Filtering and overall weight adjustment Models, realize high frequency attitude parameter optimal estimation.
2. star sensor and high frequency angular displacement sensor integrated attitude determination method according to claim 1, it is characterised in that：Step
Attitude kinematics equations represent as follows in 3,
<mrow>
<mover>
<mi>q</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>q</mi>
<mo>&CircleTimes;</mo>
<mi>&omega;</mi>
</mrow>
<mrow>
<mover>
<mi>q</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>&omega;</mi>
<mi>x</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>&omega;</mi>
<mi>y</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>&omega;</mi>
<mi>z</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>x</mi>
</msub>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>z</mi>
</msub>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>&omega;</mi>
<mi>y</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>y</mi>
</msub>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>&omega;</mi>
<mi>z</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>x</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>z</mi>
</msub>
</mtd>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>y</mi>
</msub>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>&omega;</mi>
<mi>x</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>q</mi>
<mn>0</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>q</mi>
<mn>1</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>q</mi>
<mn>2</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>q</mi>
<mn>3</mn>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>q</mi>
<mn>0</mn>
</msub>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>q</mi>
<mn>1</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>q</mi>
<mn>2</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>q</mi>
<mn>3</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>q</mi>
<mn>1</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>q</mi>
<mn>0</mn>
</msub>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>q</mi>
<mn>3</mn>
</msub>
</mrow>
</mtd>
<mtd>
<msub>
<mi>q</mi>
<mn>2</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>q</mi>
<mn>2</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>q</mi>
<mn>3</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>q</mi>
<mn>0</mn>
</msub>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>q</mi>
<mn>1</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>q</mi>
<mn>3</mn>
</msub>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>q</mi>
<mn>2</mn>
</msub>
</mrow>
</mtd>
<mtd>
<msub>
<mi>q</mi>
<mn>1</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>q</mi>
<mn>0</mn>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>x</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>y</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>z</mi>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein,Represent the differential value of quaternary number, q and ω represent appearance of the satellite body coordinate system relative to inertial coodinate system respectively
State quaternary number and three axis angular velocity of rotations, q=[q0 q1 q2 q3]T, ω=(ωx,ωy,ωz)。
3. star sensor according to claim 1 or claim 2 and high frequency angular displacement sensor integrated attitude determination method, it is characterised in that：
Step 4 realize it is as follows,
(1) attitude prediction is carried out based on angle displacement measurement information
Based on angle displacement measurement information in tk-1Moment integrates following formula, obtains attitude of satellite quaternary number predicted value
<mrow>
<msub>
<mover>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msub>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&CircleTimes;</mo>
<msub>
<mover>
<mi>&omega;</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
Wherein,Represent attitude of satellite quaternary number predicted value,Represent tk-1Moment quaternary number optimal estimation value,Represent
tk-1Moment angular speed optimal estimation value；
Angular displacement drift forecasting valuePrediction model it is as follows,
<mrow>
<msub>
<mover>
<mi>b</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>b</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
Wherein,Represent tk-1Moment angular displacement drift optimal estimation value；
For the predicted value of error covariance matrixIt is as follows to resolve model,
<mrow>
<msub>
<mover>
<mi>P</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>&Phi;</mi>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mover>
<mi>P</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<msubsup>
<mi>&Phi;</mi>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mi>T</mi>
</msubsup>
<mo>+</mo>
<msub>
<mi>&Gamma;</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>Q</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<msubsup>
<mi>&Gamma;</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mi>T</mi>
</msubsup>
</mrow>
Wherein,Represent tk-1Moment error covariance matrix estimate, Qk-1Represent system interference variance matrix；
(2) attitude rectification is carried out based on star sensor measured value
In tkMoment, according to system measurements equation calculation observing matrix Hk, further calculate filtering gain Kk,
<mrow>
<msub>
<mi>K</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<msubsup>
<mi>H</mi>
<mi>k</mi>
<mi>T</mi>
</msubsup>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>H</mi>
<mi>k</mi>
</msub>
<msub>
<mi>P</mi>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<msubsup>
<mi>H</mi>
<mi>k</mi>
<mi>T</mi>
</msubsup>
<mo>+</mo>
<msub>
<mi>R</mi>
<mi>k</mi>
</msub>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
Wherein, Pk/k-1Represent error covariance matrix predicted value, then corresponding system state variablesFor,
<mrow>
<msub>
<mover>
<mi>X</mi>
<mo>^</mo>
</mover>
<mi>k</mi>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>X</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>K</mi>
<mi>k</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>Z</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<msub>
<mi>H</mi>
<mi>k</mi>
</msub>
<msub>
<mover>
<mi>X</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
Attitude of satellite quaternary number tkThe amendment updated value at momentWith the amendment updated value of angular displacement driftRespectively,
<mrow>
<msub>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mi>k</mi>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&CircleTimes;</mo>
<mi>&Delta;</mi>
<msub>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mi>k</mi>
</msub>
</mrow>
<mrow>
<msub>
<mover>
<mi>b</mi>
<mo>^</mo>
</mover>
<mi>k</mi>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>b</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<mi>&Delta;</mi>
<msub>
<mover>
<mi>b</mi>
<mo>^</mo>
</mover>
<mi>k</mi>
</msub>
</mrow>
Wherein,Represent error quaternion estimate,Represent error drift amount estimate；
Error covariance matrix PkRenewal be calculated as,
<mrow>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mi>I</mi>
<mo>-</mo>
<msub>
<mi>K</mi>
<mi>k</mi>
</msub>
<msub>
<mi>H</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>P</mi>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<msup>
<mrow>
<mo>(</mo>
<mi>I</mi>
<mo>-</mo>
<msub>
<mi>K</mi>
<mi>k</mi>
</msub>
<msub>
<mi>H</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
<mi>T</mi>
</msup>
<mo>+</mo>
<msub>
<mi>K</mi>
<mi>k</mi>
</msub>
<msub>
<mi>R</mi>
<mi>k</mi>
</msub>
<msubsup>
<mi>K</mi>
<mi>k</mi>
<mi>T</mi>
</msubsup>
</mrow>
Wherein, RkRepresent star sensor measuring noise square difference battle array, I represents unit matrix, HkUsing the state variable corrected after updatingRe-start calculating；
Initial filter, inverse filtering and forward filtering are carried out according to the above process (1) (2), be based ultimately upon forward filtering with it is anti-
Overall weight adjustment is carried out to filter result.
4. a kind of star sensor and high frequency angular displacement sensor integrated attitude determination system, it is characterised in that including with lower module：
First module, it is as follows for building angular displacement sensor measurement model,
ωg=(1+ Δs+Λ) ω+b+ ηg
Wherein, ωgThe angular speed size obtained for angular displacement sensor measurement, Δ represent angular displacement sensor installation error, Λ tables
Show angular displacement sensor scale factor error, ω is true angular velocity of the satellite body relative to inertial space, represents satellite sheet
Body coordinate system is relative to three axis angular velocity of rotations of inertial coodinate system, b expression angular displacement sensor drift sizes, ηgFor angular displacement
Sensor measurement noise；
Second module, for building system measurements equation based on multi-star sensor information fusion result, realization is as follows,
Equipped with one group of orthogonal vector,Represent orthogonal vector actual value under body coordinate system,Represent orthogonal arrow
The measured value under inertial coodinate system is measured,Represent orthogonal vector actual value under inertial coodinate system；
It is as follows to obtain measurement equation,
Zk=HkXk+Vk
<mrow>
<msub>
<mi>H</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<msub>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mn>2</mn>
<msubsup>
<mi>A</mi>
<mrow>
<mi>b</mi>
<mi>i</mi>
</mrow>
<mi>T</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<msubsup>
<mi>l</mi>
<mi>b</mi>
<mn>1</mn>
</msubsup>
<mo>&times;</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<msub>
<mn>0</mn>
<mrow>
<mn>3</mn>
<mo>&times;</mo>
<mn>3</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mn>2</mn>
<msubsup>
<mi>A</mi>
<mrow>
<mi>b</mi>
<mi>i</mi>
</mrow>
<mi>T</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<msubsup>
<mi>l</mi>
<mi>b</mi>
<mn>2</mn>
</msubsup>
<mo>&times;</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<msub>
<mn>0</mn>
<mrow>
<mn>3</mn>
<mo>&times;</mo>
<mn>3</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mn>2</mn>
<msubsup>
<mi>A</mi>
<mrow>
<mi>b</mi>
<mi>i</mi>
</mrow>
<mi>T</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<msubsup>
<mi>l</mi>
<mi>b</mi>
<mn>3</mn>
</msubsup>
<mo>&times;</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<msub>
<mn>0</mn>
<mrow>
<mn>3</mn>
<mo>&times;</mo>
<mn>3</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mrow>
<mn>9</mn>
<mo>&times;</mo>
<mn>9</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>Z</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<msub>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>l</mi>
<mrow>
<mi>m</mi>
<mi>i</mi>
</mrow>
<mn>1</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>A</mi>
<mrow>
<mi>b</mi>
<mi>i</mi>
</mrow>
<mi>T</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
<msubsup>
<mi>l</mi>
<mi>b</mi>
<mn>1</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>l</mi>
<mrow>
<mi>m</mi>
<mi>i</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>A</mi>
<mrow>
<mi>b</mi>
<mi>i</mi>
</mrow>
<mi>T</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
<msubsup>
<mi>l</mi>
<mi>b</mi>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>l</mi>
<mrow>
<mi>m</mi>
<mi>i</mi>
</mrow>
<mn>3</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>A</mi>
<mrow>
<mi>b</mi>
<mi>i</mi>
</mrow>
<mi>T</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
<msubsup>
<mi>l</mi>
<mi>b</mi>
<mn>3</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mrow>
<mn>9</mn>
<mo>&times;</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
Wherein, ZkRepresent measurement vector, HkRepresent observing matrix, XkRepresent state variable,Represent quaternary number optimal estimation value,Represent by body to inertial system transition matrix, VkRepresent tkMoment observation noise sequence；
3rd module, for building system mode side according to satellite attitude kinematics equation and angular displacement sensor measurement model
Journey, realization is as follows,
The state of being based on is obtained according to attitude kinematics equationsSystem state equation it is as follows,
<mrow>
<mover>
<mi>X</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mi>X</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>W</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mo>&lsqb;</mo>
<mover>
<mi>&omega;</mi>
<mo>^</mo>
</mover>
<mo>&times;</mo>
<mo>&rsqb;</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mn>0.5</mn>
<msub>
<mi>I</mi>
<mrow>
<mn>3</mn>
<mo>&times;</mo>
<mn>3</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mn>0</mn>
<mrow>
<mn>3</mn>
<mo>&times;</mo>
<mn>3</mn>
</mrow>
</msub>
</mtd>
<mtd>
<msub>
<mn>0</mn>
<mrow>
<mn>3</mn>
<mo>&times;</mo>
<mn>3</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
W (t)=[- 0.5 ηg ηb]T
Wherein,Represent quantity of state differential value, X (t) represents quantity of state, and F (t) represents state-transition matrix differential, and W (t) is represented
System noise sequence,Represent angular velocity vector multiplication cross, I3×3Expression unit matrix, 03×3Represent the matrix that element is 0,
Represent error quaternion vector section, Δ bTRepresent error drift, ηgFor angular displacement sensor measurement noise, ηbPassed for angular displacement
Sensor and the noise of time correlation；
Linearisation discretization is carried out to system above state equation to obtain,
Xk=Φk,k-1Xk-1+Γk-1Wk-1
Wherein, Xk、Xk-1Represent tkMoment, tk-1Moment state variable, Φk,k-1Represent state-transition matrix, Γk-1Represent system noise
Sound-driving battle array, Wk-1Represent system noise sequence；
4th module, for the system measurements equation and system state equation built respectively based on the second module and the 3rd module,
Using two-way Kalman filtering and overall weight adjustment Models, high frequency attitude parameter optimal estimation is realized.
5. star sensor and high frequency angular displacement sensor integrated attitude determination system according to claim 4, it is characterised in that：3rd
Attitude kinematics equations represent as follows in module,
<mrow>
<mover>
<mi>q</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>q</mi>
<mo>&CircleTimes;</mo>
<mi>&omega;</mi>
</mrow>
<mrow>
<mover>
<mi>q</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>&omega;</mi>
<mi>x</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>&omega;</mi>
<mi>y</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>&omega;</mi>
<mi>z</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>x</mi>
</msub>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>z</mi>
</msub>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>&omega;</mi>
<mi>y</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>y</mi>
</msub>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>&omega;</mi>
<mi>z</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>x</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>z</mi>
</msub>
</mtd>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>y</mi>
</msub>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>&omega;</mi>
<mi>x</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>q</mi>
<mn>0</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>q</mi>
<mn>1</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>q</mi>
<mn>2</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>q</mi>
<mn>3</mn>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>q</mi>
<mn>0</mn>
</msub>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>q</mi>
<mn>1</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>q</mi>
<mn>2</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>q</mi>
<mn>3</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>q</mi>
<mn>1</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>q</mi>
<mn>0</mn>
</msub>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>q</mi>
<mn>3</mn>
</msub>
</mrow>
</mtd>
<mtd>
<msub>
<mi>q</mi>
<mn>2</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>q</mi>
<mn>2</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>q</mi>
<mn>3</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>q</mi>
<mn>0</mn>
</msub>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>q</mi>
<mn>1</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>q</mi>
<mn>3</mn>
</msub>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>q</mi>
<mn>2</mn>
</msub>
</mrow>
</mtd>
<mtd>
<msub>
<mi>q</mi>
<mn>1</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>q</mi>
<mn>0</mn>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>x</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>y</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>z</mi>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein,Represent the differential value of quaternary number, q and ω represent appearance of the satellite body coordinate system relative to inertial coodinate system respectively
State quaternary number and three axis angular velocity of rotations, q=[q0 q1 q2 q3]T, ω=(ωx,ωy,ωz)。
6. according to the star sensor of claim 4 or 5 and high frequency angular displacement sensor integrated attitude determination system, it is characterised in that：
The realization of 4th module is as follows,
(1) attitude prediction is carried out based on angle displacement measurement information
Based on angle displacement measurement information in tk-1Moment integrates following formula, obtains attitude of satellite quaternary number predicted value
<mrow>
<msub>
<mover>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msub>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&CircleTimes;</mo>
<msub>
<mover>
<mi>&omega;</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
Wherein,Represent attitude of satellite quaternary number predicted value,Represent tk-1Moment quaternary number optimal estimation value,Represent
tk-1Moment angular speed optimal estimation value；
Angular displacement drift forecasting valuePrediction model it is as follows,
<mrow>
<msub>
<mover>
<mi>b</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>b</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
Wherein,Represent tk-1Moment angular displacement drift optimal estimation value；
For the predicted value of error covariance matrixIt is as follows to resolve model,
<mrow>
<msub>
<mover>
<mi>P</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>&Phi;</mi>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mover>
<mi>P</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<msubsup>
<mi>&Phi;</mi>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mi>T</mi>
</msubsup>
<mo>+</mo>
<msub>
<mi>&Gamma;</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>Q</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<msubsup>
<mi>&Gamma;</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mi>T</mi>
</msubsup>
</mrow>
Wherein,Represent tk-1Moment error covariance matrix estimate, Qk-1Represent system interference variance matrix；
(2) attitude rectification is carried out based on star sensor measured value
In tkMoment, according to system measurements equation calculation observing matrix Hk, further calculate filtering gain Kk,
<mrow>
<msub>
<mi>K</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<msubsup>
<mi>H</mi>
<mi>k</mi>
<mi>T</mi>
</msubsup>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>H</mi>
<mi>k</mi>
</msub>
<msub>
<mi>P</mi>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<msubsup>
<mi>H</mi>
<mi>k</mi>
<mi>T</mi>
</msubsup>
<mo>+</mo>
<msub>
<mi>R</mi>
<mi>k</mi>
</msub>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
Wherein, Pk/k-1Represent error covariance matrix predicted value, then corresponding system state variablesFor,
<mrow>
<msub>
<mover>
<mi>X</mi>
<mo>^</mo>
</mover>
<mi>k</mi>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>X</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>K</mi>
<mi>k</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>Z</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<msub>
<mi>H</mi>
<mi>k</mi>
</msub>
<msub>
<mover>
<mi>X</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
Attitude of satellite quaternary number tkThe amendment updated value at momentWith the amendment updated value of angular displacement driftRespectively,
<mrow>
<msub>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mi>k</mi>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&CircleTimes;</mo>
<mi>&Delta;</mi>
<msub>
<mover>
<mi>q</mi>
<mo>^</mo>
</mover>
<mi>k</mi>
</msub>
</mrow>
<mrow>
<msub>
<mover>
<mi>b</mi>
<mo>^</mo>
</mover>
<mi>k</mi>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>b</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<mi>&Delta;</mi>
<msub>
<mover>
<mi>b</mi>
<mo>^</mo>
</mover>
<mi>k</mi>
</msub>
</mrow>
Wherein,Represent error quaternion estimate,Represent error drift amount estimate；
Error covariance matrix PkRenewal be calculated as,
<mrow>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mi>I</mi>
<mo>-</mo>
<msub>
<mi>K</mi>
<mi>k</mi>
</msub>
<msub>
<mi>H</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>P</mi>
<mrow>
<mi>k</mi>
<mo>/</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<msup>
<mrow>
<mo>(</mo>
<mi>I</mi>
<mo>-</mo>
<msub>
<mi>K</mi>
<mi>k</mi>
</msub>
<msub>
<mi>H</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
<mi>T</mi>
</msup>
<mo>+</mo>
<msub>
<mi>K</mi>
<mi>k</mi>
</msub>
<msub>
<mi>R</mi>
<mi>k</mi>
</msub>
<msubsup>
<mi>K</mi>
<mi>k</mi>
<mi>T</mi>
</msubsup>
</mrow>
Wherein, RkRepresent star sensor measuring noise square difference battle array, I represents unit matrix, HkUsing the state variable corrected after updatingRe-start calculating；
Initial filter, inverse filtering and forward filtering are carried out according to the above process (1) (2), be based ultimately upon forward filtering with it is anti-
Overall weight adjustment is carried out to filter result.
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4567564A (en) * | 1980-08-19 | 1986-01-28 | Messerschmitt-Bolkow-Blohm Gesellschaft Mit Beschrankter Haftung | Arrangement for the attitude stabilization of flexible vehicles with weakly-dampened structural vibrations and discontinuous control intervention |
| CN101556155A (en) * | 2009-05-20 | 2009-10-14 | 上海微小卫星工程中心 | Small satellite attitude determination system and method thereof |
| CN102114918A (en) * | 2010-12-31 | 2011-07-06 | 北京航空航天大学 | Attitude control feedback loop based on combined fixed attitude of multi-rate sensor |
| CN102607564A (en) * | 2012-03-09 | 2012-07-25 | 北京航空航天大学 | Small satellite autonomous navigation system based on starlight/ geomagnetism integrated information and navigation method thereof |
| CN102879011A (en) * | 2012-09-21 | 2013-01-16 | 北京控制工程研究所 | Lunar inertial navigation alignment method assisted by star sensor |
| CN103940433A (en) * | 2014-05-12 | 2014-07-23 | 哈尔滨工业大学 | Satellite attitude determining method based on improved self-adaptive square root UKF (Unscented Kalman Filter) algorithm |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2012009198A2 (en) * | 2010-07-14 | 2012-01-19 | University Of Florida Research Foundation, Inc. | System and method for assessing the performance of an attitude control system for small satellites |
-
2016
- 2016-01-30 CN CN201610067447.XA patent/CN105486312B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4567564A (en) * | 1980-08-19 | 1986-01-28 | Messerschmitt-Bolkow-Blohm Gesellschaft Mit Beschrankter Haftung | Arrangement for the attitude stabilization of flexible vehicles with weakly-dampened structural vibrations and discontinuous control intervention |
| CN101556155A (en) * | 2009-05-20 | 2009-10-14 | 上海微小卫星工程中心 | Small satellite attitude determination system and method thereof |
| CN102114918A (en) * | 2010-12-31 | 2011-07-06 | 北京航空航天大学 | Attitude control feedback loop based on combined fixed attitude of multi-rate sensor |
| CN102607564A (en) * | 2012-03-09 | 2012-07-25 | 北京航空航天大学 | Small satellite autonomous navigation system based on starlight/ geomagnetism integrated information and navigation method thereof |
| CN102879011A (en) * | 2012-09-21 | 2013-01-16 | 北京控制工程研究所 | Lunar inertial navigation alignment method assisted by star sensor |
| CN103940433A (en) * | 2014-05-12 | 2014-07-23 | 哈尔滨工业大学 | Satellite attitude determining method based on improved self-adaptive square root UKF (Unscented Kalman Filter) algorithm |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111649766A (en) * | 2020-06-01 | 2020-09-11 | 哈尔滨理工大学 | Method and device for actively suppressing noise of angle value of magnetoelectric encoder |
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