CN108021138A - A kind of Geomagnetic Field Model simplifies design method - Google Patents
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Abstract
The invention discloses a kind of method that winged satellite obtains earth's magnetic field, the earth's magnetic field for establishing satellite orbit changes over time curve, convert thereof into polar coordinates earth's magnetic field curve, every axis is individually normalized again, show that polar coordinates normalize earth's magnetic field curve, earth's magnetic field curve is normalized under reconvert coordinate system at a right angle, calculate the discrete curvature of every, pass through the discrete curvature of every, with reference to K curvature weighting nonuniform sampling methods, multiple sampled points are selected, form anisotropically magnetic field data form, and store onto winged satellite；Obtain and fly satellite real-time true anomaly, with reference to anisotropically magnetic field data form, draw the magnetic field value in real time of winged satellite；According to the weaker characteristic of winged satellite processor calculated performance, Geomagnetic Field Model higher to satellite attitude control system complexity, that memory space is larger simplifies.
Description
【Technical field】
The invention belongs to field of aerospace technology, and in particular to a kind of Geomagnetic Field Model simplifies design method.
【Background technology】
In past 15 years, with the increasingly increase of different application field mission requirements, miniaturization, high performance-price ratio satellite
Technology has obtained vigorous growth.Grapefruit satellite can be by electronic industry large-scale industrial production basis and framework, to the greatest extent may be used
Energy small quality, volume and the mode of mass production realize mission requirements, are mainly directed towards teaching and communicate with scientific research, low rail, is new
Technical identification, and the task such as future space remote sensing networking, space junk monitoring.International approval at present to grapefruit satellite foundation
Quality is categorized as：Microsatellite is 10-100Kg, and Nano satellite 1-10Kg, skin satellite is 0.1-1Kg, flies satellite 10-100g.
Grapefruit satellite is just towards smaller, lighter, more cheap direction is developed.TR Perez,K Subbarao.A Survey of
Current Femto-satellite Designs,Technologies,and Mission Concepts.Journal of
Small satellites.2016. point out cube astrology ratio with 1U, and it is low, intrinsic by redundancy alleviation with cost to fly satellite
The single Nano satellite such as risk and networking control is difficult to the advantage possessed.Hadaegh F Y,Chung S J,Manohara H
M.On Development of 100-Gram-Class Spacecraft for Swarm Applications[J].IEEE
Systems Journal,2014,10(2):For 1-12. again shows that relatively single large satellite, divided using what winged satellite was set up
Cloth Space Vehicle System has more preferable flexibility and robustness.
The research in the field such as task design, system design, power design and Sensor Design for flying satellite at present is
Through gradually abundant.Post M,Bauer R,Li J,et al.Study for femto satellites using micro
Control Moment Gyroscope[C].IEEE Aerospace Conference.IEEE,2016:1-8. proposes one
The winged satellite gravity anomaly actuator that kind is designed using MEMS control-moment gyros (Control Moment Gyroscope), it is right
MEMS CMG are modeled and describe the winged design of satellites scheme of one in detail.In order to reduce manufacture cost, TR Perez, K
Subbarao.A Survey ofCurrent Femto-satellite Designs,Technologies,and Mission
Concepts.Journal ofsmall satellites.2016. are using commercialization Component selection, to the matter of embedded satellite
Amount, the energy, hardware, software, heat dissipation problem have been described in detail, but analyze deficiency to attitude control system, fail to be directed to
The performance of chip proposes software design scheme.Tahri N,Hamrouni C,Alimi A M.Study ofCurrent
Femto-Satellite Approches[J].International Journal of Advanced Computer
Science＆Applications, 2013,4 (5) selective analysis, the function of two winged satellites of PCBSat and WikiSat, knot
The characteristics of structure, power consumption etc..PCBSat is designed with two sun sensors, a GPS navigation receiver and passive pneumatic control
System processed, and WikiSat includes 4 optical sensors, 3 axis accelerometers, a 3 axis gyroscopes and magnetic force and is used away from device
In gesture stability.But due to flying the quality of satellite, volume and power consumption in terms of limitation, at present winged satellite seldom design posture and
Orbits controlling task.As shown in figure 23, the MCU performance comparisons of three kinds of winged satellite micro-control units have been counted.
Compared with Nano satellite and skin satellite gravity anomaly, the MCU computing capabilitys of winged satellite attitude control system are on the weak side, and deposit
Space smaller is stored up, therefore considers the feasibility of Project Realization, flying satellite gravity anomaly modeling also should be with Nano satellite and skin satellite
Gesture stability modeling is not quite similar.For the limited winged satellite of MCU disposal abilities and storage capacity, each byte RAM and
Flash resources are all pretty valuables, so that can hardly support the operation of IGRF Geomagnetic Field Models.Generally make in engineering
Such complex model computational problem is solved with the method for ephemeris.
【The content of the invention】
The object of the present invention is to provide a kind of Geomagnetic Field Model to simplify design method, to solve existing winged satellite control system
The problem of middle complexity is high, storage data occupied space is big.
The present invention uses following technical scheme：A kind of method that winged satellite obtains earth's magnetic field, specifically includes following steps：
Step 1, the Geomagnetic Field Model for 10 rank spherical harmonic series, setting satellite orbital altitude are 650Km, and orbit inclination angle is
97 °, right ascension of ascending node is 10 °, and the earth's magnetic field for establishing the satellite orbit changes over time curve；
Step 2, by the earth's magnetic field drawn in step 1 change over time Curve transform into polar coordinates earth's magnetic field curve；
Step 3, individually normalized every axis of the polar coordinates earth's magnetic field curve drawn in step 2, show that pole is sat
Mark normalization earth's magnetic field curve；
Step 4, will normalize ground under the polar coordinates drawn in step 3 normalization earth's magnetic field Curve transform coordinate system at a right angle
Field curve；
Step 5, the normalization earth magnetism curvature of field is calculated under the rectangular coordinate system drawn in step 4 by U chord length curvature methods
The discrete curvature of every in line：
Wherein, QiIt is that p in the curve of earth's magnetic field is normalized under rectangular coordinate systemiDiscrete curvature at point,For discrete curvature QiConcavity and convexity, xi、yi
Respectively piTransverse and longitudinal coordinate of the point in rectangular coordinate system,It is a little respectivelyWithIn rectangular coordinate system
Under coordinate,It isThe Euclidean distance of this point-to-point transmission；U is the length for supporting neighborhood；
Step 6, the discrete curvature for normalizing every in the curve of earth's magnetic field by being drawn in step 5, with reference to K curvature weightings
Nonuniform sampling method, earth's magnetic field in step 1, which changes over time, selects multiple sampled points in curve, form anisotropically magnetic field
Data form, and by earth's magnetic field data form storage to winged satellite；
Step 7, obtain the real-time true anomaly of winged satellite, with reference to the anisotropically magnetic field data form drawn in step 7, obtains
Go out the magnetic field value in real time of winged satellite.
Further, the specific method of step 6 is：
Step 6.1, pass through formula：
The value for the K for causing E minimums in specified values is calculated, wherein, K is intrinsic weights,For the earth magnetism number of fields for arbitrarily magnetic field data form obtain after linear interpolation
According to,The earth magnetism field data being calculated for standard Geomagnetic Field Model, E lkAnd lsIt is flat
Equal error；
Step 6.2, the K values by being drawn in step 6.1, with reference to formula
Earth's magnetic field in step 1 changes over time and n sampled point is selected in curve, forms anisotropically magnetic field data table
Lattice；
Wherein, n=1,2 ..., N；J=1,2 ..., n；N is total points in Geomagnetic Field Model；mjRepresent each sampling
Position in the corresponding master pattern of point,For under rectangular coordinate system normalize earth's magnetic field curve in all the points from
The sum of the mould of non-dramatic song rate；
In step 6.3, the anisotropically magnetic field data form storage for drawing step 6.2 to winged satellite.
Further, earth's magnetic field data form is included into multigroup earth magnetism field data, included in magnetic field data to each group：Adopt
The corresponding earth magnetism field data of sampling point number, each sampled point and winged satellite true anomaly data, to each group magnetic field data be respectively less than
Equal to 12n+8 bytes.
Further, the method for the real-time true anomaly that acquisition flies satellite is specially in step 7：
When fly satellite in there are during effective gps data, pass through formula：
The real-time true anomaly of winged satellite is calculated, wherein, λ0To fly the right ascension of ascending node at 0 moment of satellite, λs(t) it is
Fly the longitude of satellite,To fly the latitude of satellite, α is the orbit inclination angle for flying satellite, and θ is true anomaly, ωeFor earth rotation
Angular speed,
When winged satellite does not have effective gps data, pass through formula：
θ=ωst+θ0
The real-time true anomaly of winged satellite is calculated, wherein, ωsTo fly the angular speed that satellite flies around the earth's core, t is winged
The flight time of satellite, θ0To fly the initial true anomaly of satellite.
The beneficial effects of the invention are as follows：The present invention characteristic weaker according to satellite processor calculated performance is flown, to Satellite Attitude
The Geomagnetic Field Model that state control system complexity is higher, memory space is larger is simplified, devise homogeneous model and
Non-homogeneous model, and determine middle comparative analysis by the way that model is applied to the attitude of satellite, finally summarize and choose suitable for flying to defend
The anisotropically magnetic field ephemeris model of 80 points of star MCU.
【Brief description of the drawings】
Fig. 1 is the Geomagnetic Field Model of 10 rank spherical harmonic series in the present invention, and it is 650Km to simulate orbit altitude, orbit inclination angle
For 97 °, three axis geomagnetic fieldvectors on the satellite orbit that 10 ° of right ascension of ascending node change over time curve map；
Fig. 2 is polar coordinates earth's magnetic field curvilinear coordinate form figure in the present invention；
Fig. 3 normalizes earth's magnetic field curve map for polar coordinates in the present invention；
Fig. 4 is normalization earth's magnetic field curve map under rectangular coordinate system in the present invention；
Fig. 5 is the graph of a relation of K and E when sampling number is 120 in the present invention；
Fig. 6 is the graph of a relation of K and E when sampling number is 80 in the present invention；
Fig. 7 is the graph of a relation of K and E when sampling number is 50 in the present invention；
Fig. 8 is the graph of a relation of K and E when sampling number is 20 in the present invention；
Fig. 9 is the Geomagnetic Field Model figure of 120 points obtained in the present invention using K curvature weighting non-uniform sampling methods；
Figure 10 is the Geomagnetic Field Model figure of 80 points obtained in the present invention using K curvature weighting non-uniform sampling methods；
Figure 11 is the Geomagnetic Field Model figure of 50 points obtained in the present invention using K curvature weighting non-uniform sampling methods；
Figure 12 is the Geomagnetic Field Model figure of 20 points obtained in the present invention using K curvature weighting non-uniform sampling methods；
Figure 13 is the form storage under the earth's magnetic field ephemeris model of different starting true anomalies and form length in the present invention
Form schematic diagram；
Figure 14 is the schematic diagram of track six roots of sensation number；
Figure 15 is that double vector postures in verification process of the present invention determine flow chart；
Figure 16 is the X-axis ARMSE comparison diagrams in verification process of the present invention；
Figure 17 is the Y-axis ARMSE comparison diagrams in verification process of the present invention；
Figure 18 is the Z axis ARMSE comparison diagrams in verification process of the present invention；
Figure 19 is IGRF model attitude definitive result figures in verification process of the present invention；
Figure 20 is 80 sampled point uniform sampling posture definitive result figures in verification process of the present invention；
Figure 21 is that the K curvature weighting postures of 80 sampled points in verification process of the present invention determine to scheme；
Figure 22 is Geomagnetic Field Model algorithm flow chart of the present invention；
Figure 23 is the MCU performance comparison figures of three kinds of winged satellite micro-control units.
【Embodiment】
The present invention is described in detail with reference to the accompanying drawings and detailed description.
The invention discloses a kind of method that winged satellite obtains earth's magnetic field, following steps are specifically included：
Step 1, the Geomagnetic Field Model for 10 rank spherical harmonic series, setting satellite orbital altitude are 650Km, and orbit inclination angle is
97 °, right ascension of ascending node is 10 °, and the earth's magnetic field for establishing the satellite orbit changes over time curve.
Geomagnetic model can be usually divided into high-altitude global models and regional model, global models are mainly referred to international earth magnetism
IGRF is representative, and the foundation of its model utilizes ground, ocean, high-altitude and satellite magnetic survey data, is built by Gauss theories
It is vertical.From nineteen sixty-eight, international earth magnetism can issue international earth magnetism reference model every 5 years with high empty physical association (IAGA)
(IGRF)。
The Geomagnetic Field Model of the present invention uses the IGRF2010 models that IAGA is provided.The earth represented using spherical harmonic function
Magnetic potential gesture is：
Wherein, ReFor earth radius；R is the east longitude that Greenwich is started at；λ and β is respectively geographic logitude and geocentric colatitude；WithFor the gaussian coefficient of main field；For n m ranks association Legendre function.
Earth magneticpotential difference is geomagnetic fieldvector in the gradient of three direction of principal axis：
WhereinWithCalculated using recursive fashion.
Ground magnetic vector used in simulation analysis is obtained by IGRF modelings, but is constrained to spaceborne computer and is calculated speed
Memory capacity on degree and star, load on actual star the series of geomagnetic model cannot take it is excessive.In order to simulation analysis, such as Fig. 1 institutes
Showing, the present invention have selected the Geomagnetic Field Model of 10 rank spherical harmonic series, and it is 650Km to simulate orbit altitude, and orbit inclination angle is 97 °,
The geomagnetic fieldvector on satellite orbit that 10 ° of right ascension of ascending node changes over time curve.
Step 2, observation Fig. 1 have found that magnetic field data is not with time even variation, but in some period magnetic fields
Curved degree is big, other magnetic field data degree of crook, therefore, it is small to be bound to cause curvature using the method for uniform sampling
Period in magnetic field data redundancy sampling, and magnetic field data deficiency causes loss of significance within the curvature larger period.For
The contradiction between field curve degree of crook and sampling number is solved, the present invention borrows the concept of curvature, big in curvature of curve
The more samplings in place, the small place of curvature samples less.
Need to seek second-order differential to formula (2) in the curvature calculating process of earth's magnetic field curve, therefore, computation complexity compared with
Height, the present invention is replaced directly to the process of earth's magnetic field immediate derivation using the method for discrete curvature, so as to fulfill to calculating process
Simplification.
Abscissa unit in view of field curve is the time, and ordinate unit is tesla, directly to the curve in Fig. 1
It is nonsensical to seek curvature, therefore, earth's magnetic field is first changed over time Curve transform into polar coordinates earth magnetism before curvature is sought
Curvature of field line coordinates form, it is this to represent that the method for two dimension target profile also has in terms of Shape Feature Extraction using one-dimensional curve
Using.Curve transform in Fig. 1 can be obtained into Fig. 2 into polar form.
Step 3, in view of three-axle magnetic field curve be mutually independent, then, as shown in figure 3, the pole that will be drawn in step 2
Every axis of coordinate earth's magnetic field curve is individually normalized, and show that polar coordinates normalize earth's magnetic field curve.
Step 4, it should be noted that due to rectangular co-ordinate be converted into it is polar during figure different zones curvature
Relative size is changed, and have lost the relative information of curvature, therefore it is necessary to which field curve conversion will be normalized under polar coordinates
, just can be to curve derivation after the form that earth's magnetic field curve is normalized under coordinate system at a right angle.Therefore, as shown in figure 4, will step
Earth's magnetic field curve is normalized under the polar coordinates normalization earth's magnetic field Curve transform coordinate system at a right angle drawn in rapid 3.
Step 5, the normalization earth magnetism curvature of field is calculated under the rectangular coordinate system drawn in step 4 by U chord length curvature methods
The discrete curvature of every in line.
U chord length curvature is a kind of discrete curvature computational methods, and compared with existing discrete curvature computational methods, U chord lengths are bent
Rate has stronger anti-rotation and noise immunity, suitable for completing the one kind high to curvature estimation stability requirement such as Curve Matching
Task.Its method basic thought is：For the parameter U of input, a support is determined at curve current point according to Euclidean distance
Field, and application curves refinement strategy improves computational accuracy, thus calculates discrete curvature.
Note：L={ pi：(xi, yi, i=1,2 ..., N) } it is a digital curve, calculate pi, should during the U chord length curvature at place
It is as discrete curvature, specific formula for calculation by the use of with supporting the relevant cosine value of field arm before and after vector angle：
Wherein, QiIt is that p in the curve of earth's magnetic field is normalized under rectangular coordinate systemiDiscrete curvature at point,For discrete curvature QiConcavity and convexity, xi、
yiRespectively piTransverse and longitudinal coordinate of the point in rectangular coordinate system,It is a little respectivelyWithIn rectangular coordinate system
Under coordinate,It isThe Euclidean distance of this point-to-point transmission；U is the length for supporting neighborhood.
Step 6, the discrete curvature for normalizing every in the curve of earth's magnetic field by being drawn in step 5, with reference to K curvature weightings
Nonuniform sampling method, in step 1 the earth's magnetic field change over time and multiple sampled points selected in curve, formed anisotropically
Magnetic field data form, and by earth's magnetic field data form storage to winged satellite.Specific method is：
Step 6.1, pass through formula：
The value for the K for causing E minimums in specified values is calculated, wherein, K is intrinsic weights,For to arbitrarily anisotropically magnetic field data form carries out the ground obtained after linear interpolation
Magnetic field data,The earth magnetism field data being calculated for standard Geomagnetic Field Model, E lK
And lSMean error.
The N=5875 of the earth magnetism field data for the track that the present invention chooses.E is used for the deviation for describing two field curves
Degree, E is smaller, represent two curves more close to.
As shown in Fig. 5 to Fig. 8, respectively represent sampling number be 120,80,50 and 20 when K and E relation, Fig. 6, Fig. 7 and
It is identical in the implication of 6 curves and Fig. 5 in Fig. 8.It can be seen from the figure that when sampling number is identical, the E of uniform sampling is normal
Number, is denoted as EJ, and the E of K curvature weightings sampling changes with K, takes the E of minimum to be denoted asPresence can be found
The field curve and former field curve that expression K curvature weightings sample are more close to so as to demonstrate the validity of algorithm.Separately
Outside, with the reduction of sampling number,And EJAll increasing, represent sampling number reduce, the matched curve of two methods and
Error between virgin curve all increases.
Step 6.2, the method for K curvature weightings are a kind of methods being weighted to each discrete point proposed by the present invention, K
The intrinsic weights of discrete point are represented, optimal K values are chosen by the above method.Make earth magnetism field data for a row it is N number of it is orderly from
Scatterplot, in piThe discrete curvature at place is Qi, then it is the discrete curvature of all the points in normalization earth's magnetic field curve under rectangular coordinate system
Mould and be
The discrete curvature of N number of discrete point in order is normalized, obtains piThe mould of discrete curvature at point isWhen magnetic field data over the ground carries out non-uniform discreteization processing, if only considering the curvature weight each put, easily make
Gathered into the point sampled is excessive at the larger position of curvature.So for each discrete point except considering curvature weight
Outside, itself intrinsic weight should be also added, to balance this situation about excessively assembling.Intrinsic weights K is assigned to N by the present invention
It is a, then piPoint weight beTherefore, the method for sampling of K curvature weightings needs to meet：
Wherein, n=1,2 ..., N；J=1,2 ..., n；mjRepresent that each sampled point corresponds to the position in master pattern, easily
Know, the selection of K determines the nonuniform sampling of curve as a result, when K is infinitely close to just infinite, the sampling side of K curvature weightings
Method has just degenerated into uniform sampling.The K curvature weighting method of samplings are the fusions of curvature and uniform sampling, and different K values can obtain
Different nonuniform samplings are as a result, filter out optimal K by above-mentioned method so that the point of nonuniform sampling can be more preferable
Virgin curve is described.
It is 120,80,50 and 20 obtained using K curvature weighting non-uniform sampling methods respectively as shown in Fig. 9 to Figure 12
The Geomagnetic Field Model of a point, the higher place of sampling density concentrate on the larger region of curvature.It can be seen that with sampling number
Reduction, three axis earth's magnetic field figures become more and more simpler and cruder, and the information expressed by discrete point is also fewer and fewer, and the profile of figure becomes
Obtain increasingly fuzzyyer.
Therefore, earth's magnetic field changes over time and N number of sampled point is selected in curve in step 1, forms anisotropically magnetic field number
According to form.
Step 6.3, by the anisotropically magnetic field data form drawn storage on winged satellite, to each group in magnetic field data
Including：Sampled point number, each corresponding earth magnetism field data of sampled point and winged satellite true anomaly data, described in every group
Magnetic field data, which is respectively less than, is equal to 12n+8 bytes.
Earth's magnetic field on satellite orbit be it is continuously distributed, in theory for we can collect the earth magnetism of infinite multiple spot
Field data, but actually form length choose it is excessive can undoubtedly increase storage burden, while the storage of redundant data also without
Help improve the precision of algorithm.On the contrary, in the case that list data is too small, there are larger error in itself for look-up table ephemeris model
Even mistake, the precision for the double vector operations for leading to not determine posture using this ephemeris model are tested.Therefore select
A suitable form length is selected to be particularly important.
The earth's magnetic field ephemeris model that the present invention designs has taken into full account that Geomagnetic Field Model may be deposited under different application scene
Different accuracy demand, that is, consider the ephemeris model of same track difference form length.The earth's magnetic field that the present invention designs is gone through
The storage format of table model is made of three parts：Originate true anomaly θ0, form length n (i.e. the number of sampled point) and earth's magnetic field
Data M0.As shown in figure 13, the form described under the earth's magnetic field ephemeris model of different starting true anomalies and form length is deposited
Form is stored up, present invention storage real data uses single-precision floating point form, therefore storing initial true anomaly and form length are equal
Using 4 bytes, and three axis earth's magnetic fields of every bit need to take the memory space of 12 bytes in storage track, therefore store form
The ephemeris model that length is needs 12n+8 bytes.
Step 7, obtain the real-time true anomaly of winged satellite, with reference to the anisotropically magnetic field data form drawn in step 6, obtains
Go out the magnetic field value in real time of winged satellite.Obtain and fly the method for real-time true anomaly of satellite and be specially：
During satellite flight, it is believed that the running orbit of satellite is circle, and orbit altitude is fixed, its round dot exists
The earth's core.Track six roots of sensation number is that the classical law of universal gravitation describes necessary 6 parameters when celestial body is moved by conic section, is such as schemed
Shown in 14.
The gps data at any point can be calculated by track six roots of sensation number and determined on track, can be true by track six roots of sensation number
Determine satellite longitude and latitude.I.e. when flying effective gps data in satellite, pass through formula：
The true anomaly of winged satellite is calculated, wherein, λ0To fly the right ascension of ascending node at 0 moment of satellite, λs(t) it is to fly to defend
The longitude of star,To fly the latitude of satellite, α is the orbit inclination angle for flying satellite, and θ is true anomaly, ωeFor earth rotation angle speed
Degree,And have
In the case where not providing gps data, the movement of satellite can approximation regard uniform circular motion as, i.e., satellite is around the earth's core
The angular velocity omega of flightsFor definite value, true anomaly θ is with time even variation.Therefore, in given initial true anomaly θ0And flight
In the case of satellite flight time t, the true anomaly that we can extrapolate orbital position residing for current time satellite is：
θ=ωst+θ0 (8)
The true anomaly of winged satellite is calculated, wherein, ωsTo fly the angular speed that satellite flies around the earth's core, t is to fly satellite
Flight time, θ0To fly the initial true anomaly of satellite.
Use the method for calculating true anomaly, it is only necessary to satellite orbit parameter, flight angular speed and at least one initial true
Anomaly or gps data, you can orbital position after reckoning residing for any time satellite and at this geomagnetic field intensity it is big
It is small.
Geomagnetic Field Model could obtain the precision of satisfaction, the meter that this real-time iterative resolves only when precision is higher
Calculation amount is that On board computer is difficult to bear.By taking IGRF2000 models as an example, which includes 195 of newest revision in 2003
Gaussian coefficient, within the weak solar activity period, computational accuracy is up to below 100nT.Ephemeris model is to lose precision, increase is deposited
Reserves are cost, ensure that the computational efficiency of Geomagnetic Field Model and the normal operation of double vector operations.
The present invention design earth's magnetic field ephemeris model main thought be：In the case of there are effective gps data, by defending
The orbital position (GPS) of star calculates the true anomaly in track six roots of sensation number, and then utilizes true anomaly and pair of geomagnetic field intensity
It should be related to and carry out building table and table look-up, linear interpolation then is carried out to the ephemeris data found, finally calculates track residing for satellite
The magnetic field strength date of position.In the case of ineffective gps data, satellite orbital position is calculated by satellite transit track
True anomaly, then table look-up, interpolation obtains the magnetic field intensity of orbital position residing for satellite.
In addition, the present invention also verifies the above method.
Double vector postures determine model：The attitude and heading reference system for flying satellite in the present invention uses sun sensor and magnetometer
Combination as sensor, and based on vector operation carry out flying the attitude of satellite determining the design of algorithm.Double vectors determine the thinking of appearance
It is as follows：
Unit vector S in orbital coordinate systemo, Bo, new orthogonal coordinate system L is established in orbital coordinate system, it is each to sit
The unit vector of mark table axis is：
l1=So,l2=(So×Bo)/|So×Bo|,l3=(So×(So×Bo))/|So×Bo| (9)
Unit vector S in satellite body coordinate systemb, BbAn orthogonal coordinate system S is established in satellite body system,
The unit vector of each reference axis is：
s1=Sb,s2=(Sb×Bb)/|Sb×Bb|,s3=(Sb×(Sb×Bb))/|Sb×Bb| (10)
Define matrix ML=[l1 l2 l3],MS=[s1 s2 s3], M can be obtaineds=AboML, then the orthogonal posture of existence anduniquess
Matrix, meets：
As shown in figure 15, the flow that double vector postures determine is described, wherein the use of magnetic field data is included in figure over the ground
3 flows in dotted line frame.First, orbital position, loading track system earth magnetism field data are measured；Secondly, the rail of satellite is initialized
Road position simultaneously carries out track deduction；Finally corresponding track system geomagnetic fieldvector data are resolved using Geomagnetic Field Model.
Monte Carlo simulation：
During simulation earth magnetism field data and solar vector data, due to the introducing of random error, mould is often led to
There are deviation, in order to reduce such deviation to improve simulation precision, this paper between the metric data of plan and the data actually measured
The influence of such error is reduced using Monte Carlo simulation.Monte Carlo mode is a kind of numerical value of Probability Statistics Theory for guidance
Computational methods, the method for referring to solving many computational problems using random number.
Perform M single track posture using Monte Carlo simulation herein to determine to resolve, using IGRF Geomagnetic Field Models as track
It is that the Eulerian angles that earth's magnetic field data calculation goes out are denoted asWherein i=1,2 ..., N, j=1,2 ..., M.Equally, using uniform
The Eulerian angles that sampling Geomagnetic Field Model resolves are denoted asThe Eulerian angles resolved using K curvature weightings Geomagnetic Field Model are denoted asFor descriptionWithRespectively withBetween error, invention introduces the general of average root-mean-square error (ARMSE)
Read：
Wherein, subscript SU indicates uniform sampling, subscript SK sign nonuniform samplings.The smaller explanations of ARMSEOrPoint
Not withBetween difference it is smaller, i.e., sampled result is more accurate.
In experiment, Monte Carlo simulation number M=50, orbital period T=5875s, earth radius 6385km, rail are chosen
Road is highly 650km, and right ascension of ascending node is 10 degree, and argument of perigee is 10 degree, eccentricity 0.1, and orbit inclination angle is 97 degree, rail
Road constant is 3.986*10^14, and orbit angular velocity is calculated by track constant and orbit radius；Geomagnetic Field Model noise it is equal
It is worth for 0, standard deviation is 10^ (- 8) tesla；The average of solar vector model is 0, standard deviation 0.01.
As shown in Figure 16, Figure 17 and Figure 18, it can be seen that ARMSESK＜ ARMSESUAll the time set up, illustrate to add using K curvature
The posture definitive result and be more nearly using standard posture definitive result that the Geomagnetic Field Model of power obtains, so as to demonstrate K songs
The method of rate weighting is more superior than the method for uniform sampling；In addition, when sampling number is less, ARMSESKAnd ARMSESUIt
Between difference become apparent from, illustrate that sampling number is fewer, K curvature weightings sample the advantages of protrude become apparent from；Finally, sampling number is worked as
For 80 or so when, three axis ARMSESKTend towards stability, therefore on the premise of attitude determination accuracy is not influenced, deposited to reduce ephemeris
Space is stored up, it is relatively reasonable as the number of samples of earth magnetism ephemeris model to choose 80 points.
As shown in figure 19, it is the posture definitive result being calculated using IGRF models, as shown in Figure 19, Figure 20, Figure 21,
The posture respectively obtained using the uniform sampling Geomagnetic Field Model and K curvature weighting Geomagnetic Field Models of 80 sampled points determines to tie
Fruit, as can be seen from the figure three attitude determination accuracies are close, but the Monte Carlo simulation result of Figure 16, Figure 17 and Figure 18 are still
So it can be seen that the attitude determination accuracy of K curvature weightings is with respect to higher.
The problem of simplifying calculation amount and memory space the present invention specifically addresses Geomagnetic Field Model, gives earth's magnetic field ephemeris
The form storage format of model；And the nonuniform sampling Geomagnetic Field Model of K curvature weightings is proposed, in the feelings that sampling number is fixed
Under condition, the choosing method of non-uniform point is provided；Finally, to verify the correctness of K curvature weighting models, using Monte Carlo simulation
Method is analyzed and verified to attitude of satellite determination process.K curvature weightings model is before meeting that the attitude of satellite determines precision
Put, reduce the sampling number of selection to the greatest extent, so as to reduce required memory space, computing capability is on the weak side, memory space compared with
The small winged attitude of satellite determines that field has very spacious wealthy application prospect.
The present invention determines and control system (Attitude Determination and Control for the attitude of satellite is flown
System in), the problem of computation complexities of IGRF Geomagnetic Field Models is high and amount of memory is big, uniform sampling and K are devised
Two kinds of ephemeris models of curvature weighting.The software flow of uniform ephemeris model, storage format, track deduction method are given first；
The discrete curvature of earth magnetism field data is solved using U curvature estimations method, and proposes K curvature weightings method and designs non-homogeneous ephemeris
Model；The fitting degree to virgin curve of uniform sampling approach and non-homogeneous method is compared, and result is applied in ADCS
Comparison.Final design is suitable for flying the non-homogeneous ephemeris model based on K curvature weightings of 80 points of satellite, it is only necessary to
0.96KB memory spaces, it was demonstrated that in calculating speed and memory space etc. compared to the prior art there is greater advantage.
For a three axis earth magnetism field data of track (5875s), the earth's magnetic field ephemeris model using 80 sampled points is basic
Effect of the IGRF models in posture determines can be substituted.If with the float form storage tape data of 4 bytes, need altogether
128.2KB.Do not become rail function due to flying satellite, substantial amounts of data redundancy is stored in gridding magnetic field model.Compare
Under, if the earth magnetism field data of IGRF models and 80 sampled points is stored with the float forms of 4 bytes, respectively need 70.5KB
And 0.96KB.It can be seen from the above that the earth's magnetic field ephemeris model proposed by the present invention based on K curvature weightings do not only take up memory space compared with
It is small, meet the demand that lightweight stores in the flash for three kinds of winged satellites being mentioned above, while can realize in flash
Earth magnetism field data is disposably loaded into the RAM of MCU, so as to achieve the purpose that quickly accessing to geomagnetic data.So this hair
The magnetic field ephemeris model of bright design has not only largely saved memory space, but also improves the speed of service of program, from
And shorten the controlling cycle of algorithm.
Claims (4)
1. a kind of method that winged satellite obtains earth's magnetic field, it is characterised in that specifically include following steps：
Step 1, the Geomagnetic Field Model for 10 rank spherical harmonic series, setting satellite orbital altitude are 650Km, and orbit inclination angle is 97 °,
Right ascension of ascending node is 10 °, and the earth's magnetic field for establishing the satellite orbit changes over time curve；
Step 2, by the earth's magnetic field drawn in step 1 change over time Curve transform into polar coordinates earth's magnetic field curve；
Step 3, individually normalized every axis of the polar coordinates earth's magnetic field curve drawn in step 2, show that polar coordinates are returned
One changes earth's magnetic field curve；
Step 4, will normalize earth's magnetic field under the polar coordinates drawn in step 3 normalization earth's magnetic field Curve transform coordinate system at a right angle
Curve；
Step 5, by U chord length curvature methods be calculated under the rectangular coordinate system drawn in step 4 normalize earth's magnetic field curve in
The discrete curvature of every：
<mrow>
<msub>
<mi>Q</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<msub>
<mi>s</mi>
<mi>i</mi>
</msub>
<msqrt>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mi>D</mi>
<mi>i</mi>
</msub>
<mrow>
<mn>2</mn>
<mi>U</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mrow>
Wherein, QiIt is that p in the curve of earth's magnetic field is normalized under rectangular coordinate systemiDiscrete curvature at point,For discrete curvature QiConcavity and convexity, xi、yiRespectively piPoint
Transverse and longitudinal coordinate in rectangular coordinate system,It is a little respectivelyWithCoordinate under rectangular coordinate system,It isThe Euclidean distance of this point-to-point transmission；U is the length for supporting neighborhood；
Step 6, the discrete curvature for normalizing every in the curve of earth's magnetic field by being drawn in step 5, it is non-with reference to K curvature weightings
Even sampling method, in step 1 the earth's magnetic field change over time and multiple sampled points selected in curve, form anisotropically magnetic field
Data form, and by earth's magnetic field data form storage to winged satellite；
Step 7, obtain the real-time true anomaly of winged satellite, with reference to the anisotropically magnetic field data form drawn in step 7, draws winged
The magnetic field value in real time of satellite.
2. the method that winged satellite obtains earth's magnetic field as claimed in claim 1, it is characterised in that the specific method of the step 6
For：
Step 6.1, pass through formula：
<mrow>
<mi>E</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msubsup>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</msubsup>
<mrow>
<mo>|</mo>
<mrow>
<msubsup>
<mi>B</mi>
<mi>i</mi>
<mi>S</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>B</mi>
<mi>i</mi>
<mi>K</mi>
</msubsup>
</mrow>
<mo>|</mo>
</mrow>
</mrow>
<mi>N</mi>
</mfrac>
</mrow>
The value for the K for causing E minimums in specified values is calculated, wherein, K is intrinsic weights,
To carry out the earth magnetism field data that obtains after linear interpolation to arbitrarily magnetic field data form,For standard
The earth magnetism field data that geomagnetic field model calculation obtains, E lkAnd lsMean error；
Step 6.2, the K values by being drawn in step 6.1, with reference to formula
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<msub>
<mi>m</mi>
<mi>j</mi>
</msub>
</mrow>
<msub>
<mi>m</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</munderover>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mo>|</mo>
<msub>
<mi>Q</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
</mrow>
<msub>
<mi>Q</mi>
<mrow>
<mi>s</mi>
<mi>u</mi>
<mi>m</mi>
</mrow>
</msub>
</mfrac>
<mo>+</mo>
<mfrac>
<mi>K</mi>
<mi>N</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mi>K</mi>
</mrow>
<mrow>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mfrac>
</mrow>
The earth's magnetic field changes over time and n sampled point is selected in curve in step 1, forms anisotropically magnetic field data table
Lattice；
Wherein, n=1,2 ..., N；J=1,2 ..., n；N is total points in Geomagnetic Field Model；mjRepresent that each sampled point corresponds to
Position in master pattern,To normalize the discrete curvature of all the points in the curve of earth's magnetic field under rectangular coordinate system
Mould sum；
In step 6.3, the anisotropically magnetic field data form storage for drawing step 6.2 to winged satellite.
3. the method that winged satellite obtains earth's magnetic field as claimed in claim 1 or 2, it is characterised in that by the earth magnetism field data
Form includes multigroup earth magnetism field data, includes in magnetic field data to each group：Sampled point number, each sampled point are corresponding
Earth magnetism field data and winged satellite true anomaly data, earth magnetism field data described in every group, which is respectively less than, is equal to 12n+8 bytes.
4. the method that winged satellite obtains earth's magnetic field as claimed in claim 1 or 2, it is characterised in that obtained in step 7 and fly satellite
The method of real-time true anomaly be specially：
When fly satellite in there are during effective gps data, pass through formula：
The real-time true anomaly of winged satellite is calculated, wherein, λ0To fly the right ascension of ascending node at 0 moment of satellite, λs(t) it is to fly to defend
The longitude of star,To fly the latitude of satellite, α is the orbit inclination angle for flying satellite, and θ is true anomaly, ωeFor earth rotation angle speed
Degree,
When winged satellite does not have effective gps data, pass through formula：
θ=ωst+θ0
The real-time true anomaly of winged satellite is calculated, wherein, ωsTo fly the angular speed that satellite flies around the earth's core, t is to fly satellite
Flight time, θ0To fly the initial true anomaly of satellite.
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| CN109344512A (en) * | 2018-10-09 | 2019-02-15 | 中国人民解放军国防科技大学 | Thermal control structure of flying satellite and processing method |
| CN109344512B (en) * | 2018-10-09 | 2022-11-11 | 中国人民解放军国防科技大学 | Thermal control structure of flying satellite and processing method |
| CN109856569A (en) * | 2018-12-12 | 2019-06-07 | 上海航天控制技术研究所 | A method of space magnetic field intensity is determined based on look-up table |
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| CN111813135A (en) * | 2020-06-29 | 2020-10-23 | 西南电子技术研究所（中国电子科技集团公司第十研究所） | Dual-coordinate system full-airspace array beam tracking method |
| CN111813135B (en) * | 2020-06-29 | 2023-03-31 | 西南电子技术研究所（中国电子科技集团公司第十研究所） | Dual-coordinate system full-airspace array beam tracking method |
| CN115406467A (en) * | 2022-11-01 | 2022-11-29 | 北京开拓航宇导控科技有限公司 | Automatic calibration method for MEMS gyroscope |
| CN116592861A (en) * | 2023-07-18 | 2023-08-15 | 天津云圣智能科技有限责任公司 | Magnetic compass calibration model construction method, magnetic compass calibration method and device |
| CN116592861B (en) * | 2023-07-18 | 2023-09-29 | 天津云圣智能科技有限责任公司 | Magnetic compass calibration model construction method, magnetic compass calibration method and device |
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