CN103018783A - Gravity satellite formation orbital stability optimization design and earth gravity field precision inversion method - Google Patents

Gravity satellite formation orbital stability optimization design and earth gravity field precision inversion method Download PDF

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CN103018783A
CN103018783A CN2012105779732A CN201210577973A CN103018783A CN 103018783 A CN103018783 A CN 103018783A CN 2012105779732 A CN2012105779732 A CN 2012105779732A CN 201210577973 A CN201210577973 A CN 201210577973A CN 103018783 A CN103018783 A CN 103018783A
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Institute of Geodesy and Geophysics of CAS
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Abstract

The invention relates to a gravity satellite formation orbital stability optimization design and an earth gravity field precision inversion method on the basis of disturbing inter-satellite distance principle, in particular to an orbital stability optimization design method for a four-satellite system (FSS). In order to guarantee the stability of the four-satellite system, the quantity of satellite orbits is optimally designed, orbital semi-major axes, orbital eccentricities, orbital inclinations and right ascensions of ascending nodes keep unchanged, the difference of arguments of perigees each pair of satellites and the difference of mean anomalies of the pair of satellites are 180 degrees respectively, an initial argument of perigee of each satellite is arranged at the equator, an initial mean anomaly of each satellite is arranged at a pole, and the ratio of the semi-major axis of each elliptical orbit of the four-satellite system to a semi-minor axis of the elliptical orbit of the four-satellite system is 2:1. The gravity satellite formation orbital stability optimization design and the earth gravity field precision inversion method have the advantages that an earth gravity field is precisely and quickly inverted on the basis of a disturbing inter-satellite distance process; and the orbits are high in stability owing to the method, the earth gravity field computation precision is effectively improved, the gravity field inversion speed is increased to a great extent, and requirements on the performance of a computer are low.

Description

The design of Gravity Satellite Formation Orbit optimizing stability and accurate inverting terrestrial gravitation field method
Technical field
The present invention relates to the interleaving techniques fields such as space geodesy, satellite gravimetry, geophysics, cosmonautics, particularly relate to a kind of four stars formation system (FSS:Four-Satellite System) orbital stability Optimization Design, and then utilize the interstellar distance of satellite borne laser interference measuring instrument, the satellite orbital position of GPS receiver and the satellite nonconservative force observation data of accelerometer, based on disturbance interstellar distance method of inversion Effective Raise earth gravity field precision.
Background technology
Be to utilize Satellite Tracking satellite height/low low technical (SST-HL/LL:Satellite-to-Satellite Tracking in the High-Low/Low-Low mode) to promote the New Times to " the wisdom earth " cognitive ability this century.As shown in Figure 1, international Gravity Satellite CHAMP(Challenging Minisatellite Payload), GRACE(Gravity Recovery and Climate Experiment) and GOCE(Gravity Field and Steady-State Ocean Circulation Explorer) in succession succeed in sending up and more the emission that is about to of high precision GRACE Follow-On satellite indicating that the mankind will welcome unprecedented high precision Satellite gravity Detection Techniques epoch.Although the more traditional gravimetry technology of GRACE satellite gravity survey technology (vehicle-mounted, boat-carrying and airborne) can be efficiently, high precision and high spatial resolution are surveyed the earth static (middle long wave) and the time change (long wave) gravity field, but the inherent defect of GRACE Gravity Satellite system (the first, can't reduce satellite orbital altitude; The second, can't improve the load measurement precision; The 3rd, can't obtain vertical gravity gradient; The 4th, can't deduct high-frequency signal and obscure) can't eliminate by self-regulation.Therefore, in order effectively to remedy the weak point of GRACE, and then high precision and high spatial resolution set up earth static state (medium short wave) and the time become (middle long wave) gravity field model, only have the New Satellite of enforcement gravimetry plan just can efficient solution to determine (as shown in Figure 2).
Massonnet was applied to the passive radar interferometry with the four stars Formation Technology first in 1998; Sneeuw and Schaub have proposed the new technology based on four stars formation system precision detection earth gravity field in 2004.As shown in Figure 2, as follows based on the main thought of four stars Formation Technology high-acruracy survey earth gravity field: (1) every single star orbits the earth along elliptical orbit separately; (2) barycenter of four stars formation system is with the earth movements of circular orbit pattern ring; (3) every single star rotates (semi-major axis around formation system barycenter with the elliptical orbit form :Semi-minor axis=2 :1).Gravitation potential of earth
Figure 532728DEST_PATH_IMAGE002
Right respectively Second derivative be expressed as follows
Figure 257681DEST_PATH_IMAGE006
（1）
Wherein, the gravitation potential of earth second derivative is symmetric tensor, satisfies the Laplace equation simultaneously under vacuum condition and shows as without mark V Xx + V Yy + V Zz =0, therefore in 9 gravity gradient components, there are 5 to be independently.GRACE is the string type Formation Technology of rail double star employing front and back tracking altogether, and being equivalent to base length is interstellar distance
Figure 542032DEST_PATH_IMAGE008
The horizontal gravity gradient instrument, therefore only can measure the horizontal gravity gradient component of direction of visual lines
Figure 892242DEST_PATH_IMAGE010
The four stars Formation Technology can be measured horizontal and vertical gravity gradient component simultaneously
Figure 920241DEST_PATH_IMAGE012
Because the power spectrum of vertical gravity gradient is about 2 times of the horizontal gravity gradient power spectrum
Figure 39506DEST_PATH_IMAGE014
Therefore, owing to not only having increased vertical gravity gradient signal, and reduced largely satellite orbital altitude and improved the combined influence of crucial load measurement precision, improve at least 10 times based on the precision of four stars Formation Technology inverting earth gravity field than the measuring accuracy of GRACE string type Formation Technology.
Because asymmetry and heterogeneity and the compression of the earth item of earth gravity field J 2Combined influence and effect, the orbital stability of four stars formation system will occur sharply and fast drift.Although the stability that can keep total system by track and the attitude thruster of every satellite self, a large amount of jet fuel consumption will cause the rapidly shortening of four stars formation lifetime of system.Therefore, the optimal design of four stars formation system track radical is to set up the gordian technique of high precision, high spatial resolution and high order earth gravity field model.
Summary of the invention
The objective of the invention is: proposed the orbital stability optimal design of four stars formation system, and further improved the earth gravity field precision based on the disturbance interstellar distance method of inversion.
For achieving the above object, the present invention has adopted following technical scheme:
1) optimal design of orbit elements of satellite
Obtain four Gravity Satellites (FSS-1/2/3/4) formation systematic survey data, every single star edge elliptical orbit separately orbits the earth in described four Gravity Satellites, the barycenter of four stars formation system is with the earth movements of circular orbit pattern ring, and every single star rotates with the elliptical orbit form around formation system barycenter.
Four stars formation system can be by setting 6 Kepler orbit elements (semi-major axis of orbits a, orbital eccentricity e, orbit inclination i, right ascension of ascending node Ω, argument of perigee ωWith initial mean anomaly M) realize, specific rules is as follows: (1) semi-major axis of orbit a, orbital eccentricity e, orbit inclination iAnd right ascension of ascending node ΩRemain unchanged; (2) argument of perigee of every pair of satellite (FSS-1/2 and FSS-3/4) ω 1, ω 2, ω 3With ω 4And mean anomaly M 1, M 2, M 3With M 4Differ respectively 180 o( ω 1= ω 2+ 180 o, ω 3= ω 4+ 180 o M 1= M 2+ 180 o, M 3= M 4+ 180 o), the initial argument of perigee of every satellite is arranged at the place, equator and initial mean anomaly designs in the limit place; (3) setting the semi-major axis of four stars formation system elliptical orbit and the ratio of semi-minor axis is ρ Max : ρ Min=2 :1.The initial argument of perigee of every satellite is arranged at the place, equator and but initial mean anomaly is arranged at the drift of limit place establishment four stars formation system, and then guarantees earth gravity field Measurement sensibility and the accuracy of the system of forming into columns.
The measurement data of described four Gravity Satellite formation systems comprises interstellar distance, satellite orbital position and satellite nonconservative force; By described measurement data inverting earth gravity field.
2) the accurate inverting of earth gravity field
Based on Newton's interpolation formula, single star actual measurement orbital position
Figure 229179DEST_PATH_IMAGE016
Taylor expansion be expressed as follows
Figure 66685DEST_PATH_IMAGE018
（2）
Wherein,
Figure 632796DEST_PATH_IMAGE020
The expression binomial coefficient,
Figure 934464DEST_PATH_IMAGE022
,
Figure 731257DEST_PATH_IMAGE024
The moment of expression calculation level, The initial time of expression interpolation point,
Figure 425860DEST_PATH_IMAGE028
The expression sampling interval,
Figure 316456DEST_PATH_IMAGE030
The quantity of expression interpolation point.
Single star reference orbit position
Figure 51194DEST_PATH_IMAGE032
Taylor expansion be expressed as follows
Figure 660029DEST_PATH_IMAGE034
（3）
By calculating the poor of actual measurement track and reference orbit , can obtain the Taylor expansion of single star disturbance orbital position
Figure 781886DEST_PATH_IMAGE038
（4）
Based on the second derivative of formula (4), single star disturbance orbital acceleration is expressed as follows
Figure 177271DEST_PATH_IMAGE040
（5）
Based on formula (5), double star disturbance orbital acceleration differential representation is as follows
Figure 273403DEST_PATH_IMAGE042
（6）
Wherein,
Figure 985008DEST_PATH_IMAGE044
With
Figure 787878DEST_PATH_IMAGE046
Represent respectively double star Relative Perturbation orbital position vector and Relative Perturbation orbital acceleration vector,
Figure 926736DEST_PATH_IMAGE048
With Represent respectively double star disturbance orbital position vector separately,
Figure 697563DEST_PATH_IMAGE052
With
Figure 620519DEST_PATH_IMAGE054
Represent respectively double star disturbance orbital acceleration vector separately.
In formula (6),
Figure 930278DEST_PATH_IMAGE056
The sight line representation in components as follows
Figure 1002DEST_PATH_IMAGE058
（7）
Wherein,
Figure 490627DEST_PATH_IMAGE060
The unit vector of second satellite is pointed in expression by first satellite.
In formula (7),
Figure 330407DEST_PATH_IMAGE062
Can be rewritten as
Figure 748750DEST_PATH_IMAGE064
（8）
Wherein,
Figure 41191DEST_PATH_IMAGE066
Expression The sight line component,
Figure 530258DEST_PATH_IMAGE070
Expression
Figure 181820DEST_PATH_IMAGE068
Vertical component.
With in the formula (8)
Figure 164819DEST_PATH_IMAGE072
Replace with
Figure 560028DEST_PATH_IMAGE074
, formula (7) can be rewritten as
Figure 108821DEST_PATH_IMAGE076
（9）
Wherein,
Figure 636011DEST_PATH_IMAGE078
,
Figure 903044DEST_PATH_IMAGE080
The disturbance interstellar distance observed quantity of expression laser interferometry instrument.
In formula (9),
Figure 39628DEST_PATH_IMAGE056
Concrete form be expressed as follows,
Figure 442927DEST_PATH_IMAGE082
（10）
Wherein, Expression other Relative Perturbation conservative force except terrestrial gravitation mainly comprises: lunisolar attraction, solid tide power, oceanic tide power, atmospheric tide power and utmost point tidal force, and it can calculate acquisition by setting up model;
Figure 393883DEST_PATH_IMAGE086
Expression Relative Perturbation nonconservative force mainly comprises: atmospherical drag, sun optical pressure, terrestrial radiation are pressed and orbit altitude and attitude control, and it can measure acquisition in real time by star accelerometer; Expression Relative Perturbation center gravitation
Figure 591963DEST_PATH_IMAGE090
（11）
Wherein,
Figure 21807DEST_PATH_IMAGE092
The expression earth quality
Figure 434072DEST_PATH_IMAGE094
And universal gravitational constant
Figure 974774DEST_PATH_IMAGE096
Long-pending;
Figure 555928DEST_PATH_IMAGE098
Disturbance the earth's core radius of expression double star,
Figure 891095DEST_PATH_IMAGE100
Expression disturbance orbital position vector
Figure 620016DEST_PATH_IMAGE102
3 components;
Figure 636514DEST_PATH_IMAGE104
Represent relative earth disturbance gravitation,
Figure 134491DEST_PATH_IMAGE106
,
Figure 578242DEST_PATH_IMAGE108
The expression gradient operator,
Figure 794460DEST_PATH_IMAGE110
With The earth disturbing potential that represents respectively double star
Figure 468597DEST_PATH_IMAGE114
With
Figure 411145DEST_PATH_IMAGE116
Gradient, earth disturbing potential
Figure 786763DEST_PATH_IMAGE118
Be expressed as follows
（12）
Wherein,
Figure 617633DEST_PATH_IMAGE122
Represent respectively the earth's core radius, geocentric colatitude degree and geocentric longitude,
Figure 465503DEST_PATH_IMAGE124
Expression earth mean radius, LThe maximum order that expression earth disturbing potential is pressed spherical function expansion;
Figure 390734DEST_PATH_IMAGE126
Represent normalized association Legendre function, lThe expression exponent number, mThe expression number of times;
Figure 552725DEST_PATH_IMAGE128
With Represent Geopotential coefficient to be estimated.
By with formula (10) substitution formula (9), disturbance interstellar distance observation equation is expressed as follows
Figure 600370DEST_PATH_IMAGE132
（13）
The earth gravity field inversion step of the four stars formation system principle among the present invention is as follows: the FSS-1/2 Double Satellites Observation data of the system of at first four stars being formed into columns and FSS-3/4 Double Satellites Observation data are substitution disturbance interstellar distance observation equation (13) respectively, then unites and finds the solution Geopotential coefficient With
Figure 775316DEST_PATH_IMAGE130
Because disturbance moonscope amount (actual measured amount-reference quantity) is more responsive to the earth gravity field precision, therefore can improve than before 3～5 times based on disturbance interstellar distance observation equation (13) inverting earth gravity field precision.
The orbital stability optimal design that the present invention is based on four stars formation system is conducive to accurately and the characteristics of fast inversion earth gravity field design, and its advantage is: 1) orbital stability of four stars formation system is better; 2) the earth gravity field computational accuracy is higher; 3) orbital stability design process physical meaning is clear and definite; 4) improve largely the earth gravity field inversion speed; 5) require lower to computing power.Be different from domestic and international prior art achievement, the present invention has carried out the stability Design research of four stars formation system track radical again, adopts the initial argument of perigee with every satellite ωBe arranged at place, equator and initial mean anomaly MDesign in north and south limit place, be conducive to keep four stars formation Systems balanth, the drift of establishment four stars formation system; Based on disturbance interstellar distance method, accurately and fast inversion the FSS-1/2/3/4 earth gravity field.
Four, description of drawings
Fig. 1Be the international three phase Gravity Satellites that succeeded in sending up, comprise the single star of CHAMP, NASA (NASA) and the GRACE double star of German space agency (DLR) and the GOCE gravity gradient satellite of European Space Agency (ESA) at German Potsdam earth science research center (GFZ).
Fig. 2Four stars formation systematic survey schematic diagram, wherein satellite orbit semi-major axis a, orbital eccentricity e, orbit inclination iAnd right ascension of ascending node ΩRemain unchanged the argument of perigee of every pair of satellite ωAnd mean anomaly MDiffer respectively 180 o, the initial argument of perigee of every satellite ωBe arranged at place, equator and initial mean anomaly MDesign in north and south limit place, and the ratio of the semi-major axis of satellites formation system elliptical orbit and semi-minor axis is 2:1.
Fig. 3It is the optimal design parameter table of four stars formation system track radical.
Fig. 4 aIt is the argument of perigee (north and south limit) of FSS-1/2 satellite.
Fig. 4 bIt is the mean anomaly (equator) of FSS-1/2 satellite.
Fig. 4 cIt is the interstellar distance of FSS-1/2 in the four stars formation system.
Fig. 5 aIt is the argument of perigee (equator) of FSS-3/4 satellite.
Fig. 5 bIt is the mean anomaly (north and south limit) of FSS-3/4 satellite.
Fig. 5 cIt is the interstellar distance of FSS-3/4 in the four stars formation system.
Fig. 6 aIt is the interstellar distance coloured noise of laser interferometry instrument.
Fig. 6 bIt is the orbital position coloured noise of GPS receiver.
Fig. 6 cIt is the nonconservative force coloured noise of accelerometer.
Fig. 7Be based on disturbance interstellar distance method inverting 120 rank FSS-1/2/3/4 accumulative total geoid surface precision.
Embodiment
Below in conjunction with accompanying drawing, the specific embodiment of the present invention is further described.
The design of Gravity Satellite Formation Orbit optimizing stability and accurate inverting terrestrial gravitation field method are:
1) optimal design of orbit elements of satellite
Obtain four Gravity Satellites (FSS-1/2/3/4) formation systematic survey data, every single star edge elliptical orbit separately orbits the earth in described four Gravity Satellites, the barycenter of four stars formation system is with the earth movements of circular orbit pattern ring, and every single star rotates with the elliptical orbit form around formation system barycenter.
As shown in Figure 2, four stars formation system can be by setting 6 Kepler orbit elements (semi-major axis of orbits a, orbital eccentricity e, orbit inclination i, right ascension of ascending node Ω, argument of perigee ωWith initial mean anomaly M) realize, specific rules is as follows: (1) semi-major axis of orbit a, orbital eccentricity e, orbit inclination iAnd right ascension of ascending node ΩRemain unchanged; (2) argument of perigee of every pair of satellite (FSS-1/2 and FSS-3/4) ω 1, ω 2, ω 3With ω 4And mean anomaly M 1, M 2, M 3With M 4Differ respectively 180 o( ω 1= ω 2+ 180 o, ω 3= ω 4+ 180 o M 1= M 2+ 180 o, M 3= M 4+ 180 o), the initial argument of perigee of every satellite is arranged at the place, equator and initial mean anomaly designs in north and south limit place; (3) setting the semi-major axis of four stars formation system elliptical orbit and the ratio of semi-minor axis is ρ Max : ρ Min=2 :1.The measurement data of described four Gravity Satellite formation systems comprises the interstellar distance of satellite borne laser interference measuring instrument, the satellite orbital position of GPS receiver and the satellite nonconservative force of accelerometer; By described measurement data inverting earth gravity field.
The present invention utilize the linear single-step process of Runge-Kutta in conjunction with 12 rank Adams-Cowell linear multistep method Numerical Integral Formulas analogue simulations the FSS-1/2/3/4 satellite orbit, wherein orbit altitude 250 km, observation time 30 days, sampling interval 10 s, reference to gravitational model E GM2008, Kepler orbit elements as shown in Figure 3.When the satellite argument of perigee ω(Fig. 4 a) and mean anomaly to be arranged at limit place, north and south MWhen being arranged at Chi Daochu (Fig. 4 b), four stars formation system drifting will increasingly sharpen; Shown in Fig. 4 c, the interstellar distance of FSS-1/2 increases by 50 km every day at least in the four stars formation system, and then can't realize the stable mutually tracking of FSS-1/2 satellite.The present invention adopts the argument of perigee of every satellite ω(Fig. 5 a) and mean anomaly to be arranged at Chi Daochu MBe arranged at limit place, north and south (Fig. 5 b), so four stars formation system is highly stable; Shown in Fig. 5 c, the interstellar distance stable maintenance of FSS-3/4 does not increase and unlimited the increase in time at 50～110 km in the four stars formation system.Contrast as can be known by Fig. 4 c and 5c, the initial argument of perigee of every satellite is arranged at the place, equator and but initial mean anomaly is arranged at the drift of limit place, north and south establishment four stars formation system, and then guarantees earth gravity field Measurement sensibility and the accuracy of the system of forming into columns.
2) the accurate inverting of earth gravity field
Based on Newton's interpolation formula, the Taylor expansion of single star actual measurement orbital position is expressed as follows
（14）
Wherein, The expression binomial coefficient,
Figure 187340DEST_PATH_IMAGE022
,
Figure 753451DEST_PATH_IMAGE024
The moment of expression calculation level,
Figure 727223DEST_PATH_IMAGE026
The initial time of expression interpolation point, The expression sampling interval,
Figure 740496DEST_PATH_IMAGE030
The quantity of expression interpolation point.
Single star reference orbit position
Figure 283866DEST_PATH_IMAGE134
Taylor expansion be expressed as follows
Figure 440041DEST_PATH_IMAGE034
（15）
Based on formula (14)-(15), single star disturbance orbital position
Figure 174778DEST_PATH_IMAGE136
Taylor expansion be expressed as follows
（16）
Wherein,
Figure 957107DEST_PATH_IMAGE036
Based on the second derivative of formula (16), single star disturbance orbital acceleration is expressed as follows
Figure 905471DEST_PATH_IMAGE040
（17）
Based on formula (17), double star disturbance orbital acceleration differential representation is as follows
（18）
Wherein, With
Figure 353267DEST_PATH_IMAGE046
Represent respectively double star Relative Perturbation orbital position vector and Relative Perturbation orbital acceleration vector,
Figure 920252DEST_PATH_IMAGE048
With
Figure 59110DEST_PATH_IMAGE050
Represent respectively double star disturbance orbital position vector separately,
Figure 642538DEST_PATH_IMAGE052
With
Figure 829937DEST_PATH_IMAGE054
Represent respectively double star disturbance orbital acceleration vector separately.
In formula (18), The sight line representation in components as follows
Figure 62652DEST_PATH_IMAGE058
（19）
Wherein,
Figure 133376DEST_PATH_IMAGE060
The unit vector of second satellite is pointed in expression by first satellite.
In formula (19), Can be rewritten as
Figure 964246DEST_PATH_IMAGE064
（20）
Wherein,
Figure 444906DEST_PATH_IMAGE066
Expression
Figure 188213DEST_PATH_IMAGE068
The sight line component, Expression Vertical component.
With in the formula (20)
Figure 328842DEST_PATH_IMAGE072
Replace with
Figure 374158DEST_PATH_IMAGE074
, formula (19) can be rewritten as
Figure 707051DEST_PATH_IMAGE076
（21）
Wherein,
Figure 255844DEST_PATH_IMAGE078
,
Figure 281568DEST_PATH_IMAGE080
The disturbance interstellar distance observed quantity of expression laser interferometry instrument.
In formula (21),
Figure 548602DEST_PATH_IMAGE056
Concrete form be expressed as follows,
（22）
Wherein,
Figure 587020DEST_PATH_IMAGE084
Expression other Relative Perturbation conservative force (established model calculating) except terrestrial gravitation mainly comprises: lunisolar attraction, solid tide power, oceanic tide power, atmospheric tide power, utmost point tidal force etc.;
Figure 845963DEST_PATH_IMAGE086
Expression Relative Perturbation nonconservative force (star accelerometer measurement) mainly comprises: atmospherical drag, sun optical pressure, terrestrial radiation pressure, orbit altitude and attitude control etc.;
Figure 272396DEST_PATH_IMAGE088
Expression Relative Perturbation center gravitation
Figure 274987DEST_PATH_IMAGE090
（23）
Wherein, The expression earth quality
Figure 900320DEST_PATH_IMAGE094
And universal gravitational constant
Figure 141946DEST_PATH_IMAGE096
Long-pending;
Figure 620332DEST_PATH_IMAGE098
Disturbance the earth's core radius of expression double star,
Figure 998223DEST_PATH_IMAGE100
Expression disturbance orbital position vector
Figure 38117DEST_PATH_IMAGE102
3 components;
Figure 501459DEST_PATH_IMAGE104
Represent relative earth disturbance gravitation,
Figure 783536DEST_PATH_IMAGE106
,
Figure 281514DEST_PATH_IMAGE108
The expression gradient operator,
Figure 787581DEST_PATH_IMAGE110
With
Figure 941482DEST_PATH_IMAGE112
The earth disturbing potential that represents respectively double star With
Figure 114155DEST_PATH_IMAGE116
Gradient, earth disturbing potential
Figure 791124DEST_PATH_IMAGE118
Be expressed as follows
（24）
Wherein,
Figure 351473DEST_PATH_IMAGE122
Represent respectively the earth's core radius, geocentric colatitude degree and geocentric longitude, Expression earth mean radius, LThe maximum order that expression earth disturbing potential is pressed spherical function expansion;
Figure 609596DEST_PATH_IMAGE126
Represent normalized association Legendre function, lThe expression exponent number, mThe expression number of times; With
Figure 696817DEST_PATH_IMAGE130
Represent Geopotential coefficient to be estimated.
By with formula (22) substitution formula (21), disturbance interstellar distance observation equation is expressed as follows
Figure 23894DEST_PATH_IMAGE132
（25）
The earth gravity field inversion step of the four stars formation system principle among the present invention is as follows: at first, and with the four stars respectively substitution disturbance interstellar distance observation equation (25) of the FSS-1/2 Double Satellites Observation data of system and FSS-3/4 Double Satellites Observation data of forming into columns; Then, two prescription journeys are merged into a large-scale overdetermined equation group, namely the equation number is greater than the unknown number number; At last, by least square method, solve Geopotential coefficient
Figure 308244DEST_PATH_IMAGE128
With
Figure 392875DEST_PATH_IMAGE130
It will be understood by those skilled in the art that based on above-mentioned about Geopotential coefficient
Figure 420874DEST_PATH_IMAGE128
With System of equations, also can adopt other data processing method combined calculation to obtain earth gravity field.Because disturbance moonscope amount (actual measured amount-reference quantity) is more responsive to the earth gravity field precision, therefore can improve than before 3～5 times based on disturbance interstellar distance observation equation (25) inverting earth gravity field precision.
Based on the Gauss-Markov model, the coloured noise of analog satellite observed reading is expressed as follows
Figure 496857DEST_PATH_IMAGE138
（26）
Wherein,
Figure 396679DEST_PATH_IMAGE140
The expression related coefficient; The random white noise of expression normal distribution, jThe number of expression observation station;
Figure 936562DEST_PATH_IMAGE144
The coloured noise that expression has correlativity.
Fig. 6 a～6c represents respectively based on Gauss-Markov coloured noise model, utilizes interstellar distance coloured noise and orbital position and the axial coloured noise of nonconservative force x of related coefficient (nonconservative force 0.90 of the interstellar distance 0.85 of laser interferometry instrument, the orbital position 0.95 of GPS receiver, star accelerometer) and sampling interval 10 s simulation.By adding coloured noise, make the nonconservative force observation data of the orbital position of interstellar distance, GPS receiver of the four stars formation system laser interferometry instrument of numerical simulation and star accelerometer closer to measured data, improve the checking precision of earth gravity field inverting of the present invention.
As shown in Figure 7, dotted line represents the measured precision of the 120 terrace gravity field model E IGEN-GRACE02S that announce at German Potsdam earth science research center (GFZ), and accumulative total geoid surface precision is 1.894 * 10 at place, 120 rank -1M; Asterisk line and solid line represent respectively based on double star string type (GRACE-II) and four stars formation system of the present invention (FSS-1/2/3/4), by related coefficient (nonconservative force 0.90 of the interstellar distance 0.85 of laser interferometry instrument, the orbital position 0.95 of GPS receiver and star accelerometer), observation time 30 days and sampling interval 10 s, based on the simulation precision of disturbance interstellar distance method inverting GRACE-II and FSS-1/2/3/4 earth gravity field, accumulative total geoid surface precision is respectively 4.785 * 10 at place, 120 rank -4M and 1.162 * 10 -4M.Result of study shows: the first, with respect to GRACE-II double star string type formation system because FSS-1/2/3/4 four stars formation of the present invention system has increased the measurement of vertical gravity gradient signal, so Effective Raise the sensing precision of middle long wave earth gravity field.At 120 rank places, improve approximately 4 times based on the precision of FSS-1/2/3/4 four stars formation parity inversion earth gravity field of the present invention than the inversion accuracy of GRACE-II double star string type formation system.The second, improve at least 10 times based on the inversion accuracy of the more current GRACE satellite of precision of FSS-1/2/3/4 four stars formation parity inversion earth gravity field of the present invention.
3) characteristics of four stars formation system
The first, can reduce largely satellite orbital altitude.Because GRACE double star string type formation system adopts star accelerometer to measure in real time nonconservative force at rail, then deducts the nonconservative force effect in Data Post again.Therefore, because the negative interference of nonconservative force, the orbit altitude of GRACE satellite (500 km) can't effectively reduce.Studies show that both at home and abroad: every reduction by 100 km of Gravity Satellite orbit altitude, the nonconservative force (take atmospherical drag as main) that acts on satelloid approximately increases by 10 times.For quiet and stable working environment and then its measuring accuracy of Effective Raise (suitably shorten and measure dynamic range) being provided for the crucial load of Gravity Satellite, and by shielding action in the nonconservative force (atmospherical drag, sun optical pressure, terrestrial radiation pressure, orbit altitude and attitude control etc.) of satelloid and then effectively prolong serviceable life of satellite, nonconservative force bucking-out system (DFCS:Drag-Free Control System) will be carried by four stars formation system.Therefore, four stars formation system can substantively reduce satellite orbital altitude (250 km), and then establishment terrestrial gravitation field signal is with the exponential damping effect of satellite orbital altitude increase.
The second, can substantively improve crucial load measurement precision.GRACE double star string type formation system adopts K wave band measuring instrument to measure speed (1 μ m/s) between interstellar distance (10 μ m) and star, acts on simultaneously the nonconservative force (10 of satelloid based on the SuperSTAR accelerometer measures -10M/s 2).In order further to reduce crucial load error to the negative effect of earth gravity field precision, four stars formation system will carry more high-precision laser interferometry instrument and accurately measure speed (1 nm/s) between interstellar distance (10 nm) and star, act on simultaneously the nonconservative force (10 of satelloid by nonconservative force bucking-out system high precision balance -13M/s 2).Because the crucial load measurement precision of four stars formation system is able to significant lifting, therefore can improve at least 10 times based on the more current model accuracy based on GRACE double star string type formation system made of the earth gravity field model precision of four stars formation system made.
The 3rd, can measure simultaneously three-dimensional gravity gradient observed reading.Because GRACE double star string type formation system is equivalent to the horizontal gravity gradient instrument that base length is interstellar distance (220 km), so GRACE can't obtain vertical gravity gradient signal, and then lost largely the earth gravity field precision.Four stars formation system can accurately obtain three-dimensional gravity gradient (level and vertical) observation signal simultaneously, not only can increase substantially precision and the spatial resolution of earth gravity field, and can effectively remove the warp-wise band error (isotropy is more excellent) that terrestrial time that the disappearance owing to vertical gravity gradient signal causes becomes gravity field.
The 4th, but the confusion effect of establishment high-frequency signal.The confusion effect of the high frequency errors such as atmosphere and oceanic tide variation is the most critical factor of loss GRACE earth gravity field inversion accuracy.Because the high frequency errors such as GRACE atmosphere and oceanic tide variation are close to atmosphere and oceanic tide computation model error, thus the high frequency errors such as atmosphere and oceanic tide variation difficult from the GRACE earth gravity field model accurate deduction.Four stars formation system, not only can be similar to the gravity gradient component of GRACE double star string type formation systematic survey direction of visual lines, to increase simultaneously the gravity gradient signal of measuring perpendicular to direction of visual lines, be intended to cut down the high frequency confusion effect to the negative interference of earth gravity field inversion accuracy.
The 5th, become the gravity field signal in the detectable earth during long wave.Become gravity field signal (spatial resolution is 400 km approximately) when GRACE double star string type formation system only can survey earth long wave, become gravity field signal (spatial resolution is better than 200 km) when can't high precision determining in the earth long wave.Four stars formation system becomes the sensing precision of gravity field signal when adopting measuring instrument and nonconservative force bucking-out system between novel and accurate laser interference star will increase substantially long wave in the earth, be intended to for the science such as seismology, thalassography, glaciology, hydrology and national defence crossing research field provide more high precision and more the terrestrial time of high spatial resolution become gravity field information.

Claims (2)

1. one kind is adopted Gravity Satellite formation inverting terrestrial gravitation field method, it is characterized in that:
Obtain four Gravity Satellite FSS-1/2/3/4 formation systematic survey data, every single star of described four Gravity Satellites orbits the earth along elliptical orbit separately, the barycenter of four stars formation system is with the earth movements of circular orbit pattern ring, and every single star rotates with the elliptical orbit form around formation system barycenter;
Wherein, 6 Kepler orbit elements of four Gravity Satellite formation defaults comprise semi-major axis of orbit a, orbital eccentricity e, orbit inclination i, right ascension of ascending node Ω, argument of perigee ωWith initial mean anomaly M, wherein,
The semi-major axis of orbit of the first, four Gravity Satellite a, orbital eccentricity e, orbit inclination iAnd right ascension of ascending node ΩIn the satellite transit process, remain unchanged;
The second, the argument of perigee of the every couple of satellite FSS-1/2 and FSS-3/4 ω 1, ω 2, ω 3With ω 4And mean anomaly M 1, M 2, M 3With M 4Differ respectively 180 o, ω 1= ω 2+ 180 o, ω 3= ω 4+ 180 o, M 1= M 2+ 180 o, M 3= M 4+ 180 o, the initial argument of perigee of every satellite is arranged at the place, equator and initial mean anomaly designs in the limit place;
The semi-major axis of the three, four Gravity Satellite formation system elliptical orbit ρ MaxAnd semi-minor axis ρ MinRatio be ρ Max : ρ Min=2 :1;
The measurement data of described four Gravity Satellite formation systems comprises the interstellar distance of satellite borne laser interference measuring instrument, the satellite orbital position of GPS receiver and the satellite nonconservative force of accelerometer; By described measurement data inverting earth gravity field.
2. according to the method for the described Gravity Satellite formation of claim 1 inverting earth gravity field, it is characterized in that,
Described method by measurement data inverting earth gravity field is,
Calculate the Taylor expansion of single star actual measurement orbital position based on Newton's interpolation formula
Figure 981162DEST_PATH_IMAGE001
（1）
Wherein,
Figure 377509DEST_PATH_IMAGE002
The expression binomial coefficient, , The moment of expression calculation level,
Figure 5302DEST_PATH_IMAGE005
The initial time of expression interpolation point,
Figure 521734DEST_PATH_IMAGE006
The expression sampling interval,
Figure 831493DEST_PATH_IMAGE007
The quantity of expression interpolation point;
The Taylor expansion of single star reference orbit position is expressed as follows
Figure 902217DEST_PATH_IMAGE008
（2）
Can obtain single star disturbance orbital position based on formula (1)-(2)
Figure 362148DEST_PATH_IMAGE009
Taylor expansion
Figure 201928DEST_PATH_IMAGE010
（3）
Wherein,
Figure 213746DEST_PATH_IMAGE011
Second derivative based on formula (3) can obtain single star disturbance orbital acceleration
Figure 506187DEST_PATH_IMAGE012
（4）
Can obtain double star disturbance orbital acceleration difference based on formula (4)
Figure 363285DEST_PATH_IMAGE013
（5）
Wherein,
Figure 713364DEST_PATH_IMAGE014
With
Figure 364925DEST_PATH_IMAGE015
Represent respectively double star Relative Perturbation orbital position vector and Relative Perturbation orbital acceleration vector,
Figure 941400DEST_PATH_IMAGE016
With
Figure 336609DEST_PATH_IMAGE017
Represent respectively double star disturbance orbital position vector separately,
Figure 885402DEST_PATH_IMAGE018
With
Figure 379969DEST_PATH_IMAGE019
Represent respectively double star disturbance orbital acceleration vector separately;
In formula (5), Concrete form be expressed as follows
Figure 377060DEST_PATH_IMAGE021
（6）
Wherein,
Figure 780360DEST_PATH_IMAGE022
Expression other Relative Perturbation conservative force except terrestrial gravitation mainly comprises: lunisolar attraction, solid tide power, oceanic tide power, atmospheric tide power and utmost point tidal force;
Figure 39303DEST_PATH_IMAGE023
Expression Relative Perturbation nonconservative force mainly comprises: atmospherical drag, sun optical pressure, terrestrial radiation are pressed and orbit altitude and attitude control;
Figure 449425DEST_PATH_IMAGE024
Expression Relative Perturbation center gravitation
Figure 186436DEST_PATH_IMAGE025
（7）
Wherein, The expression earth quality
Figure 670824DEST_PATH_IMAGE027
And universal gravitational constant It is long-pending,
Figure 594098DEST_PATH_IMAGE029
Disturbance the earth's core radius of expression double star,
Figure 768727DEST_PATH_IMAGE030
Expression disturbance orbital position vector 3 components;
Figure 488608DEST_PATH_IMAGE032
Represent relative earth disturbance gravitation,
Figure 567422DEST_PATH_IMAGE033
,
Figure 65400DEST_PATH_IMAGE034
The expression gradient operator,
Figure 102626DEST_PATH_IMAGE035
With The earth disturbing potential that represents respectively double star
Figure 607873DEST_PATH_IMAGE037
With
Figure 960357DEST_PATH_IMAGE038
Gradient, earth disturbing potential Be expressed as follows
Figure 871999DEST_PATH_IMAGE040
（8）
Wherein,
Figure 292616DEST_PATH_IMAGE041
Represent respectively the earth's core radius, geocentric colatitude degree and geocentric longitude,
Figure 420978DEST_PATH_IMAGE042
Expression earth mean radius, LThe maximum order that expression earth disturbing potential is pressed spherical function expansion;
Figure 268848DEST_PATH_IMAGE043
Represent normalized association Legendre function, lThe expression exponent number, mThe expression number of times;
Figure 725237DEST_PATH_IMAGE044
With
Figure 949545DEST_PATH_IMAGE045
Represent Geopotential coefficient to be estimated;
By with formula (6) substitution formula (5), disturbance interstellar distance observation equation is expressed as follows
Figure 276621DEST_PATH_IMAGE046
（9）
Wherein,
Figure 967497DEST_PATH_IMAGE047
, The disturbance interstellar distance observed quantity of expression laser interferometry instrument, The unit vector of second satellite is pointed in expression by first satellite;
With the measurement data difference substitution disturbance interstellar distance observation equation (9) of two couples of double star FSS-1/2 and FSS-3/4, then unite and find the solution Geopotential coefficient
Figure 855184DEST_PATH_IMAGE044
With
Figure 310436DEST_PATH_IMAGE045
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