CN105138005A - Method for determining relative orbit elements based on inter-satellite distance - Google Patents
Method for determining relative orbit elements based on inter-satellite distance Download PDFInfo
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Abstract
The invention discloses a method for determining the relative orbit elements based on inter-satellite distance. The method comprises the following steps: S1, acquiring four extreme values of the distance between two satellites within a sampling period; S2, establishing the relationship between the relative distance and the relative orbit elements; and S3, establishing the mapping relationship between the inter-satellite distance extreme value error and the relative orbit element error, parsing out the relative semi-major axis error and the relative angle-of-tilt error based on the relative orbit element error, and obtaining the relative orbit elements. According to the technical scheme, complex three-dimensional spatial motion is converted into two-dimensional planar motion on the basis of a formation flight relative kinematics equation. The error between the actual value and the nominal value of inter-satellite distance and the error between the actual value and the nominal value of relative orbit elements are converted into linear relationship characterization, and the error between the actual value and the nominal value of relative orbit elements can be directly determined according to the error between the actual value and the nominal value of inter-satellite distance.
Description
Technical field
The present invention relates to a kind of Relative Orbit Elements defining method of satellite formation flying, more particularly, is adopt primary, from the relative distance of four between star to determine Relative Orbit Elements.
Background technology
" Technology of Modern Small Satellites and application " that author Yu Jinpei published in March, 2004, discloses the composition of general satellite system, as shown in Figure 1 in " 3. small satellite system ".Spaceborne computer also claims house keeping computer, is responsible for the coordinated management of the storage of data and program on star, process and each subsystem.GPS is the instrument of receiving world locational system satellite-signal space of planes position definitely.
Satellite formation flying system needs to keep certain configuration in flight course, but owing to being subject to the impact of the perturbation factors such as compression of the earth, atmospherical drag and solar light pressure, the orbital elements of Satellite Formation Flying can constantly change, for long-term formation flight task, necessary track must be carried out based on the change of orbital elements to system to maintain, otherwise formation flight system will lose initial design configuration, and finally cause the failure of task.
To the determination of the actual Relative Orbit Elements of satellite in formation flight system, normally measure relative position and relative velocity by certain technological means, and utilize the relation between they and Relative Orbit Elements, determine actual Relative Orbit Elements when formation flight system is flown in-orbit, error is obtained again by deducting corresponding nominal value, and in certain accuracy rating, eliminate these errors accordingly, thus realize the long-term maintenance of formation flight system configuration.
But this method determining Relative Orbit Elements error in the past, is after the actual track key element directly utilizing conversion relation to obtain, then makes comparisons with nominal value.Thisly directly make difference and to obtain the method precision of error not high, and metrical information is too much, proposes higher requirement to measurement mechanism on star.Therefore, how to make full use of metrical information on star, design a kind of simple, effectively and there is the method for the Relative Orbit Elements error of the determination satellites formation system of degree of precision, be in engineering in the urgent need to, but numerous scholar does not clearly provide under study for action and solves the method for this problem in the past.
Summary of the invention
In the present invention, utilize satellite within a sampling period Real-time Collection to star between relative distance (i.e. star spacing) data have maximal value, secondary maximal value, secondary minimum value and minimum value, and using the input aequum of these data as determination formation flight system Relative Orbit Elements method of the present invention.
The invention discloses a kind of method that only can obtain formation flight system Relative Orbit Elements according to four extreme values of Satellite spacing in formation flight system.In formation flight system primary orbital coordinate system, Satellite Formation Flying diametrically move much smaller than along mark to the relative motion of orbital plane normal direction.Therefore, the three-dimensional space motion of Satellite Formation Flying is reduced to the two dimensional motion in plane by this method, and the error giving actual star spacing and its nominal value is with a kind of mapping relations between Relative Orbit Elements.Be different from conventional satellite relative position defining method and need to rely on the third party signalling such as land station or GPS source to determine the method for Relative Orbit Elements, this method only needs by resolving with the mapping relations between actual Relative Orbit Elements and its nominal value error the error between actual interstellar distance and its nominal value, the error of actual Relative Orbit Elements and nominal value can be determined, and then determine actual Relative Orbit Elements in conjunction with the design nominal value of Relative Orbit Elements.
A kind of Relative Orbit Elements defining method based on interstellar distance of the present invention, in Mission design, several do relative motion from star F around primary M, and the spaceborne computer of primary M receives the star spacing within a sampling period of GPS output; It is characterized in that determining to include the following step based on the Relative Orbit Elements of interstellar distance:
Step one, obtains the extreme value of spacing between star;
Without the star spacing maximum in perturbation situation
and minimum value
The multiple star spacing will gathered in a sampling period T;
Step 2, formulates star spacing with the relation between Relative Orbit Elements;
At the primary orbital coordinate system M-X without perturbation situation
my
mz
munder, primary M with from star F at described M-X
my
mz
munder star spacing be expressed as:
Δ y
nominal=a
nominal(Δ Ω × sini
nominal× cosu
m-Δ i × sinu
m)
Δ z
nominal=a
nominal(Δ e
x× cosu
m+ Δ e
y× sinu
m)
In formation flight process, primary M with from star F at primary orbital coordinate system M-X
my
mz
munder star spacing be expressed as:
Δ y
actual=a
m(Δ Ω × sini
m× cosu
m-Δ i × sinu
m)
Δ z
actual=a
m(Δ e
x× cosu
m+ Δ e
y× sinu
m)
Step 3, formulates the mapping relations of the error between star spacing actual value and nominal value and the error between Relative Orbit Elements actual value and nominal value;
In the present invention, consider formation flight system respectively under " without perturbation " and " having perturbation " situation, the configuration giving formation flight system simplifies relation (as shown in Fig. 4 A, Fig. 4 B, Fig. 5), and successively give without in perturbation situation based on Relative Kinematics, the mapping relations between the Relative Orbit Elements under the maximal value of nominal star spacing and minimum value and nominal case.On this basis, when considering in perturbation situation, namely directly variational method is utilized, variation is got to former nominal value (star spacing and Relative Orbit Elements), namely represent the error between actual value and nominal value, so just can obtain the mapping relations of the error between star spacing actual value and nominal value and the error between Relative Orbit Elements actual value and nominal value.By direct representation star interval error with the relation between this two classes error of Relative Orbit Elements, systematic error during data processing can be reduced, thus the final determination precision improving Relative Orbit Elements.
The present invention, according to the real-time star spacing of Satellite Formation Flying system, proposes a kind of simple method that also comparatively accurately can obtain satellite Relative Orbit Elements, possesses higher engineer applied and be worth.The method, directly according to the change of the star spacing data that can directly be obtained by measurement device on satellite, utilizes actual maximal value (secondary maximal value), actual minimum value (secondary minimum value) difference poor with maximal value nominal value, minimum value nominal value accordingly.On the engineering simplification carried out based on Relative Kinematics realizes, directly can be obtained the error of Relative Orbit Elements by star interval error, and add nominal value, Relative Orbit Elements during practical flight can be accessed.
The Relative Orbit Elements defining method advantage of the formation flight that the present invention proposes is:
1. on formation flight Relative Kinematics basis, by engineering simplification effectively, the three dimensions problem of complexity is converted into two dimensional surface problem, directly utilize the variational method, actual star spacing and the direct and actual Relative Orbit Elements of error of nominal value and the error of its nominal value are connected, is convenient to determine error.
2. method proposed by the invention is the error change being obtained Relative Orbit Elements by the error change of star spacing, and be different from the Relative Orbit Elements directly being obtained reality in classic method by actual star spacing, and then to compare with nominal value and obtain error, thus improve the computational accuracy that error is determined.
3. by analyzing the star spacing change curve that obtained by the real-time measurement of formation flight system, the situation of change of Satellite Formation Flying Relative Orbit Elements can be analyzed intuitively, thus provide foundation for the formulation of Orbital Control Strategy.
Accompanying drawing explanation
Fig. 1 is the structured flowchart of the general satellite system of tradition.
Fig. 2 is the relation schematic diagram of geocentric coordinate system and primary orbital coordinate system.
Fig. 3 is the variation relation schematic diagram of star spacing with the formation flight time.
Fig. 4 A be without formation flight system in perturbation situation under the line position time nominal configuration floor map.
Fig. 4 B is without the nominal configuration floor map of formation flight system in perturbation situation when position, the two poles of the earth.
Fig. 5 is the star spacing change schematic diagram of actual formation flight system.
Embodiment
Below in conjunction with drawings and Examples, the present invention is described in further detail.
Usually, in Mission design, several Inspector satellite do relative motion around central satellite.In the present invention with the formation of two satellites composition for research object, and they are divided into primary and from star.
In fig. 2, the orbit of primary M is called reference orbit.With the barycenter of primary M for true origin, the direction being pointed to the earth's core by initial point is Z
maxle, the negative normal direction in reference orbit face is Y
maxle, X
mdirection of principal axis is by Y
mand Z
mdirection is determined according to right-hand rule, and points to heading.
Shown in Figure 1, the spaceborne computer in satellite system is for being responsible for the coordinated management of the storage of data and program on star, process and each subsystem.
GPS in satellite system receives the positional information of other satellite by antenna.
Shown in Fig. 2, Fig. 3, usually, in Mission design, several Inspector satellite (also claiming from star) do relative motion around central satellite (also claiming primary).The spaceborne computer of primary receives the star spacing L within a sampling period of GPS output
actual.In the present invention, spaceborne computer only according to four star spacing extreme values selecting to determine the Relative Orbit Elements of the inter-satellite reality of formation flight.As shown in Figure 3, four described star spacing extreme values refer to the maximum star spacing between two stars respectively
secondary large star spacing
most starlet spacing
with secondary starlet spacing
Step one, obtains the extreme value of spacing between star;
Shown in Figure 3, in the present invention, the formation flight time is designated as T
flight, at described T
flightin have multiple sampling period T, in described T, have multiple time-sampling point t
sampling, previous time-sampling point is designated as t
before, a rear time-sampling point is designated as t
after, multiple star spacing will be gathered in described T.Gather primary M and from the distance between star F, this distance is called star spacing.Then the maximal value successively occurred in described star spacing is selected
minimum value
second largest value
with secondary minimum value
and
in figure,
with
for without the star spacing maximum in perturbation situation and minimum value.
Step 2, formulates star spacing with the relation between Relative Orbit Elements;
Shown in Figure 2, at the primary orbital coordinate system M-X without perturbation situation
my
mz
munder, primary M with from star F at described M-X
my
mz
munder star spacing be expressed as:
Δ x
nominalrepresent that star spacing is at primary orbital coordinate system M-X
my
mz
mx
mprojection on axle;
Δ y
nominalrepresent that star spacing is at primary orbital coordinate system M-X
my
mz
my
mprojection on axle;
Δ z
nominalrepresent that star spacing is at primary orbital coordinate system M-X
my
mz
mz
mprojection on axle.
Introducing the key element (in Dec nineteen ninety-five the 1st edition " spacecraft flight principle of dynamics ", Xiao Yelun writes, the 44th page) of spacecraft orbit, is at geocentric coordinate system O-x
iy
iz
i(axes O x
ithe axis pointing to the first point of Aries with the earth's core O) undefined.
In the present invention, in the formation flight of satellite, representing primary symbol M, representing with meeting F from star according to Relative Orbit Elements, then have:
(1) semi-major axis
The semi-major axis of orbit of primary M is designated as a
m, be designated as a from the semi-major axis of orbit of star F
f, unit is rice; Therefore, Δ a is designated as from the relative semi-major axis between star F with primary M, i.e. Δ a=a
f-a
m.A in without perturbation situation
f=a
m, be designated as a
nominal.
(2) excentricity
The orbital eccentricity of primary M is designated as e
m, be designated as e from the orbital eccentricity of star F
f, unit is dimensionless; Therefore, the x of the coordinate system defined from star F and primary M in orbital elements
iexcentricity on axle is designated as
relative eccentric ratio vector is designated as Δ e
x, i.e. Δ e
x=e
fcos ω
f-e
mcos ω
m; The y of the coordinate system defined in orbital elements from star F and primary M
iexcentricity on axle is designated as
relative eccentric ratio vector is designated as Δ e
y, i.e. Δ e
y=e
fsin ω
f-e
msin ω
m.E in without perturbation situation
f=e
m, be designated as e
nominal.
(3) argument of perigee
The argument of perigee of primary M is designated as ω
m, be designated as ω from the argument of perigee of star F
f, unit is degree; Therefore, Δ ω is designated as from the relative argument of perigee between star F with primary M, i.e. Δ ω=ω
f-ω
m.ω in without perturbation situation
f=ω
m, be designated as ω
nominal.
(4) inclination angle
The orbit inclination of primary M is designated as i
m, be designated as i from the orbit inclination of star F
f, unit is degree; Therefore, be designated as Δ i from the relative inclination between star F and primary M, i.e. Δ i=i
f-i
m.I in without perturbation situation
f=i
m, be designated as i
nominal.
(5) latitude argument
The latitude argument of primary M is designated as u
m, be designated as u from the latitude argument of star F
f, unit is degree; Therefore, Δ u is designated as from the relative altitude argument between star F and primary M, i.e. Δ u=u
f-u
m.
(6) right ascension of ascending node
The ascending node of orbit right ascension of primary M is designated as Ω
m, be designated as Ω from the ascending node of orbit right ascension of star F
f, unit is degree; Therefore, Δ Ω is designated as from the relative orbit right ascension of ascending node between star F and primary M, i.e. Δ Ω=Ω
f-Ω
m.
Shown in Figure 2, in formation flight process, primary M with from star F at primary orbital coordinate system M-X
my
mz
munder star spacing be expressed as:
Δ x
actualrepresent that star spacing is at primary orbital coordinate system M-X
my
mz
mx
mprojection on axle;
Δ y
actualrepresent that star spacing is at primary orbital coordinate system M-X
my
mz
my
mprojection on axle;
Δ z
actualrepresent that star spacing is at primary orbital coordinate system M-X
my
mz
mz
mprojection on axle.
In the present invention, at formation flight system primary orbital coordinate system M-X
my
mz
min, due to Satellite Formation Flying diametrically move much smaller than along mark to the relative motion of orbital plane normal direction, then Z
mprojection value on axle is 0, therefore described M-X
my
mz
mbe reduced to plane coordinate system M-X
my
m(as shown in Figure 4 A), formula (2) is reduced to:
According to the range formula of point-to-point transmission, at time-sampling point t
samplingthe primary M gathered and be from the star spacing between star F:
For in the formation flight object that the present invention studies, when satellite under the line position time, star spacing reaches maximal value; When the two poles of the earth, north and south, star spacing arrives minimum value; When other positions, star spacing constantly changes between a minimum value and a maximum value.
Step 3, formulates the mapping relations of the error between star spacing actual value and nominal value and the error between Relative Orbit Elements actual value and nominal value;
In the present invention, consider formation flight system respectively under " without perturbation " and " having perturbation " situation, the configuration giving formation flight system simplifies relation (as shown in Fig. 4 A, Fig. 4 B, Fig. 5), and successively give without in perturbation situation based on Relative Kinematics, the mapping relations between the Relative Orbit Elements under the maximal value of nominal star spacing and minimum value and nominal case.On this basis, when considering in perturbation situation, namely directly variational method is utilized, variation is got to former nominal value (star spacing and Relative Orbit Elements), namely represent the error between actual value and nominal value, so just can obtain the mapping relations of the error between star spacing actual value and nominal value and the error between Relative Orbit Elements actual value and nominal value.By direct representation star interval error with the relation between this two classes error of Relative Orbit Elements, systematic error during data processing can be reduced, thus the final determination precision improving Relative Orbit Elements.
Step 31, without in perturbation situation:
Consider without the star spacing in perturbation situation, namely two stars are run on the nominal track preset completely, and there is not the situation that Relative Orbit Elements changes.
In Figure 4 A, from star F at plane coordinate system M-X
my
min, from star F at X
msubpoint on axle is designated as
from star F at Y
msubpoint on axle is designated as
primary M and be designated as L from the star spacing nominal value between star F
nominal.Primary M with from the line of star F and Y
maxial angle is designated as β (being called formation configuration angle β).Δ x
nominalfor from star F at X
mthe distance nominal value that axle projects, Δ y
nominalfor from star F at Y
mthe distance nominal value that axle projects.
When formation flight system arrives empty position, now u on equator
m=0 ° or 180 °, star spacing reaches maximal value, as shown in Figure 4 A.Then square being expressed as of maximum star spacing:
In figure 4b, from star F at plane coordinate system M-X
my
min, from star F at Y
mwithout projection on axle, i.e. Δ y
nominal=0, from star F at X
msubpoint on axle is self, i.e. Δ x
nominalfor minor increment.
From star F relative to primary M along Y
mdirection of principal axis does pendular movement, after formation flight system crosses equatorial positions, has two specific positions, i.e. empty position, now u on the two poles of the earth, north and south
m=90 ° or 270 °, star spacing reaches minimum value, as shown in Figure 4 B.Now be positioned at X from star F
mon axle, due to Δ e
xwith Δ e
ydifference is very little, can be approximated to be Δ e
xequal Δ e
y, therefore most starlet spacing almost with Δ x
nominalequal, then square being expressed as of most starlet spacing:
Step 32, under considering perturbation situation:
In the present invention, for the formation flight system that reality is flown in-orbit, owing to there is the orbit perturbation that the factors such as compression of the earth, lunisolar attraction, solar light pressure cause, the orbital elements of Satellite Formation Flying will change, the actual configuration of system is not without the nominal configuration in perturbation situation, and nominal position will be departed from the Relative distribution position of satellite.But the distance that formation configuration departs from nominal value is again very little relative to the distance scale of configuration, therefore the actual motion formation configuration going up empty position under the line can be reduced to Fig. 5.
M in Figure 5
actualfor primary M is at plane coordinate system M-X
my
mphysical location, F
actualfor from star F at plane coordinate system M-X
my
mphysical location, M
actualwith F
actualline be parallel to the line of M and F.Cross primary M to do perpendicular to M
actualf
actualline is designated as vertical line MA, crosses and does perpendicular to M from star F
actualf
actualline is designated as vertical line FB.
In the present invention, the deviation of the configuration that the flight in practical situations both of formation flight system occurs and nominal configuration is considered.Formula (5) changes persuing is divided, can obtain:
δ L
maxrepresent the maximum star spacing/actual value of time large star spacing and the nominal value of maximum star spacing difference (
or
), δ represents variation symbol;
In the present invention, in order to keep the stability of formation configuration, generally get Δ e when formation flight system
y=0, formula (7) is arranged, can obtain:
In formula,
Again formula (6) changes persuing is divided, can obtain
δ L
minrepresent the actual value of most starlet spacing/time starlet spacing and the nominal value of most starlet spacing difference (
or
), δ represents variation symbol;
In formula (9),
formula (9) is simplified:
δ L
min=a
nominal(δ Δ u+ δ Δ Ω × cosi
nominal± 2 δ Δ e
x) (10)
Simultaneous formula (8) and formula (10), can obtain system of linear equations is:
for described Δ e
yget the δ L of timing
maxvalue;
for described Δ e
yδ L when getting negative
maxvalue;
for described Δ e
xget the δ L of timing
minvalue;
for described Δ e
xδ L when getting negative
minvalue;
Due to δ Δ e
xwith δ Δ e
ythere is positive and negative uncertainty in previous symbol, therefore, as shown in Figure 3, it adopts matrix form to be expressed as to the star spacing of actual formation flight system change relation in time:
Solve formula (12) and relative altitude argument in the Relative Orbit Elements of master and slave star reality in formation flight system, relatively right ascension of ascending node, nominal value error that relative eccentric ratio vector is corresponding with it can be obtained, that is:
Error between relative altitude argument actual value and relative altitude argument nominal value, is designated as relative altitude argument error delta Δ u;
Error between relative right ascension of ascending node actual value with relative right ascension of ascending node nominal value, is designated as relative right ascension of ascending node error delta Δ Ω;
At geocentric coordinate system O-x
iy
iz
ix
irelative eccentric ratio vector actual value on axle and the error between relative eccentric ratio vector nominal value, be designated as relative eccentric ratio vector error δ Δ e
x;
At geocentric coordinate system O-x
iy
iz
iy
irelative eccentric ratio vector actual value on axle and the error between relative eccentric ratio vector nominal value, be designated as relative eccentric ratio vector error δ Δ e
y.
In the system of derivation formation flight below master and slave star reality Relative Orbit Elements in relative semi-major axis Δ a, the error between the nominal value that relative inclination Δ i is corresponding with it, that is:
Error between relative semi-major axis actual value with relative semi-major axis nominal value, is designated as relative semi-major axis error delta Δ a;
Error between relative inclination actual value and relative inclination nominal value, is designated as relative inclination error delta Δ i;
In the present invention, according to the relation of latitude argument and semi-major axis
μ=3.986005 × 10
14m
3/ s
2for Gravitational coefficient of the Earth; U can be the latitude argument of primary, also can be the latitude argument from star; A can be the semi-major axis of orbit of primary, also can be the semi-major axis of orbit from star; U ' can be the latitude argument rate of change of primary, also can be the latitude argument rate of change from star.
In the present invention, the error between the actual value of the relative semi-major axis of track and the nominal value of relative semi-major axis, can be expressed as:
for at a rear time-sampling point t
afterunder the value of described δ Δ u;
for at previous time-sampling point t
beforeunder the value of described δ Δ u;
In the present invention, J is considered
2with the impact of humorous item Gravitational perturbation, and be with humorous constant J
2=0.0010826, earth radius R
e=6378.137km, the error between the actual value at relative orbit inclination angle and the nominal value at relative orbit inclination angle, is designated as relative orbit error of tilt δ Δ i, then:
for at a rear time-sampling point t
afterunder the value of described δ Δ Ω;
for at previous time-sampling point t
beforeunder the value of described δ Δ Ω;
N is the operation mean angular velocity of primary M;
Therefore, in the present invention according to Δ a, Δ e
x, Δ e
y, Δ i, Δ u and Δ Ω; δ Δ a, δ Δ e
x, δ Δ e
y, δ Δ i, δ Δ u and δ Δ Ω, actual Relative Orbit Elements in formation flight system can be determined, and then determine the configuration of formation flight system.
embodiment 1
The present invention analyzes for two star formation flight systems, and master and slave star is distributed in two orbital planes respectively, the semi-major axis of orbit a in the orbital elements of two kinds of tracks
nominal, eccentric ratio e
nominal, inclination angle i
nominalbe identical, right ascension of ascending node Ω is different with latitude argument u.Get semi-major axis of orbit a
nominal=7478.137km, eccentric ratio e
nominal=0, orbit inclination i
nominal=63.43 °, argument of perigee ω
nominal=45 °, relative right ascension of ascending node is Δ Ω=0.8764 °, and relative altitude argument is Δ u=0.0602 °.This formation flight system is constant with Formation keeping during position, the two poles of the earth, north and south under the line in without perturbation situation, and position clock star spacing under the line
position, the two poles of the earth clock star spacing is Δ x
nominal=59km, as shown in Figure 5, now just in time has formation configuration angle β=30 °.
Adopt a kind of method Relative Orbit Elements estimated according to star spacing proposed by the invention in embodiment 1, and same STK (SatelliteToolKit, satellite kit) data of Software Create contrast, to verify the validity of the inventive method.
Adopt Relative Orbit Elements defining method of the present invention, comprise the following steps:
Steps A, by STK simulation software, when arranging the orbital elements of satellite, relative to nominal value to the certain deviation of Relative Orbit Elements, as the Relative Orbit Elements of the actual formation flight system of simulation;
Step B, utilize the star spacing data that the actual formation flight system of simulation produces, based on the Relative Orbit Elements defining method that the present invention proposes, directly obtain the error between actual Relative Orbit Elements and its nominal value, thus determine the actual track key element of formation flight system.
Step C, the Relative Orbit Elements error obtained the method proposed by the present invention is made comparisons with the nominal error of setting, and carries out error analysis, to verify the validity and reliability of this method.
Getting scheduling time section is UTCG time (if on the X X month 1 12 is when the 12 days 12 X X month), actual semi-major axis is relatively Δ a=0.1m (is 0.1m with nominal value, namely the relative semi-major axis nominal error set is 0.1m), actual relative eccentric ratio Δ e=0.0001 (is 0.0001 with nominal value, namely the relative eccentric ratio nominal error set is 0.0001), actual relative orbit inclination angle Δ i=0.001 ° (is 0.001 ° with nominal value, namely the relative orbit inclination angle nominal error set is 0.001 °), actual right ascension of ascending node is relatively Δ Ω=0.96404 ° (is 0.08764 ° with nominal value, namely the relative right ascension of ascending node nominal error set is 0.08764 °), actual relative altitude argument is Δ u=0.06622 ° (is 0.00602 ° with nominal value, namely the relative altitude argument nominal error set is 0.00602 °), the argument of perigee of two stars is all taken as 45 °.
Get the emulated data of first sampling period interstellar distance of scheduling time section, star spacing can be obtained
can obtain actual Relative Orbit Elements (relative altitude argument, relatively right ascension of ascending node, relative eccentric ratio) by formula (12) with the error between corresponding nominal value is:
δ Δ u=0.005953 °, δ Δ Ω=0.08770 °, δ Δ e
x=0.00007057 and δ Δ e
y=0.00007136.
Relative Orbit Elements (relative altitude argument, relatively right ascension of ascending node, the relative eccentric ratio) error that the inventive method is determined reaches 98.89%, 99.93%, 98.80% and 99.09% respectively with the relative accuracy of actual error.
From formula (13), because relative semi-major axis exists error, in the different sampling times, relative altitude argument can change.Therefore get the emulated data of second sampling period interstellar distance of scheduling time section again, star spacing can be obtained
can obtain relative altitude argument with actual relative altitude argument error by formula (12) is 0.005864 °, then can determine that relative semi-major axis is 0.092m by formula (13), and with the contrast of actual semi-major axis relatively, relative accuracy reaches 92.00%.
From formula (14), owing to being subject to the impact of orbit perturbation, right ascension of ascending node can drift about.In different sample times, relative right ascension of ascending node also can change.Get the emulated data of the 3rd sampling period interstellar distance of scheduling time section, star spacing can be obtained
the relative right ascension of ascending node determined respectively by formula (12) is 0.005864 ° and 0.005953 °.Can determine that relative inclination error is 0.00102 ° by formula (14), and practical relative error is 0.001 °, relative accuracy reaches 97.89%.
Can see from this enforcement example, determined Relative Orbit Elements error defining method in the present invention, precision can reach more than 95%, and this is feasible in engineering.
A kind of Relative Orbit Elements defining method based on interstellar distance that the present invention proposes, the method only can obtain the technological means of formation flight system Relative Orbit Elements according to four extreme values of Satellite spacing in formation flight system, the three-dimensional space motion of Satellite Formation Flying is reduced to the two dimensional motion in plane by this method, and the error giving actual star spacing and its nominal value is with a kind of mapping relations between Relative Orbit Elements.Be different from conventional satellite relative position defining method and need to rely on the third party signalling such as land station or GPS source to determine the method for Relative Orbit Elements, this method only needs by resolving with the mapping relations between actual Relative Orbit Elements and its nominal value error the error between actual interstellar distance and its nominal value, the error of actual Relative Orbit Elements and nominal value can be determined, and then determine actual Relative Orbit Elements in conjunction with the design load of Relative Orbit Elements.
Claims (5)
1. based on a Relative Orbit Elements defining method for interstellar distance, in Mission design, several do relative motion from star F around primary M, and the spaceborne computer of primary M receives the star spacing within a sampling period of GPS output; It is characterized in that determining to include the following step based on the Relative Orbit Elements of interstellar distance:
Step one, obtains the extreme value of spacing between star;
Without the star spacing maximum in perturbation situation
and minimum value
The multiple star spacing will gathered in a sampling period T;
Step 2, formulates star spacing with the relation between Relative Orbit Elements;
At the primary orbital coordinate system M-X without perturbation situation
my
mz
munder, primary M with from star F at described M-X
my
mz
munder star spacing be expressed as:
Δ y
nominal=a
nominal(Δ Ω × sini
nominal× cosu
m-Δ i × sinu
m) (1)
Δ z
nominal=a
nominal(Δ e
x× cosu
m+ Δ e
y× sinu
m)
Δ x
nominalrepresent that star spacing is at primary orbital coordinate system M-X
my
mz
mx
mprojection on axle;
Δ y
nominalrepresent that star spacing is at primary orbital coordinate system M-X
my
mz
my
mprojection on axle;
Δ z
nominalrepresent that star spacing is at primary orbital coordinate system M-X
my
mz
mz
mprojection on axle.
In the formation flight of satellite, representing primary symbol M, representing with meeting F from star according to Relative Orbit Elements, then have:
(1) semi-major axis
The semi-major axis of orbit of primary M is designated as a
m, be designated as a from the semi-major axis of orbit of star F
f, unit is rice; Therefore, Δ a is designated as from the relative semi-major axis between star F with primary M, i.e. Δ a=a
f-a
m.A in without perturbation situation
f=a
m, be designated as a
nominal.
(2) excentricity
The orbital eccentricity of primary M is designated as e
m, be designated as e from the orbital eccentricity of star F
f, unit is dimensionless; Therefore, the x of the coordinate system defined from star F and primary M in orbital elements
iexcentricity on axle is designated as
relative eccentric ratio vector is designated as Δ e
x, i.e. Δ e
x=e
fcos ω
f-e
mcos ω
m; The y of the coordinate system defined in orbital elements from star F and primary M
iexcentricity on axle is designated as
relative eccentric ratio vector is designated as Δ e
y, i.e. Δ e
y=e
fsin ω
f-e
msin ω
m.E in without perturbation situation
f=e
m, be designated as e
nominal.
(3) argument of perigee
The argument of perigee of primary M is designated as ω
m, be designated as ω from the argument of perigee of star F
f, unit is degree; Therefore, Δ ω is designated as from the relative argument of perigee between star F with primary M, i.e. Δ ω=ω
f-ω
m.ω in without perturbation situation
f=ω
m, be designated as ω
nominal.
(4) inclination angle
The orbit inclination of primary M is designated as i
m, be designated as i from the orbit inclination of star F
f, unit is degree; Therefore, be designated as Δ i from the relative inclination between star F and primary M, i.e. Δ i=i
f-i
m.I in without perturbation situation
f=i
m, be designated as i
nominal.
(5) latitude argument
The latitude argument of primary M is designated as u
m, be designated as u from the latitude argument of star F
f, unit is degree; Therefore, Δ u is designated as from the relative altitude argument between star F and primary M, i.e. Δ u=u
f-u
m.
(6) right ascension of ascending node
The ascending node of orbit right ascension of primary M is designated as Ω
m, be designated as Ω from the ascending node of orbit right ascension of star F
f, unit is degree; Therefore, Δ Ω is designated as from the relative orbit right ascension of ascending node between star F and primary M, i.e. Δ Ω=Ω
f-Ω
m.
In formation flight process, primary M with from star F at primary orbital coordinate system M-X
my
mz
munder star spacing be expressed as:
Δ y
actual=a
m(Δ Ω × sini
m× cosu
m-Δ i × sinu
m) (2)
Δ z
actual=a
m(Δ e
x× cosu
m+ Δ e
y× sinu
m)
Δ x
actualrepresent that star spacing is at primary orbital coordinate system M-X
my
mz
mx
mprojection on axle;
Δ y
actualrepresent that star spacing is at primary orbital coordinate system M-X
my
mz
my
mprojection on axle;
Δ z
actualrepresent that star spacing is at primary orbital coordinate system M-X
my
mz
mz
mprojection on axle.
Step 3, formulates the mapping relations of the error between star spacing actual value and nominal value and the error between Relative Orbit Elements actual value and nominal value.
2. a kind of Relative Orbit Elements defining method based on interstellar distance according to claim 1, is characterized in that the multiple star spacing extreme values obtained in step one have:
Maximal value
minimum value
second largest value
with secondary minimum value
and
3. a kind of Relative Orbit Elements defining method based on interstellar distance according to claim 1, is characterized in that: in step 2 due to Satellite Formation Flying diametrically move much smaller than along mark to the relative motion of orbital plane normal direction, then Z
mprojection value on axle is 0, therefore described M-X
my
mz
mbe reduced to plane coordinate system M-X
my
m, formula (2) is reduced to:
Δ y
actual=a
m(Δ Ω × sini
m× cosu
m-Δ i × sinu
m)
According to the range formula of point-to-point transmission, at time-sampling point t
samplingthe primary M gathered and be from the star spacing between star F:
Therefore in formation flight object, when satellite under the line position time, star spacing reaches maximal value; When the two poles of the earth, north and south, star spacing arrives minimum value; When other positions, star spacing constantly changes between a minimum value and a maximum value.
4. a kind of Relative Orbit Elements defining method based on interstellar distance according to claim 1, it is characterized in that: in step 3 without the star spacing in perturbation situation, namely two stars are run on the nominal track preset completely, and there is not the situation that Relative Orbit Elements changes;
From star F at plane coordinate system M-X
my
min, from star F at X
msubpoint on axle is designated as
from star F at Y
msubpoint on axle is designated as
primary M and be designated as L from the star spacing nominal value between star F
nominal.Primary M with from the line of star F and Y
maxial angle is designated as β, i.e. formation configuration angle β.Δ x
nominalfor from star F at X
mthe distance nominal value that axle projects, Δ y
nominalfor from star F at Y
mthe distance nominal value that axle projects.
When formation flight system arrives empty position, now u on equator
m=0 ° or 180 °, star spacing reaches maximal value, then square being expressed as of maximum star spacing:
From star F at plane coordinate system M-X
my
min, from star F at Y
mwithout projection on axle, i.e. Δ y
nominal=0, from star F at X
msubpoint on axle is self, i.e. Δ x
nominalfor minor increment.
From star F relative to primary M along Y
mdirection of principal axis does pendular movement, after formation flight system crosses equatorial positions, has two specific positions, i.e. empty position, now u on the two poles of the earth, north and south
m=90 ° or 270 °, star spacing reaches minimum value; Now be positioned at X from star F
mon axle, due to Δ e
xwith Δ e
ydifference is very little, can be approximated to be Δ e
xequal Δ e
y, therefore most starlet spacing almost with Δ x
nominalequal, then square being expressed as of most starlet spacing:
。
5. a kind of Relative Orbit Elements defining method based on interstellar distance according to claim 1, it is characterized in that: in the consideration perturbation situation in step 3, nominal position will be departed from the Relative distribution position of satellite, but the distance that formation configuration departs from nominal value is again very little relative to the distance scale of configuration, therefore the actual motion formation configuration going up empty position under the line can be reduced to: primary M is at plane coordinate system M-X
my
mphysical location, F
actualfor from star F at plane coordinate system M-X
my
mphysical location, M
actualwith F
actualline be parallel to the line of M and F.Cross primary M to do perpendicular to M
actualf
actualline is designated as vertical line MA, crosses and does perpendicular to M from star F
actualf
actualline is designated as vertical line FB;
Consider the deviation of the configuration that the flight in practical situations both of formation flight system occurs and nominal configuration, can obtain:
δ L
maxrepresent the difference of the maximum star spacing/actual value of time large star spacing and the nominal value of maximum star spacing
δ represents variation symbol;
In order to keep the stability of formation configuration, generally get Δ e when formation flight system
y=0, formula (7) is arranged, can obtain:
In formula,
Again formula (6) changes persuing is divided, can obtain
δ L
minrepresent the difference of the actual value of most starlet spacing/time starlet spacing and the nominal value of most starlet spacing
δ represents variation symbol;
In formula (9),
formula (9) is simplified:
δ L
min=a
nominal(δ Δ u+ δ Δ Ω × cosi
nominal± 2 δ Δ e
x) (10)
Simultaneous formula (8) and formula (10), can obtain system of linear equations is:
for described Δ e
yget the δ L of timing
maxvalue;
for described Δ e
yδ L when getting negative
maxvalue;
for described Δ e
xget the δ L of timing
minvalue;
for described Δ e
xδ L when getting negative
minvalue;
Due to δ Δ e
xwith δ Δ e
ythere is positive and negative uncertainty in previous symbol, therefore, the star spacing change relation in time of actual formation flight system characterizes with formula (12), namely
Solve an equation (12) relative altitude argument in the Relative Orbit Elements of master and slave star reality in formation flight system, relatively right ascension of ascending node, nominal value error that relative eccentric ratio vector is corresponding with it can be obtained, that is:
Error between relative altitude argument actual value and relative altitude argument nominal value, is designated as relative altitude argument error delta Δ u;
Error between relative right ascension of ascending node actual value with relative right ascension of ascending node nominal value, is designated as relative right ascension of ascending node error delta Δ Ω;
At geocentric coordinate system O-x
iy
iz
ix
irelative eccentric ratio vector actual value on axle and the error between relative eccentric ratio vector nominal value, be designated as relative eccentric ratio vector error δ Δ e
x;
At geocentric coordinate system O-x
iy
iz
iy
irelative eccentric ratio vector actual value on axle and the error between relative eccentric ratio vector nominal value, be designated as relative eccentric ratio vector error δ Δ e
y.
Error between relative semi-major axis actual value with relative semi-major axis nominal value, is designated as relative semi-major axis error delta Δ a, and
for at a rear time-sampling point t
afterunder the value of described δ Δ u;
for at previous time-sampling point t
beforeunder the value of described δ Δ u;
Error between relative inclination actual value and relative inclination nominal value, is designated as relative inclination error delta Δ i, and
for at a rear time-sampling point t
afterunder the value of described δ Δ Ω;
for at previous time-sampling point t
beforeunder the value of described δ Δ Ω;
N is the operation mean angular velocity of primary M;
According to Δ a, Δ e
x, Δ e
y, Δ i, Δ u and Δ Ω; δ Δ a, δ Δ e
x, δ Δ e
y, δ Δ i, δ Δ u and δ Δ Ω, actual Relative Orbit Elements in formation flight system can be determined, and then determine the configuration of formation flight system.
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