CN109506645A - A kind of star sensor installation matrix ground accurate measurement method - Google Patents
A kind of star sensor installation matrix ground accurate measurement method Download PDFInfo
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- CN109506645A CN109506645A CN201811522696.9A CN201811522696A CN109506645A CN 109506645 A CN109506645 A CN 109506645A CN 201811522696 A CN201811522696 A CN 201811522696A CN 109506645 A CN109506645 A CN 109506645A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/02—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by astronomical means
- G01C21/025—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by astronomical means with the use of startrackers
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
- G06F17/12—Simultaneous equations, e.g. systems of linear equations
Abstract
The invention discloses a kind of star sensors to install matrix ground accurate measurement method, includes: establishing the star sensor frame of reference and the satellite frame of reference；Measurement obtains the angle between the reference axis and corresponding reference axis in the satellite frame of reference of the star sensor frame of reference；The projected angle of plane of the reference axis into the satellite frame of reference where each reference axis and corresponding projection angle in the corresponding star sensor frame of reference are obtained using angle, the reference axis of the star sensor frame of reference is rotated with two different sequences that turn, obtain two corners after the rotation is completed, according to two corners, the pose transformation matrix of corresponding two star sensor frames of reference for turning sequence is obtained；The pose transformation matrix of two star sensor frames of reference of simultaneous, obtains Nonlinear System of Equations, solves the Nonlinear System of Equations using optimal solution, obtains the accurate measurement result of star sensor installation matrix.The present invention improves the efficiency to star sensor installation matrix ground accurate measurement.
Description
Technical field
The present invention relates to spacecraft technology field, in particular to a kind of star sensor installs matrix ground accurate measurement method.
Background technique
The type satellites such as telemetering, communication in order to complete itself function, be required to first to determine itself posture information (such as
Roll angle, pitch angle, yaw angle in orbital coordinate system), and the spacecraft for there is high-acruracy survey to require, not only
It is required that determining the posture information of itself, and attitude determination accuracy is required to reach rad grade.Star sensor is as a kind of high-precision
The preferred sensor of the attitude sensor of degree, usually high-precision control requirement satellite.
Star sensor carries out pose discrimination by the way that fixed star is imaged, and due to the subtended angle very little between fixed star, fixed star image is true
It absorbs in the air, the photograph right ascension of moment fixed star, declination are accurately known, therefore can calculate the attitude angle essence of rad grade
Degree, and the highest attitude measurement instrument of precision so far.
In order to guarantee that spacecraft can obtain high-precision posture information using star sensor, star sensor itself
Installation accuracy calibration is just particularly important.But the calibration to the installation accuracy of the star sensor itself in the prior art
(accurate measurement) method, it is complex, demarcate low efficiency.
Summary of the invention
The object of the present invention is to provide a kind of star sensors to install matrix ground accurate measurement method, realizes and is reducing to angle
Measurement in the case where improving time efficiency, can equally obtain the purpose of high-precision star sensor installation matrix.
In order to achieve the goal above, the invention is realized by the following technical scheme:
A kind of star sensor installation matrix ground accurate measurement method, includes: establishing the star sensor frame of reference and satellite base
Conventional coordinates；Measurement obtains the reference axis of the star sensor frame of reference and corresponding seat in the satellite frame of reference
Angle between parameter；Utilize reference axis in the corresponding star sensor frame of reference of angle acquisition to the satellite
The projected angle of plane in the frame of reference where each reference axis and corresponding projection angle, to star sensor reference coordinate
The reference axis of system is rotated with two different sequences that turn, and two corners after the rotation is completed is obtained, according to described two turns
Angle, corresponded to described in turn sequence two star sensor frames of reference pose transformation matrix；Two star sensor bases of simultaneous
The pose transformation matrix of conventional coordinates, obtains Nonlinear System of Equations, solves the Nonlinear System of Equations using optimal solution, obtains star
The accurate measurement result of sensor installation matrix.
Further, described the step of establishing the star sensor frame of reference, further includes:
Using star sensor prism centers as reference axis axle center OaL, OaLXaLThe mounting surface for being defined as vertical prism is quick backwards to star
The axis of sensor；OaLYaLIt is defined as towards+OaLXaLDirection, perpendicular to the axis of prism right plane；OaLZaLMeet right-hand rule；?
To star sensor frame of reference OaLXaLYaLZaL；
Described the step of establishing the satellite frame of reference, further includes:
Using satellite prism centers as reference axis axle center Ob, ObYbIt is defined as being directed toward south orientation solar wing with celestial body mounting surface in parallel
Axis；OaLZaLIt is defined as the axis that vertical celestial body mounting surface is directed toward load；ObXbMeet right-hand rule and obtains the satellite frame of reference
ObXbYbZb。
Further, the reference axis of the star sensor frame of reference and corresponding seat in the satellite frame of reference
Angle between parameter is obtained using transit survey.
Further, the reference axis of the star sensor frame of reference and corresponding seat in the satellite frame of reference
Angle between parameter further comprises: OaLXaLAxis and ObXbAngle ∠ A, O between axisaLXaLAxis and ObZbAngle between axis
∠ B, OaLZaLAxis and ObXbAngle the ∠ C and O of between centersaLZaLAxis and ObZbAngle ∠ D between axis.
Further, O is calculatedaLXaLAxis and ObXbZbThe projected angle α of plane1, the projected angle α1It is carried out using following formula
It calculates:
When star sensor prism X-axis is more than or equal to 90 degree with ontology Y-axis angle,
When star sensor prism X-axis with ontology Y-axis angle less than 90 degree when,
The OaLXaLAxis is in ObXbZbPlane is projected as OaLXaL', calculate OaLXaL' and ObXbThe projection angle β of axis1, institute
State projection angle β1It is calculated using following formula:
In formula, pi π.
Calculate OaLZaLAxis and ObXbZbThe projected angle α of plane2, the projected angle α2It is calculated by the following formula:
When star sensor prism Z axis is less than or equal to 90 degree with ontology Y-axis angle,
When star sensor prism Z axis is greater than 90 degree with ontology Y-axis angle,
OaLZaLAxis is to ObXbZbPlane is projected as OaLZaL', calculate OaLZaL' and ObZbThe projection angle β of axis2, the throwing
Shadow angle β2It is calculated by the following formula:
In formula, pi π.
Further, it is assumed that the first third time corner for turning sequence YZX is γ1, establish the star sensor reference coordinate
First pose transformation matrix C of systemOHB1,
Assuming that the third time corner of second turn of sequence YXZ is γ2, establish the second appearance of the star sensor frame of reference
State transition matrix COHB2,
Further, the first pose transformation matrix COHB1=the second pose transformation matrix COHB2, solved using optimal solution
The solution of Nonlinear System of Equations obtains the first third time corner γ for turning sequence YZX1With the third time of the second turn of sequence YXZ
Corner γ2。
Further, by the OaLXaLAxis and ObXbZbThe projected angle α of plane1, the OaLZaLAxis and ObXbZbThe throwing of plane
Shadow angle α2, the OaLXaL' and ObXbThe projection angle β of axis1, the OaLZaL' and ObZbThe projection angle β of axis2, the first turns sequence
The third time corner γ of YZX1With the third time corner γ of the second turn of sequence YXZ2, substitute into first pose transformation matrix
COHB1With the second pose transformation matrix COHB2It solves, later, finds out the star sensor installation matrix accurate measurement knot in the following way
Fruit COHB,
Compared with the prior art, the present invention has the following advantages:
The present invention only needs to carry out the measurement of four space angles, reduces the requirement to accurate measurement number of devices, simplifies
The time of star sensor installation calibration, using the corresponding projected angle of angle calcu-lation and projection angle between coordinate system, further according to throwing
Two kinds of differences of shadow angle calcu-lation turn the star sensor installation matrix of sequence, solve the non-thread of installation matrix equality by using optimal solution
Property equation group, finally obtain six rotation angles and the installation matrix of star sensor be calculated.The method of calculating can be by generally counting
Value resolves software and is calculated, and by simple calculation, high-precision believable star sensor installation matrix can be obtained,
Improve the efficiency to star sensor installation matrix ground accurate measurement.
Detailed description of the invention
Fig. 1 is the flow chart that star sensor provided in an embodiment of the present invention installs matrix ground accurate measurement method；
Fig. 2 a is the star sensor benchmark in star sensor provided in an embodiment of the present invention installation matrix ground accurate measurement method
The schematic diagram of prism coordinate system；
Fig. 2 b is the satellite benchmark prism in star sensor provided in an embodiment of the present invention installation matrix ground accurate measurement method
The schematic diagram of coordinate system.
Specific embodiment
It holds as stated in the background art, in the prior art to calibration (accurate measurement) side of the installation accuracy of the star sensor itself
Method is complex and demarcates low efficiency, specifically, this is because the installation accuracy calibration mode of star sensor is to utilize high-precision
Measuring device (angular instrument or theodolite) carry out, calibrate star usually using more (at least 3) high-precision measuring devices
Installation matrix between sensor coordinate system and satellite platform coordinate system, to meet the requirement of control system.Because adopting
With high-precision measuring instrument, need to need the stability to more test equipments itself, vertical in calibration test process
The contents such as the calibration between degree, the depth of parallelism and more test equipments are adjusted, while at least to calculate 2 axis, 6 angles
Installation matrix could be obtained, therefore, matrix is installed to obtain high-precision star sensor, it usually needs taking hours could obtain
It arrives.
The present invention only needs to carry out the measurement of four space angles, reduces the requirement to accurate measurement number of devices, simplifies
The time of star sensor installation calibration, using the corresponding projected angle of angle calcu-lation and projection angle between coordinate system, further according to throwing
Two kinds of differences of shadow angle calcu-lation turn the star sensor installation matrix of sequence, solve the non-thread of installation matrix equality by using optimal solution
Property equation group, finally obtain six rotation angles and the installation matrix of star sensor be calculated.
The present invention is further elaborated by the way that a preferable specific embodiment is described in detail below in conjunction with attached drawing.
As shown in Figure 1, a kind of star sensor provided in this embodiment installs matrix ground accurate measurement method, it include following mistake
Journey:
Step S1, the star sensor frame of reference (star sensor benchmark prism coordinate system) and the satellite frame of reference are established
(satellite benchmark prism coordinate system), enters step S2.Specifically, as shown in Figure 2 a, using star sensor prism centers as reference axis
Axle center OaL, OaLXaLIt is defined as axis of the mounting surface backwards to star sensor of vertical prism；OaLYaLIt is defined as towards+OaLXaLDirection,
Perpendicular to the axis of prism right plane；OaLZaLMeet right-hand rule；Obtain star sensor frame of reference OaLXaLYaLZaL。
As shown in Figure 2 b, using satellite prism centers as reference axis axle center Ob, ObYbIt is defined as being directed toward with celestial body mounting surface in parallel
The axis of south orientation solar wing；OaLZaLIt is defined as the axis that vertical celestial body mounting surface is directed toward load；ObXbMeet right-hand rule and obtains satellite
Frame of reference ObXbYbZb。
Star sensor benchmark prism coordinate system OaLXaLYaLZaL, the optical reference of star sensor is described, with star sensor benchmark
Prism connects firmly.Satellite benchmark prism coordinate system ObXbYbZb, the control benchmark of satellite is described, is connected firmly with satellite benchmark prism.Star is quick
Sensor is mounted on after satellite, need to determine star sensor benchmark prism coordinate system and satellite to obtain star sensor installation matrix
The relationship of benchmark prism coordinate system.
Step S2, measurement obtains the angle of star sensor benchmark prism coordinate system and satellite benchmark prism coordinate system, enters
Step S3 and step S4.Specifically, the theodolite used is to described when using demarcating to star sensor installation matrix
The angle of star sensor benchmark prism coordinate system and satellite benchmark prism coordinate system carries out precise measurement, i.e., with satellite benchmark prism
On the basis of coordinate system, the O of star sensor benchmark prism coordinate system is measured respectively using the theodoliteaLXaLAxis and satellite benchmark
The O of prism coordinate systembXb、ObZbThe O of relationship and star sensor benchmark prism coordinate system between axisaLZaLAxis and satellite benchmark
The O of prism coordinate systembXb、ObZbRelationship between axis, obtains following four angle: angle ∠ A, angle ∠ B, angle ∠ C and
Angle ∠ D.
Wherein, angle ∠ A is OaLXaLAxis and ObXbAngle between axis, angle ∠ B are OaLXaLAxis and ObZbBetween axis
Angle, angle ∠ C are OaLZaLAxis and ObXbThe angle of between centers, angle ∠ D are OaLZaLAxis and ObZbAngle between axis.
Later, it is pressed from both sides using the corresponding projected angle of four angle calcu-lations and projection that are obtained measured by the step S2
Angle, the specific steps are as follows:
Step S3, O is calculatedaLXaLAxis and ObXbZbThe angle α of plane1, the angle α1It is calculated using following formula:
When star sensor prism X-axis is more than or equal to 90 degree with ontology Y-axis angle:
When star sensor prism X-axis with ontology Y-axis angle less than 90 degree:
The OaLXaLAxis is in ObXbZbPlane is projected as OaLXaL', calculate OaLXaL' and ObXbAngle β1, the angle
β1It is calculated using following formula:
Range [- pi, pi] (3)
In formula, pi π.
S5 is entered step later.
Step S4, O is calculatedaLZaLAxis and ObXbZbThe angle α of plane2, the angle is calculated by the following formula:
When star sensor prism Z axis is less than or equal to 90 degree with ontology Y-axis angle:
When star sensor prism Z axis is greater than 90 degree with ontology Y-axis angle:
OaLZaLAxis is to ObXbZbPlane is projected as OaLZaL', calculate OaLZaL' and ObZbThe angle β of axis2, the angle β2
It is calculated by the following formula:
Range [- pi, pi] (6)
In formula, pi π.
S6 is entered step later.
Step S5, according to the calculated result of step S3, it is assumed that it is YZX that the first, which turns sequence, it is assumed that the first turns the of sequence YZX
Corner is γ three times1, establish the first star sensor installation Matrix COHB1, enter step S7, wherein the first star sensor peace
Fill Matrix COHB1Are as follows:
Step S6, according to the calculated result of step S4, it is assumed that second turn of sequence is YXZ, it is assumed that the of second turn of sequence YXZ
Corner is γ three times2, establish the second star sensor installation Matrix COHB2Enter step S7, wherein the second star sensor installation
Matrix COHB2Are as follows:
To sum up, the first and second star sensors installation matrix is according to α1、β1、α2、β2Calculating and definition, utilize
This 4 angles turn sequence, calculated satellite benchmark prism coordinate system to star sensor benchmark prism coordinate system using two kinds of differences
Pose transformation matrix.
Step S7, using the first and second star sensors installation Matrix Solving, the first turns the third time corner γ of sequence YZX1
With the third time corner γ of the second turn of sequence YXZ2, enter step S8.Due to satellite benchmark prism coordinate system to star sensitivity
The pose transformation matrix of device benchmark prism coordinate system uniquely determines, therefore the two kinds of star sensors installation calculated using different form
Matrix is answered identical, it may be assumed that
COHB1=COHB2
The solution that Nonlinear System of Equations is solved using optimal solution, obtains the first third time corner γ for turning sequence YZX1With it is described
The third time corner γ of second turn of sequence YXZ2。
Step S8, the end value of star sensor installation matrix is calculated, specifically
The α acquired according to step S3~step S71、α2, β1、β2, γ1、γ2, the first and second stars sensitivity is calculated
Device installs Matrix COHB1And COHB2To get two kinds of numerical results for installing matrix to star sensor.
Using finding out γ1And γ2The C of calculatingOHB1And COHB2Specific value might not be stringent equal, this is because instrument
The factors such as device measurement error and test environment cause, with COHB1And COHB2Measurement twice as star sensor installation matrix samples,
The first approximation for finding out star sensor installation matrix in the following way installs matrix accurate measurement knot as final star sensor
Fruit, as follows:
In conclusion the present invention only needs to carry out the measurement of four space angles, reduces and accurate measurement number of devices is wanted
It asks, has simplified the time of star sensor installation calibration, using the corresponding projected angle of angle calcu-lation between coordinate system and project angle,
The star sensor for turning sequence further according to projection two kinds of differences of angle calcu-lation installs matrix, solves installation matrix etc. by using optimal solution
The Nonlinear System of Equations of formula finally obtains six rotation angles and the installation matrix of star sensor is calculated.The method of calculating can
Software is resolved by prevailing value to be calculated, and by simple calculation, high-precision believable star sensor can be obtained
Matrix is installed.
It is discussed in detail although the contents of the present invention have passed through above preferred embodiment, but it should be appreciated that above-mentioned
Description is not considered as limitation of the present invention.After those skilled in the art have read above content, for of the invention
A variety of modifications and substitutions all will be apparent.Therefore, protection scope of the present invention should be limited to the appended claims.
Claims (8)
1. a kind of star sensor installation matrix ground accurate measurement method, characterized by comprising:
Establish the star sensor frame of reference and the satellite frame of reference；
Measurement obtains the reference axis of the star sensor frame of reference and corresponding reference axis in the satellite frame of reference
Between angle；
Utilize reference axis in the corresponding star sensor frame of reference of angle acquisition to the satellite frame of reference
In plane where each reference axis projected angle and corresponding projection angle；
The reference axis of the star sensor frame of reference is rotated with two different sequences that turn, obtains two after the rotation is completed
A corner, according to described two corners, corresponded to described in turn sequence two star sensor frames of reference posture conversion square
Battle array；
The pose transformation matrix of two star sensor frames of reference of simultaneous, is obtained Nonlinear System of Equations, is solved using optimal solution
The Nonlinear System of Equations obtains the accurate measurement result of star sensor installation matrix.
2. star sensor as described in claim 1 installs matrix ground accurate measurement method, which is characterized in that described to establish star sensitivity
The step of device frame of reference, further includes:
Using star sensor prism centers as reference axis axle center OaL, OaLXaLThe mounting surface of vertical prism is defined as backwards to star sensor
Axis；OaLYaLIt is defined as towards+OaLXaLDirection, perpendicular to the axis of prism right plane；OaLZaLMeet right-hand rule；Obtain star
Sensor frame of reference OaLXaLYaLZaL；
Described the step of establishing the satellite frame of reference, further includes:
Using satellite prism centers as reference axis axle center Ob, ObYbIt is defined as being directed toward the axis of south orientation solar wing with celestial body mounting surface in parallel；
OaLZaLIt is defined as the axis that vertical celestial body mounting surface is directed toward load；ObXbMeet right-hand rule and obtains the satellite frame of reference
ObXbYbZb。
3. star sensor as claimed in claim 2 installs matrix ground accurate measurement method, which is characterized in that the star sensor base
Angle between the reference axis of conventional coordinates and corresponding reference axis in the satellite frame of reference is obtained using transit survey
It arrives.
4. star sensor as claimed in claim 3 installs matrix ground accurate measurement method, which is characterized in that the star sensor base
Angle between the reference axis of conventional coordinates and corresponding reference axis in the satellite frame of reference further comprises: OaLXaL
Axis and ObXbAngle ∠ A, O between axisaLXaLAxis and ObZbAngle ∠ B, O between axisaLZaLAxis and ObXbThe angle ∠ C of between centers
And OaLZaLAxis and ObZbAngle ∠ D between axis.
5. star sensor as claimed in claim 4 installs matrix ground accurate measurement method, which is characterized in that calculate OaLXaLAxis with
ObXbZbThe projected angle α of plane1, the projected angle α1It is calculated using following formula:
When star sensor prism X-axis is more than or equal to 90 degree with ontology Y-axis angle,
When star sensor prism X-axis with ontology Y-axis angle less than 90 degree when,
The OaLXaLAxis is in ObXbZbPlane is projected as OaLXaL', calculate OaLXaL' and ObXbProjection angle β1, the projection
Angle β1It is calculated using following formula:
In formula, pi π；
Calculate OaLZaLAxis and ObXbZbThe projected angle α of plane2, the projected angle α2It is calculated by the following formula:
When star sensor prism Z axis is less than or equal to 90 degree with ontology Y-axis angle,
When star sensor prism Z axis is greater than 90 degree with ontology Y-axis angle,
OaLZaLAxis is to ObXbZbPlane is projected as OaLZaL', calculate OaLZaL' and ObZbThe projection angle β of axis2, the projection folder
Angle beta2It is calculated by the following formula:
In formula, pi π.
6. star sensor as claimed in claim 5 installs matrix ground accurate measurement method, which is characterized in that assuming that the first turns sequence
The third time corner of YZX is γ1, establish the first pose transformation matrix C of the star sensor frame of referenceOHB1,
Assuming that the third time corner of second turn of sequence YXZ is γ2, establish the second posture turn of the star sensor frame of reference
Change Matrix COHB2,
7. star sensor as claimed in claim 6 installs matrix ground accurate measurement method, which is characterized in that first posture turns
Change Matrix COHB1=the second pose transformation matrix COHB2,
The solution that Nonlinear System of Equations is solved using optimal solution, obtains the first third time corner γ for turning sequence YZX1With described second
Kind turns the third time corner γ of sequence YXZ2。
8. star sensor as claimed in claim 7 installs matrix ground accurate measurement method, which is characterized in that by the OaLXaLAxis with
ObXbZbThe projected angle α of plane1, the OaLZaLAxis and ObXbZbThe projected angle α of plane2, the OaLXaL' and ObXbThe projection of axis is pressed from both sides
Angle beta1, the OaLZaL' and ObZbThe projection angle β of axis2, the first turns the third time corner γ of sequence YZX1With described second turn
The third time corner γ of sequence YXZ2, substitute into the first pose transformation matrix COHB1With the second pose transformation matrix COHB2It solves, it
Afterwards, the star sensor installation matrix accurate measurement result C is found out in the following wayOHB,
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