CN109856569A - A method of space magnetic field intensity is determined based on look-up table - Google Patents
A method of space magnetic field intensity is determined based on look-up table Download PDFInfo
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Abstract
The invention discloses a kind of methods for determining space magnetic field intensity based on look-up table, and this method includes: (1) establishing high-precision magnetic field table；(2) the southbound node geographic logitude lamda that corrects satellite flight track southbound node geographic logitude interval Gdjg and will fly over；(3) after satellite and the rocket separation, when On-board software calls magnetic field table subprogram for the first time, the southbound node geographic logitude ccl flown over is by lamda assignment；In other situations, the southbound node geographic logitude ccl flown over is updated when satellite flies to southbound node；(4) when ccl changes, the number cca and its southbound node geographic logitude of satellite current location corresponding magnetic field track in the table of magnetic field are calculated；(5) 4 mesh points of satellite current location surrounding are found out according to cca of the satellite current location in the table of magnetic field；(6) method based on linear interpolation calculates magnetic field strength of the satellite current location under orbital coordinate system.Method of the invention is not limited by order, simple easily to realize, operation is fast and computational accuracy is higher.
Description
Technical field
The present invention relates to a kind of methods of determining space magnetic field intensity, and in particular to one kind determines space magnetic based on look-up table
The method of field intensity.
Background technique
Earth's magnetic field is important geophysical field, and in low orbit satellite Shangdi, magnetic field application prospect is very extensive.Earth magnetism is sweared
Amount and geocentric vector or solar vector can be rough in such a way that double vectors determine appearance the estimation attitude of satellite.In conventional large satellite
In, which can be used as backup attitude reference when safe mode, on the miniaturization satellite of less demanding for accuracy of attitude determination,
It even more can be used as main part attitude reference when stable state.
For three axis absolute orientation satellites, projection of the ground magnetic vector under satellite body system is measured by three axis magnetometer
It arrives, and projection of the vector under orbital coordinate system is obtained generally according to international Geomagnetic Field Model (IGRF) theoretical calculation.It is theoretical
The magnetic field strength being calculated, in addition to magnetometer can be cooperated to determine appearance for double vectors, can also separately as the backup of magnetometer,
Magnetic dumping is used for when satellite attitude stabilization.
IGRF is description Global Geomagnetic Field and its change in long term, and is global earth magnetism master die general in the world
Type, in the model, the scalar potential in earth's magnetic field indicate that the order of current newest spherical harmonic series is 13 ranks with spherical harmonic series.It is logical
The order taken when crossing the model calculating magnetic field intensity is higher, then the magnetic field strength precision obtained is higher, but spherical harmonic series are by more
The multistage trigonometric function composition of item, with the increase of spherical harmonic series order, calculation amount is increased sharply in a manner of quadratic power.
According to the pertinent literature delivered both at home and abroad it is found that at present on satellite typically directly in On-board software according to IGRF
Model formation calculating magnetic field intensity, is limited to the operational capability of spaceborne computer, and the order of spherical harmonic series generally takes 1 rank or 3
Rank.
But the above method has some limitations.Order takes 1 rank, although formula is relatively simple, calculation amount is small,
But the magnetic field strength worst error being calculated is up to 28%；Order takes 3 ranks, although worst error has decreased to 8%, error
Still bigger than normal and occupy spaceborne computer more runing time relatively.
Summary of the invention
The object of the present invention is to provide a kind of methods for determining space magnetic field intensity based on look-up table, and this method solve existing
The problem of methodical bigger error, is not limited by order, and algorithm is simple, and On-board software is easy to accomplish, and operation time is shorter
And calculated magnetic field strength precision is higher.
In order to achieve the above object, the present invention provides a kind of methods for determining space magnetic field intensity based on look-up table, should
Method includes:
(1) it establishes high-precision magnetic field table: being carried out on the spherical surface that satellite flight track is passed through according to certain time interval
Grid dividing calculates the three-axle magnetic field intensity on mesh point according to international Geomagnetic Field Model most high-order formula, forms earth's magnetic field
Tables of data is loaded in satellite carried software；
(2) the southbound node geographic logitude correcting satellite flight track southbound node geographic logitude interval Gdjg and will flying over
lamda；
(3) after satellite and the rocket separation, when On-board software calls magnetic field table subprogram for the first time, the southbound node geography flown over is passed through
Degree ccl is by the southbound node geographic logitude lamda assignment that will fly over；In other situations, updated when satellite flies to southbound node
Southbound node geographic logitude ccl through flying over；
(4) when the southbound node geographic logitude ccl flown over changes, satellite current location is calculated in the table of magnetic field
Otherwise the number cca and its southbound node geographic logitude of corresponding magnetic field track keep cca constant；Wherein, southbound node geographic logitude
It is obtained according to step (3), the number cca of magnetic field track is corresponding with grid dividing；
(5) according to satellite current location, the number cca of corresponding magnetic field track finds out satellite present bit in the table of magnetic field
Set 4 mesh points of surrounding；
(6) method based on linear interpolation calculates magnetic field strength of the satellite current location under orbital coordinate system.
Preferably, in step (1), the mode of the grid dividing are as follows: laterally divided at equal intervals with southbound node geographic logitude
At n rail, n be satellite fly daily enclose number be rounded downwards；It is longitudinal that m point is taken at equal intervals with the rail time of satellite flight, as
Track clock.
Preferably, the geographic logitude interval delta L laterally between every two rail is 360 °/n, the relationship of geographic logitude and cca are as follows:
Geographic logitude=(cca-1) * 360 °/n；In longitudinal direction, it is 70~80 that the rail time takes m at equal intervals.
Preferably, the data point of the grid dividing is arranged in order since 0 ° of east longitude of southbound node moment.
Preferably, in step (2), southbound node geographic logitude interval is corrected according to the orbit altitude of satellite actual motion
Gdjg；Correct the southbound node geographic logitude lamda that will be flown in due course according to the orbit parameter of satellite accurate measurement.
Preferably, in step (3), the southbound node geographic logitude ccl flown over is updated, is passed through following formula (1)
It obtains:
Ccl=ccl-Gdjg (1).
Preferably, in step (6), in 4 mesh points, by same lengthwise position two mesh points according to
Linear interpolation method calculates the magnetic field strength of two intermediate points, two intermediate point difference intermediate points one and intermediate point two, intermediate point
One and intermediate point two and satellite current location be in same lateral position, according to the magnetic field strength for two intermediate points being calculated
The magnetic field strength of satellite current location is obtained by linear interpolation method.
Preferably, in step (6), the formula of the linear interpolation method are as follows:
When 4 mesh points are calculated with the intermediate point of two mesh points in same lengthwise position, in formula (2), Y1For
The previous mesh point in satellite current location corresponding magnetic field strength, Y in the table of magnetic field are in transverse direction2To work as in transverse direction in satellite
The latter mesh point in front position corresponding magnetic field strength in the table of magnetic field；X is southbound node the geographic logitude ccl, Y that satellite has been flown over
For the magnetic field strength of intermediate point to be asked；X1With corresponding in the table of magnetic field the southbound node of next magnetic field track for satellite current location
Manage longitude；X2The southbound node geographic logitude of a upper magnetic field track in the table of magnetic field is corresponded to for satellite current location.
When calculating the magnetic field strength of satellite current location by two intermediate points, intermediate point one is under satellite current location
The corresponding mesh point of one track clock, intermediate point two is the corresponding mesh point of a track clock on satellite current location, in formula (2), Y1
For the magnetic field strength of intermediate point one, Y2For the magnetic field strength of intermediate point two；X is satellite current time corresponding track clock；Y is to defend
The magnetic field strength of star current location；X1For intermediate point one in the table of magnetic field corresponding track clock；X2It is intermediate point two in the table of magnetic field
Corresponding track clock.
Preferably, the track clock cumulative timing since 0 when satellite passes through southbound node.
The method for determining space magnetic field intensity based on look-up table of the invention, solves asking for the bigger error of existing method
Topic, has the advantage that
Method of the invention is preset in On-board software by establishing high-precision magnetic field table, satellite in orbit when
Mode obtaining current location magnetic field strength by way of tabling look-up is solved and is limited on star in calculating magnetic field strength theory value
In the problem that spaceborne computer ability can only use low order formula lower so as to cause precision.Algorithm letter of the invention
Single, On-board software is easy to accomplish, and operation time is shorter and calculated magnetic field strength precision is higher.
Detailed description of the invention
Fig. 1 be earth's magnetic field of the invention table look-up linear interpolation calculate schematic diagram.
Specific embodiment
The technical scheme in the embodiments of the invention will be clearly and completely described below, it is clear that described implementation
Example is only a part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, this field is common
Technical staff's every other embodiment obtained without making creative work belongs to the model that the present invention protects
It encloses.
A method of determining that space magnetic field intensity, this method include based on look-up table:
(1) it establishes high-precision magnetic field table: being carried out on the spherical surface that satellite flight track is passed through according to certain time interval
Grid dividing calculates the three-axle magnetic field intensity on mesh point according to international Geomagnetic Field Model (IGRF) most high-order formula, is formed
Earth's magnetic field tables of data is loaded in satellite carried software；
(2) the southbound node geographic logitude correcting satellite flight track southbound node geographic logitude interval Gdig and will flying over
lamda；
(3) after satellite and the rocket separation, when On-board software calls magnetic field table subprogram for the first time, the southbound node geography flown over is passed through
Degree ccl is by the southbound node geographic logitude lamda assignment that will fly over；In other situations, updated when satellite flies to southbound node
Southbound node geographic logitude ccl through flying over；
(4) when the southbound node geographic logitude ccl flown over changes, satellite current location is calculated in the table of magnetic field
Otherwise the number cca and its southbound node geographic logitude of corresponding magnetic field track keep cca constant；Wherein, southbound node geographic logitude
It is obtained according to step (3), wherein the number cca of magnetic field track is corresponding with grid dividing；(5) existed according to satellite current location
The number cca of corresponding magnetic field track finds out 4 mesh points of satellite current location surrounding in the table of magnetic field；As shown in Figure 1, being
Earth's magnetic field of the invention linear interpolation of tabling look-up calculates schematic diagram, and 4 mesh points of satellite current location surrounding are A, B, C, D；
(6) method based on linear interpolation calculates magnetic field strength of the satellite current location under orbital coordinate system.
Further, in step (1), the mode of grid dividing are as follows: laterally (i.e. satellite is run by north orientation south with southbound node
When, the intersection point of orbital plane and the equatorial plane) geographic logitude is divided into n rail at equal intervals, and n is that satellite fly daily and encloses number and be rounded downwards；
It is longitudinal that m point is taken at equal intervals with the rail time of satellite flight, as track clock.
Further, the geographic logitude interval delta L laterally between every two rail is 360 °/n, the relationship of geographic logitude and cca
Are as follows: geographic logitude=(cca-1) * 360 °/n；In longitudinal direction, it is 70~80 that the rail time takes m at equal intervals.Grid is laterally divided into altogether
N rail, then number cca then corresponds to 1 and arrives n, for example, number cca is 1 when southbound node longitude is 0, southbound node longitude is 1*360 °/n,
Then number cca is 2, and when being correspondingly (n-1) * 360 °/n by intersection point longitude, then number cca is n.
Further, the data point of grid dividing is arranged in order since 0 ° of east longitude of southbound node moment.
After the orbit altitude of satellite determines, fixed value is divided between adjacent geographic logitude when flying over southbound node twice.But
It is influenced since satellite is in-orbit by the factors such as space environment disturbance torque or artificial adjustment satellite orbital altitude, the practical fortune of satellite
Capable orbit altitude can change, and need amendment southbound node geographic logitude interval Gdjg at this time.Further, since when the place of satellite
(at the time of i.e. by local longitude determination) can drift about, and the practical southbound node geographic logitude flown over of satellite may be with theory
Geographic logitude has deviation, and the southbound node geographic logitude lamda that will be flown over can be corrected in due course according to the orbit parameter of satellite accurate measurement.
Therefore, further, in step (2), southbound node geographic logitude interval is corrected according to the orbit altitude of satellite actual motion
Gdjg；Correct the southbound node geographic logitude lamda that will be flown in due course according to the orbit parameter of satellite accurate measurement.
Further, in step (3), the southbound node geographic logitude ccl flown over is updated, passes through following formula
(1) it obtains:
Ccl=ccl-Gdig (1).
Further, in step (6), in 4 mesh points, by two mesh point roots for being in same lengthwise position
The magnetic field strength of two intermediate points, two intermediate point difference intermediate points one and intermediate point two are calculated according to linear interpolation method, it is intermediate
Point one and intermediate point two and satellite current location are in same lateral position, and the magnetic field according to two intermediate points being calculated is strong
Degree obtains the magnetic field strength of satellite current location by linear interpolation method.
Further, in step (6), the formula of linear interpolation method are as follows:
When 4 mesh points are calculated with the intermediate point of two mesh points in same lengthwise position, in formula (2), Y1For
The previous mesh point in satellite current location corresponding magnetic field strength, Y in the table of magnetic field are in transverse direction2To work as in transverse direction in satellite
The latter mesh point in front position corresponding magnetic field strength in the table of magnetic field；X is southbound node the geographic logitude ccl, Y that satellite has been flown over
For the magnetic field strength of intermediate point to be asked；X1With corresponding in the table of magnetic field the southbound node of next magnetic field track for satellite current location
Manage longitude；X2The southbound node geographic logitude of a upper magnetic field track in the table of magnetic field is corresponded to for satellite current location.
When calculating the magnetic field strength of satellite current location by two intermediate points, intermediate point one is under satellite current location
The corresponding mesh point of one track clock, intermediate point two is the corresponding mesh point of a track clock on satellite current location, in formula (2), Y1
For the magnetic field strength of intermediate point one, Y2For the magnetic field strength of intermediate point two；X is satellite current time corresponding track clock；Y is to defend
The magnetic field strength of star current location；X1For intermediate point one in the table of magnetic field corresponding track clock；X2It is intermediate point two in the table of magnetic field
Corresponding track clock.
More specifically, referring to Fig.1, E point (intermediate point one) is first calculated by A (previous mesh point), C (latter mesh point),
F point (intermediate point two) is calculated by B (previous mesh point), D (latter mesh point), then calculates required X (satellite present bit by E, F
Set) point.
The formula of linear interpolation method are as follows:
Y when calculating E point by A, C, in formula (1)1For corresponding magnetic field strength in the magnetic field table of A point, Y2It is C point in magnetic field
Corresponding magnetic field strength in table；X is the southbound node geographic logitude ccl that satellite has been flown over；Y is the magnetic field strength of E point to be asked；
X1The southbound node geographic logitude of next magnetic field track in the table of magnetic field is corresponded to for satellite current location；X2For satellite current location pair
Answer the southbound node geographic logitude of a upper magnetic field track in the table of magnetic field.
The method for calculating F point by B, D is similar with the method for E point is calculated by A, C.
Y when calculating the X point wait ask by E, F, in formula (1)1For the magnetic field strength of E point, Y2For the magnetic field strength of F point；X is
Satellite current time corresponding track clock；Y is the magnetic field strength of X point；X1For A or C point in the table of magnetic field corresponding track clock；X2
For B or D point in the table of magnetic field corresponding track clock.
Further, track clock cumulative timing since 0 when satellite passes through southbound node.Those skilled in the art, which know, to be defended
Pair the intersection point in flight path and equator is ascending node when star rail lift, and the intersection point in flight path and equator is southbound node when dropping rail, i.e.,
For one rail of satellite flight, southbound node only one, southbound node is considered as a new rail and started by us, therefore corresponding track
A clearing when rail of Zhong Xin starts restarts to add up.
In conclusion the present invention is preset in On-board software by establishing high-precision magnetic field table, satellite in orbit when it is logical
The mode that the mode tabled look-up obtains current location magnetic field strength is crossed, solves and is limited on star in calculating magnetic field strength theory value
Spaceborne computer ability and can only be using the low order formula problem lower so as to cause precision.This method algorithm is simple, spaceborne soft
Part is easy to accomplish, and operation time is shorter and calculated magnetic field strength precision is higher.
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 (9)
1. a kind of method for determining space magnetic field intensity based on look-up table, which is characterized in that this method includes:
(1) it establishes high-precision magnetic field table: carrying out grid according to certain time interval on the spherical surface that satellite flight track is passed through
It divides, the three-axle magnetic field intensity on mesh point is calculated according to international Geomagnetic Field Model most high-order formula, forms earth magnetism field data
Table is loaded in satellite carried software；
(2) the southbound node geographic logitude correcting satellite flight track southbound node geographic logitude interval Gdjg and will flying over
lamda；
(3) after satellite and the rocket separation, when On-board software calls magnetic field table subprogram for the first time, the southbound node geographic logitude flown over
Ccl is by the southbound node geographic logitude lamda assignment that will fly over；In other situations, updated when satellite flies to southbound node
The southbound node geographic logitude ccl flown over；
(4) when the southbound node geographic logitude ccl flown over changes, it is right to calculate satellite current location institute in the table of magnetic field
The number cca and its southbound node geographic logitude of magnetic field track are answered, otherwise keeps cca constant；Wherein, southbound node geographic logitude according to
Step (3) obtains, and the number cca of magnetic field track is corresponding with grid dividing；
(5) according to satellite current location, the number cca of corresponding magnetic field track finds out satellite current location four in the table of magnetic field
4 mesh points in week；
(6) method based on linear interpolation calculates magnetic field strength of the satellite current location under orbital coordinate system.
2. the method according to claim 1 for determining space magnetic field intensity based on look-up table, which is characterized in that in step
(1) in, the mode of the grid dividing are as follows: n rail is laterally divided at equal intervals with southbound node geographic logitude, n is that satellite flies daily
Circle number is rounded downwards；It is longitudinal that m point is taken at equal intervals with the rail time of satellite flight, as track clock.
3. the method according to claim 2 for determining space magnetic field intensity based on look-up table, which is characterized in that lateral every two
Geographic logitude interval delta L between rail is 360 °/n, the relationship of geographic logitude and cca are as follows: geographic logitude=* 360 ° of (cca-1)/
n；In longitudinal direction, it is 70~80 that the rail time takes m at equal intervals.
4. the method according to claim 2 for determining space magnetic field intensity based on look-up table, which is characterized in that the grid
The data point of division is arranged in order since 0 ° of east longitude of southbound node moment.
5. the method according to claim 1 for determining space magnetic field intensity based on look-up table, which is characterized in that in step
(2) in, southbound node geographic logitude interval Gdjg is corrected according to the orbit altitude of satellite actual motion；According to the track of satellite accurate measurement
Parameter corrects the southbound node geographic logitude lamda that will be flown in due course.
6. the method according to claim 1 for determining space magnetic field intensity based on look-up table, which is characterized in that in step
(3) in, the southbound node geographic logitude ccl flown over is updated, is obtained by following formula (1):
Ccl=ccl-Gdjg (1).
7. the method for determining space magnetic field intensity based on look-up table described in any one of -6 according to claim 1, feature
It is, in step (6), in 4 mesh points, by two mesh points in same lengthwise position according to linear interpolation side
Method calculates the magnetic field strength of two intermediate points, two intermediate point difference intermediate points one and intermediate point two, intermediate point one and intermediate point
Two are in same lateral position with satellite current location, according to the magnetic field strength for two intermediate points being calculated by linearly inserting
The magnetic field strength of value method acquisition satellite current location.
8. the method according to claim 7 for determining space magnetic field intensity based on look-up table, which is characterized in that in step
(6) in, the formula of the linear interpolation method are as follows:
When 4 mesh points are calculated with the intermediate point of two mesh points in same lengthwise position, in formula (2), Y1For in transverse direction
In the previous mesh point in satellite current location in the table of magnetic field corresponding magnetic field strength, Y2To be in satellite current location in transverse direction
Latter mesh point corresponding magnetic field strength in the table of magnetic field；X is that southbound node the geographic logitude ccl, Y that satellite has been flown over are wait ask
Intermediate point magnetic field strength；X1The southbound node geography warp of next magnetic field track in the table of magnetic field is corresponded to for satellite current location
Degree；X2The southbound node geographic logitude of a upper magnetic field track in the table of magnetic field is corresponded to for satellite current location；
When calculating the magnetic field strength of satellite current location by two intermediate points, intermediate point one is the lower rail in satellite current location
The corresponding mesh point of road clock, intermediate point two is the corresponding mesh point of a track clock on satellite current location, in formula (2), Y1For in
Between point one magnetic field strength, Y2For the magnetic field strength of intermediate point two；X is satellite current time corresponding track clock；Y works as satellite
The magnetic field strength of front position；X1For intermediate point one in the table of magnetic field corresponding track clock；X2It is corresponding in the table of magnetic field for intermediate point two
Track clock.
9. the method according to claim 2 for determining space magnetic field intensity based on look-up table, which is characterized in that the rail
The cumulative timing since 0 when satellite passes through southbound node of road clock.
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