CN103018783B - Gravity satellite formation orbital stability optimization design and earth gravity field precision inversion method - Google Patents

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 Rigorous inversion 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 fleet system (FSS:Four-Satellite System) orbital stability Optimization Design, and then utilize the satellite nonconservative force observation data of the interstellar distance of satellite borne laser interference measuring instrument, the satellite orbital position of GPS and accelerometer, effectively improve earth gravity field precision based on the disturbance interstellar distance method of inversion.

Background technology

This century utilizes the New Times of satellite to satellite tracking height/low low technical (SST-HL/LL:Satellite-to-Satellite Tracking in the High-Low/Low-Low mode) lifting to " the wisdom earth " cognitive ability.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 high precision GRACE Follow-On satellite imply that by transmitting the mankind will welcome unprecedented high precision satellite gravity surveying technology epoch.Although GRACE satellite gravity survey technology comparatively Conventional gravity measuring technique (vehicle-mounted, boat-carrying and airborne) can efficiently, high precision and high spatial resolution detection earth static state (middle long wave) and time change (long wave) gravity field, but the inherent defect of GRACE Gravity Satellite system (the first, cannot satellite orbital altitude be reduced; The second, load measurement precision cannot be improved; 3rd, vertical gravity gradient cannot be obtained; 4th, high-frequency signal cannot be deducted and obscure) cannot be eliminated by self-regulation.Therefore, in order to effectively make up the weak point of GRACE, and then high precision and high spatial resolution set up earth static state (medium short wave) and time become (middle long wave) gravity field model, only have implement New Satellite gravimetry plan just can efficient solution certainly (as shown in Figure 2).

Four stars Formation Technology was applied to passive radar interferometry in 1998 by Massonnet first; Sneeuw and Schaub proposed the new technology based on four stars fleet system precision detection earth gravity field in 2004.As shown in Figure 2, the main thought based on four stars Formation Technology high-acruracy survey earth gravity field is as follows: the single star in (1) every orbits the earth along respective elliptical orbit; (2) barycenter of four stars fleet system is with the earth movements of circular orbit pattern ring; (3) every single star rotates (semi-major axis around fleet system barycenter with elliptical orbit form :semi-minor axis=2 :1).Gravitation potential of earth right respectively second derivative be expressed as follows

（1）

Wherein, gravitation potential of earth second derivative is symmetric tensor, meets Laplace equation simultaneously and show as without mark under vacuum condition v _xx + v _yy + v _zz =0, therefore in 9 gravity gradient component, having 5 is independently.The string type Formation Technology followed the tracks of before and after GRACE common rail double star adopts, being equivalent to base length is interstellar distance horizontal gravity gradient instrument, therefore only can measure the horizontal gravity gradient component of direction of visual lines ; Four stars Formation Technology can measure horizontal and vertical gravity gradient component simultaneously .Power spectrum due to vertical gravity gradient is about 2 times of horizontal gravity gradient power spectrum therefore, owing to not only increasing vertical gravity gradient signal, and reducing satellite orbital altitude and the combined influence that improve crucial load measurement precision largely, the precision based on four stars Formation Technology inverting earth gravity field at least improves 10 times compared with the measuring accuracy of GRACE string type Formation Technology.

Due to the asymmetry of earth gravity field and heterogeneity and compression of the earth item j ₂combined influence and effect, generation sharply and is fast drifted about by the orbital stability of four stars fleet system.Although can be maintained the stability of total system by the track of every satellite self and attitude thruster, a large amount of jet fuel consumption will cause the shortening rapidly in four stars fleet system life-span.Therefore, the optimal design of four stars fleet system orbital tracking sets up the gordian technique of high precision, high spatial resolution and high order earth gravity field model.

Summary of the invention

The object of the invention is: the orbital stability optimal design proposing four stars fleet system, and further increase earth gravity field precision based on the disturbance interstellar distance method of inversion.

For achieving the above object, present invention employs following technical scheme:

1) optimal design of orbit elements of satellite

Obtain four Gravity Satellite (FSS-1/2/3/4) fleet system measurement data, in described four Gravity Satellites, every single star orbits the earth along respective elliptical orbit, the barycenter of four stars fleet system is with the earth movements of circular orbit pattern ring, and every single star rotates with elliptical orbit form around fleet system barycenter.

Four stars fleet system is 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 often 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 180 respectively ^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 equator place and initial mean anomaly designs in limit place; (3) ratio of the semi-major axis and semi-minor axis that set four stars fleet system elliptical orbit is ρ _max : ρ _min=2 :1.The initial argument of perigee of every satellite is arranged at equator place and initial mean anomaly and is arranged at the drift that limit place effectively can suppress four stars fleet system, and then guarantees earth gravity field Measurement sensibility and the accuracy of fleet system.

The measurement data of described four Gravity Satellite fleet system comprises interstellar distance, satellite orbital position and satellite nonconservative force; By described measurement data inverting earth gravity field.

2) exact inversion of earth gravity field

Based on Newton's interpolation formula, single star actual measurement orbital position taylor expansion be expressed as follows

（2）

Wherein, represent binomial coefficient, , represent the moment of calculation level, represent the initial time of interpolation point, represent sampling interval, represent the quantity of interpolation point.

Single star reference orbit position taylor expansion be expressed as follows

（3）

By calculating the difference of actual measurement track and reference orbit , the Taylor expansion of single star disturbance orbital position can be obtained

（4）

Based on the second derivative of formula (4), single star disturbance orbital acceleration is expressed as follows

（5）

Based on formula (5), double star disturbance orbital acceleration differential representation is as follows

（6）

Wherein, with represent double star Relative Perturbation orbital position vector Relative Perturbation orbital acceleration vector respectively, with represent double star disturbance orbital position vector separately respectively, with represent double star disturbance orbital acceleration vector separately respectively.

In formula (6), sight line representation in components as follows

（7）

Wherein, represent the unit vector being pointed to second satellite by first satellite.

In formula (7), can be rewritten as

（8）

Wherein, represent sight line component, represent vertical component.

By in formula (8) replace with , formula (7) can be rewritten as

（9）

Wherein, , represent the disturbance interstellar distance observed quantity of laser interferometry instrument.

In formula (9), concrete form be expressed as follows,

（10）

Wherein, represent other Relative Perturbation conservative force except terrestrial gravitation, mainly comprise: lunisolar attraction, solid tide power, oceanic tide power, atmospheric tide power and pole tidal force, it calculates by Modling model and obtains; represent Relative Perturbation nonconservative force, mainly comprise: atmospherical drag, solar light pressure, terrestrial radiation pressure and orbit altitude and gesture stability power, it measures acquisition in real time by star accelerometer; represent Relative Perturbation center gravitation

（11）

Wherein, represent earth quality and universal gravitational constant long-pending; represent disturbance the earth's core radius of double star, represent disturbance orbital position vector 3 components; represent relative earth disturbance gravitation, , represent gradient operator, with represent the earth disturbing potential of double star respectively with gradient, earth disturbing potential be expressed as follows

（12）

Wherein, represent the earth's core radius, geocentric colatitude degree and geocentric longitude respectively, represent earth mean radius, lrepresent that earth disturbing potential presses the maximum order of spherical function expansion; represent normalized association Legendre function, lrepresent exponent number, mrepresent number of times; with represent Geopotential coefficient to be estimated.

By formula (10) is substituted into formula (9), disturbance interstellar distance observation equation is expressed as follows

（13）

The earth gravity field inversion step of the four stars fleet system principle in the present invention is as follows: first the FSS-1/2 Double Satellites Observation data of four stars fleet system and FSS-3/4 Double Satellites Observation data are substituted into disturbance interstellar distance observation equation (13) respectively, then combine and solve Geopotential coefficient with .Because disturbance moonscope amount (actual measured amount-reference quantity) is more responsive to earth gravity field precision, therefore 3 ~ 5 times can be improved than before based on disturbance interstellar distance observation equation (13) inverting earth gravity field precision.

The present invention is conducive to accurately based on the orbital stability optimal design of four stars fleet system and the feature of fast inversion earth gravity field designs, and its advantage is: 1) orbital stability of four stars fleet system is better; 2) earth gravity field computational accuracy is higher; 3) orbital stability design process physical meaning is clear and definite; 4) earth gravity field inversion speed is improved largely; 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 fleet system orbital tracking again, adopts the initial argument of perigee of every satellite ωbe arranged at equator place and initial mean anomaly mdesign in limit place, north and south, be conducive to the stability keeping four stars fleet system, effectively suppress the drift of four stars fleet system; Based on disturbance interstellar distance method, accurately and fast inversion FSS-1/2/3/4 earth gravity field.

four, accompanying drawing explanation

fig. 1be the international three phase Gravity Satellites succeeded in sending up, comprise the mono-star of CHAMP of German Potsdam earth science research center (GFZ), NASA (NASA) and the GRACE double star of German space agency (DLR) and the GOCE gravity gradient satellite of European Space Agency (ESA).

fig. 2four stars fleet system measuring principle figure, 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 often pair of satellite ωand mean anomaly mdiffer 180 respectively ^o, the initial argument of perigee of every satellite ωbe arranged at equator place and initial mean anomaly mdesign in limit place, north and south, and the semi-major axis of satellites formation system elliptical orbit and the ratio of semi-minor axis are 2:1.

fig. 3it is the optimal design parameter table of four stars fleet system orbital tracking.

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 four stars fleet 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 four stars fleet 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.

fig. 6 cit is the nonconservative force coloured noise of accelerometer.

fig. 7add up geoid surface precision based on disturbance interstellar distance method inverting 120 rank FSS-1/2/3/4.

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 Rigorous inversion terrestrial gravitation field method are:

1) optimal design of orbit elements of satellite

Obtain four Gravity Satellite (FSS-1/2/3/4) fleet system measurement data, in described four Gravity Satellites, every single star orbits the earth along respective elliptical orbit, the barycenter of four stars fleet system is with the earth movements of circular orbit pattern ring, and every single star rotates with elliptical orbit form around fleet system barycenter.

As shown in Figure 2, four stars fleet system is 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 often 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 180 respectively ^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 equator place and initial mean anomaly designs in limit place, north and south; (3) ratio of the semi-major axis and semi-minor axis that set four stars fleet system elliptical orbit is ρ _max : ρ _min=2 :1.The measurement data of described four Gravity Satellite fleet system comprises the satellite nonconservative force of the interstellar distance of satellite borne laser interference measuring instrument, the satellite orbital position of GPS and accelerometer; By described measurement data inverting earth gravity field.

The present invention's FSS-1/2/3/4 satellite orbit that utilized Runge-Kutta linear one-step method in conjunction with 12 rank Adams-Cowell linear multistep method Numerical Integral Formulas analogue simulations, 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 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), the drift of four stars fleet system will increasingly sharpen; As illustrated in fig. 4 c, in four stars fleet system, the interstellar distance of FSS-1/2 at least increases by 50 km every day, and then cannot realize the stable tracking mutually 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), therefore four stars fleet system is highly stable; As shown in Figure 5 c, in four stars fleet system, the interstellar distance stable maintenance of FSS-3/4 is at 50 ~ 110 km, does not increase in time and infinitely increases.Contrast known by Fig. 4 c and 5c, the initial argument of perigee of every satellite is arranged at equator place and initial mean anomaly and is arranged at the drift that limit place, north and south effectively can suppress four stars fleet system, and then guarantee earth gravity field Measurement sensibility and the accuracy of fleet system.

2) exact inversion 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, represent binomial coefficient, , represent the moment of calculation level, represent the initial time of interpolation point, represent sampling interval, represent the quantity of interpolation point.

Single star reference orbit position taylor expansion be expressed as follows

（15）

Based on formula (14)-(15), single star disturbance orbital position taylor expansion be expressed as follows

（16）

Wherein, .

Based on the second derivative of formula (16), single star disturbance orbital acceleration is expressed as follows

（17）

Based on formula (17), double star disturbance orbital acceleration differential representation is as follows

（18）

Wherein, with represent double star Relative Perturbation orbital position vector Relative Perturbation orbital acceleration vector respectively, with represent double star disturbance orbital position vector separately respectively, with represent double star disturbance orbital acceleration vector separately respectively.

In formula (18), sight line representation in components as follows

（19）

Wherein, represent the unit vector being pointed to second satellite by first satellite.

In formula (19), can be rewritten as

（20）

Wherein, represent sight line component, represent vertical component.

By in formula (20) replace with , formula (19) can be rewritten as

（21）

Wherein, , represent the disturbance interstellar distance observed quantity of laser interferometry instrument.

In formula (21), concrete form be expressed as follows,

（22）

Wherein, represent other Relative Perturbation conservative force (established model calculating) except terrestrial gravitation, mainly comprise: lunisolar attraction, solid tide power, oceanic tide power, atmospheric tide power, pole tidal force etc.; represent Relative Perturbation nonconservative force (star accelerometer measurement), mainly comprise: atmospherical drag, solar light pressure, terrestrial radiation pressure, orbit altitude and gesture stability power etc.; represent Relative Perturbation center gravitation

（23）

Wherein, represent earth quality and universal gravitational constant long-pending; represent disturbance the earth's core radius of double star, represent disturbance orbital position vector 3 components; represent relative earth disturbance gravitation, , represent gradient operator, with represent the earth disturbing potential of double star respectively with gradient, earth disturbing potential be expressed as follows

（24）

Wherein, represent the earth's core radius, geocentric colatitude degree and geocentric longitude respectively, represent earth mean radius, lrepresent that earth disturbing potential presses the maximum order of spherical function expansion; represent normalized association Legendre function, lrepresent exponent number, mrepresent number of times; with represent Geopotential coefficient to be estimated.

By formula (22) is substituted into formula (21), disturbance interstellar distance observation equation is expressed as follows

（25）

The earth gravity field inversion step of the four stars fleet system principle in the present invention is as follows: first, and the FSS-1/2 Double Satellites Observation data of four stars fleet system and FSS-3/4 Double Satellites Observation data are substituted into disturbance interstellar distance observation equation (25) respectively; Then, two prescription journeys are merged into a large-scale over-determined systems, namely equation number is greater than unknown number number; Finally, by least square method, solve Geopotential coefficient with .It will be understood by those skilled in the art that based on above-mentioned about Geopotential coefficient with system of equations, also can adopt other data processing method combined calculation obtain earth gravity field.Because disturbance moonscope amount (actual measured amount-reference quantity) is more responsive to earth gravity field precision, therefore 3 ~ 5 times can be improved than before based on disturbance interstellar distance observation equation (25) inverting earth gravity field precision.

Based on Gauss-Markov model, the coloured noise of analog satellite observed reading is expressed as follows

（26）

Wherein, represent related coefficient; represent the random white noise of normal distribution, jrepresent the number of observation station; represent the coloured noise with correlativity.

Fig. 6 a ~ 6c represents respectively based on Gauss-Markov coloured noise model, the interstellar distance coloured noise utilizing related coefficient (nonconservative force 0.90 of the interstellar distance 0.85 of laser interferometry instrument, the orbital position 0.95 of GPS, star accelerometer) and sampling interval 10 s to simulate and the coloured noise in orbital position and nonconservative force x-axis direction.By adding coloured noise, make the nonconservative force observation data of the interstellar distance of four stars fleet system laser interferometry instrument of numerical simulation, the orbital position of GPS 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 German Potsdam earth science research center (GFZ) is announced, and adding up geoid surface precision at 120 rank places is 1.894 × 10 ^-1m; Asterisk line and solid line represent based on double star string type (GRACE-II) and four stars fleet system of the present invention (FSS-1/2/3/4) respectively, by related coefficient (nonconservative force 0.90 of the interstellar distance 0.85 of laser interferometry instrument, the orbital position 0.95 of GPS 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, add up geoid surface precision at 120 rank places and be respectively 4.785 × 10 ^-4m and 1.162 × 10 ^-4m.Result of study shows: the first, relative to GRACE-II double star string type fleet system, because FSS-1/2/3/4 four stars fleet system of the present invention adds the measurement of vertical gravity gradient signal, therefore effectively improves the sensing precision of middle long wave earth gravity field.At 120 rank places, the precision based on FSS-1/2/3/4 four stars fleet system inverting earth gravity field of the present invention improves about 4 times compared with the inversion accuracy of GRACE-II double star string type fleet system.The second, the inversion accuracy based on the more current GRACE satellite of precision of FSS-1/2/3/4 four stars fleet system inverting earth gravity field of the present invention at least improves 10 times.

3) feature of four stars fleet system

the first, satellite orbital altitude can be reduced largely.Because GRACE double star string type fleet system adopts star accelerometer to measure nonconservative force in real time in-orbit, then in Data Post, deduct nonconservative force effect again.Therefore, due to the negative interference of nonconservative force, the orbit altitude (500 km) of GRACE satellite cannot effectively reduce.Domestic and international research shows: Gravity Satellite orbit altitude often reduces by 100 km, and the nonconservative force (based on atmospherical drag) acting on satelloid about increases by 10 times.There is provided quiet to give the crucial load of Gravity Satellite and stable working environment and then effectively its measuring accuracy of raising (suitably shortening measurement dynamic range), and by shielding action the nonconservative force (atmospherical drag, solar light pressure, terrestrial radiation pressure, orbit altitude and gesture stability power etc.) of satelloid and then the serviceable life effectively extending satellite, four stars fleet system will carry nonconservative force bucking-out system (DFCS:Drag-Free Control System).Therefore, four stars fleet system substantively can reduce satellite orbital altitude (250 km), and then the exponential damping effect effectively suppressing terrestrial gravitation field signal to increase with satellite orbital altitude.

The second, substantively can improve crucial load measurement precision.GRACE double star string type fleet system adopts K-band measuring instrument to measure speed (1 μm/s) between interstellar distance (10 μm) and star, acts on the nonconservative force (10 of satelloid based on SuperSTAR accelerometer measures simultaneously ^-10m/s ²).In order to reduce the negative effect of crucial load error to earth gravity field precision further, speed (1 nm/s) between interstellar distance (10 nm) and star accurately measured by more high-precision for lift-launch laser interferometry instrument by four stars fleet system, acts on the nonconservative force (10 of satelloid by nonconservative force bucking-out system high precision balance simultaneously ^-13m/s ²).Because the crucial load measurement precision of four stars fleet system is significantly promoted, the more current model accuracy set up based on GRACE double star string type fleet system of earth gravity field model precision therefore set up based on four stars fleet system at least can improve 10 times.

3rd, three-dimensional gravity gradient observation value can be measured simultaneously.Because GRACE double star string type fleet system is equivalent to the horizontal gravity gradient instrument that base length is interstellar distance (220 km), therefore GRACE cannot obtain vertical gravity gradient signal, and then have lost earth gravity field precision largely.Four stars fleet system accurately can 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 effectively can remove the warp-wise band error (isotropy is more excellent) of the earth Time-variable gravity caused due to the disappearance of vertical gravity gradient signal.

4th, effectively can suppress the confusion effect of high-frequency signal.The confusion effect of the high frequency errors such as air and oceanic tide change is the most critical factor of loss GRACE earth gravity field inversion accuracy.Because the high frequency errors such as GRACE air and oceanic tide change are close to air and oceanic tide computation model error, therefore high frequency error is more difficult accurately deducts from GRACE earth gravity field model for air and oceanic tide change etc.Four stars fleet system, not only can be similar to the gravity gradient component that GRACE double star string type fleet system measures direction of visual lines, to the gravity gradient signal measured perpendicular to direction of visual lines be increased simultaneously, be intended to cut down high frequency confusion effect to the negative interference of earth gravity field inversion accuracy.

5th, long wave Time-variable gravity signal in the detectable earth.GRACE double star string type fleet system only can detect earth long wave Time-variable gravity signal (spatial resolution about 400 km), cannot long wave Time-variable gravity signal (spatial resolution is better than 200 km) in the high precision determination earth.Four stars fleet system adopts novel and precision laser to interfere Cross-Link measurement instrument and nonconservative force bucking-out system to increase substantially the sensing precision of long wave Time-variable gravity signal in the earth, is intended to for the science such as seismology, thalassography, glaciology, hydrology and national defence crossing research field provide the terrestrial time of more high precision and more high spatial resolution to become gravity field information.

Claims (1)

1. adopt a Gravity Satellite formation inverting terrestrial gravitation field method, it is characterized in that:

Obtain four Gravity Satellite FSS-1/2/3/4 fleet system measurement data, described four single stars of Gravity Satellite every orbit the earth along respective elliptical orbit, the barycenter of four stars fleet system is with the earth movements of circular orbit pattern ring, and every single star rotates with elliptical orbit form around fleet system barycenter;

Wherein, four Gravity Satellite fleet system set 6 Kepler orbit elements, comprise semi-major axis of orbit a, orbital eccentricity e, orbit inclination i, right ascension of ascending node Ω, argument of perigee ω and initial mean anomaly M, wherein,

The semi-major axis of orbit a of first, four Gravity Satellites, orbital eccentricity e, orbit inclination i and right ascension of ascending node Ω remain unchanged in satellite transit process;

The argument of perigee ω of the second, often couple of satellite FSS-1/2 and FSS-3/4 ₁, ω ₂, ω ₃and ω ₄and mean anomaly M ₁, M ₂, M ₃and M ₄differ 180 respectively ^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 equator place and initial mean anomaly designs in limit place;

3rd, the semi-major axis ρ of four Gravity Satellite fleet system elliptical orbits _maxwith semi-minor axis ρ _minratio be ρ _max: ρ _min=2:1;

The measurement data of described four Gravity Satellite fleet system comprises the satellite nonconservative force of the interstellar distance of satellite borne laser interference measuring instrument, the satellite orbital position of GPS and accelerometer;

By described measurement data inverting earth gravity field, its method is as follows,

The Taylor expansion of single star actual measurement orbital position is calculated based on Newton's interpolation formula

$r\left(t\right)=r\left(t_0\right)+\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\left(\begin{array}{c}\mathrm{\α}\\ j\end{array}\right)\underset{\mathrm{\ξ}=0}{\overset{j}{\mathrm{\Σ}}}{(-1)}^{j+\mathrm{\ξ}}\left(\begin{array}{c}j\\ \mathrm{\ξ}\end{array}\right)r\left(r_{\mathrm{\ξ}}\right)---\left(1\right)$

Wherein, $\left(\begin{array}{c}\mathrm{\α}\\ j\end{array}\right)$ Represent binomial coefficient, t represents the moment of calculation level, t ₀represent the initial time of interpolation point, Δ t represents sampling interval, and n represents the quantity of interpolation point;

The Taylor expansion of single star reference orbit position is expressed as follows

$r^o\left(t\right)=r^o\left(t_0\right)+\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\left(\begin{array}{c}\mathrm{\α}\\ j\end{array}\right)\underset{\mathrm{\ξ}=0}{\overset{j}{\mathrm{\Σ}}}{(-1)}^{j+\mathrm{\ξ}}\left(\begin{array}{c}j\\ \mathrm{\ξ}\end{array}\right)r^o\left(r_{\mathrm{\ξ}}\right)---\left(2\right)$

The Taylor expansion of single star disturbance orbital position δ r can be obtained based on formula (1)-(2)

$\mathrm{\δr}\left(t\right)=\mathrm{\δr}\left(t_0\right)+\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\left(\begin{array}{c}\mathrm{\α}\\ j\end{array}\right)\underset{\mathrm{\ξ}=0}{\overset{j}{\mathrm{\Σ}}}{(-1)}^{j+\mathrm{\ξ}}\left(\begin{array}{c}j\\ \mathrm{\ξ}\end{array}\right)\mathrm{\δr}\left(r_{\mathrm{\ξ}}\right)---\left(3\right)$

Wherein, δ r=r-r ^o;

Second derivative based on formula (3) can obtain single star disturbance orbital acceleration

$\mathrm{\δ}\stackrel{..}{r}\left(t\right)=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\left(\begin{array}{c}\mathrm{\α}\\ j\end{array}\right)}^{\text{'}}\underset{\mathrm{\ξ}=0}{\overset{j}{\mathrm{\Σ}}}{(-1)}^{j+\mathrm{\ξ}}\left(\begin{array}{c}j\\ \mathrm{\ξ}\end{array}\right)\mathrm{\δ}r\left(r_{\mathrm{\ξ}}\right)---\left(4\right)$

Double star disturbance orbital acceleration difference can be obtained based on formula (4)

$\mathrm{\δ}{\stackrel{..}{r}}_{12}\left(t\right)=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\left(\begin{array}{c}\mathrm{\α}\\ j\end{array}\right)}^{\text{'}}\underset{\mathrm{\ξ}=0}{\overset{j}{\mathrm{\Σ}}}{(-1)}^{j+\mathrm{\ξ}}\left(\begin{array}{c}j\\ \mathrm{\ξ}\end{array}\right)\mathrm{\δ}{r}_{12}\left(r_{\mathrm{\ξ}}\right)---\left(5\right)$

Wherein, δ r ₁₂=δ r ₂-δ r ₁with represent double star Relative Perturbation orbital position vector Relative Perturbation orbital acceleration vector respectively, δ r ₁with δ r ₂represent double star disturbance orbital position vector separately respectively, with represent double star disturbance orbital acceleration vector separately respectively;

In formula (5), concrete form be expressed as follows

$\mathrm{\δ}{\stackrel{..}{r}}_{12}=\mathrm{\δ}{g}_{12}^0+\mathrm{\δ}{g}_{12}^T+\mathrm{\δ}{a}_{12}^C+\mathrm{\δ}{f}_{12}^N---\left(6\right)$

Wherein, represent other Relative Perturbation conservative force except terrestrial gravitation, mainly comprise: lunisolar attraction, solid tide power, oceanic tide power, atmospheric tide power and pole tidal force; represent Relative Perturbation nonconservative force, mainly comprise: atmospherical drag, solar light pressure, terrestrial radiation pressure and orbit altitude and gesture stability power; represent Relative Perturbation center gravitation

$\mathrm{\δ}{g}_{12}^0=-\mathrm{GM}(\frac{\mathrm{\δ}{r}_2}{{\left|\mathrm{\δ}{r}_2\right|}^3}-\frac{\mathrm{\δ}{r}_1}{{\left|\mathrm{\δ}{r}_1\right|}^3})---\left(7\right)$

Wherein, GM represent earth quality M and gravitational constant G long-pending, represent disturbance the earth's core radius of double star, δ x _{1 (2)}, δ y _{1 (2)}, δ z _{1 (2)}represent disturbance orbital position vector delta r _{1 (2)}3 components; represent relative earth disturbance gravitation, represent gradient operator, with represent the earth disturbing potential T of double star respectively ₁and T ₂gradient, earth disturbing potential T is expressed as follows

$T(r,\mathrm{\θ},\mathrm{\λ})=\frac{\mathrm{GM}}{R_e}\underset{l=2}{\overset{L}{\mathrm{\Σ}}}{\left(\frac{R_e}{r}\right)}^{l+1}\underset{m=0}{\overset{l}{\mathrm{\Σ}}}({\stackrel{\‾}{C}}_{\mathrm{lm}}\cos \mathrm{m\λ}+{\stackrel{\‾}{S}}_{\mathrm{lm}}\sin \mathrm{m\λ}){\stackrel{\‾}{P}}_{\mathrm{lm}}\left(\cos \mathrm{\θ}\right)---\left(8\right)$

Wherein, r, θ, λ represent the earth's core radius, geocentric colatitude degree and geocentric longitude respectively, R _erepresent earth mean radius, L represents the maximum order of earth disturbing potential by spherical function expansion; represent normalized association Legendre function, l represents exponent number, and m represents number of times; with represent Geopotential coefficient to be estimated;

By formula (6) is substituted into formula (5), disturbance interstellar distance observation equation is expressed as follows

$\begin{array}{c}{e}_{12}\left(t\right)\·\mathrm{\δ}\▿T_{12}\left(t\right)=e_{12}\left(t\right)\·\{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\left(\begin{array}{c}\mathrm{\α}\\ j\end{array}\right)}^{\text{'}}\underset{\mathrm{\ξ}=0}{\overset{j}{\mathrm{\Σ}}}{(-1)}^{j+\mathrm{\ξ}}\left(\begin{array}{c}j\\ \mathrm{\ξ}\end{array}\right)\mathrm{\δ}{r}_{\mathrm{\ρ}12}\left(t_{\mathrm{\ξ}}\right)\\ +\mathrm{GM}[\frac{\mathrm{\δ}{r}_2\left(t\right)}{{\left|\mathrm{\δ}{r}_2\left(t\right)\right|}^3}-\frac{\mathrm{\δ}{r}_1\left(t\right)}{{\left|\mathrm{\δ}{r}_1\left(t\right)\right|}^3}]-\mathrm{\δ}{a}_{12}^C\left(t\right)-\mathrm{\δ}{f}_{12}^N\left(t\right)\}\end{array}---\left(9\right)$

Wherein, δ r _{ρ 12}(t _ξ)=δ ρ ₁₂(t _ξ) e ₁₂(t _ξ)+{ δ r ₁₂(t _ξ)-[δ r ₁₂(t _ξ) e ₁₂(t _ξ)] e ₁₂(t _ξ), δ ρ ₁₂=δ r ₁₂e ₁₂represent the disturbance interstellar distance observed quantity of laser interferometry instrument, e ₁₂=δ r ₁₂/ | δ r ₁₂| represent the unit vector being pointed to second satellite by first satellite;

The measurement data of two couples of double star FSS-1/2 and FSS-3/4 is substituted into respectively disturbance interstellar distance observation equation (9), then combine and solve Geopotential coefficient with