CN108020866B - A kind of method and system and processor of the inverting of celestial body gravitational field - Google Patents
A kind of method and system and processor of the inverting of celestial body gravitational field Download PDFInfo
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- CN108020866B CN108020866B CN201711158816.7A CN201711158816A CN108020866B CN 108020866 B CN108020866 B CN 108020866B CN 201711158816 A CN201711158816 A CN 201711158816A CN 108020866 B CN108020866 B CN 108020866B
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- G01V7/00—Measuring gravitational fields or waves; Gravimetric prospecting or detecting
Abstract
The invention discloses a kind of methods of celestial body gravitational field inverting, comprising: obtains the crucial load data of celestial body；Wherein, the crucial load data, comprising: velocity error, orbital position error and nonconservative force error between star；Half numerical value composition error model is constructed according to the crucial load data；Wherein, the half numerical value composition error model is velocity error, orbital position error and the relevant mathematical model of nonconservative force error between the star；According to the rank error variance and the half numerical value composition error model determined by substar error, the inverting of celestial body gravitational field is carried out.The high-precision to celestial body gravitational field, fast inversion are realized through the invention.
Description
Technical field
The invention belongs to field of deep space exploration more particularly to a kind of method and system of celestial body gravitational field inverting, with
And processor.
Background technique
After 11 manned moon landing of Apollo after successful implementation on July 20 in 1969, around the original of " early exploitation, be first benefited "
Then, celestial body (celestial body/planet) detection has become each spacefaring nation and advises in the focus of the competition and distant view of a deep-space detection field new round
It draws.
By mars exploration and it is manned step on fire for, 21 century be by dedicated satellite gravity survey technology improve to " number
New era of word Mars " cognitive ability.Mars gravitational field not only contribute to reflection martian surface and inner material spatial distribution,
Movement and migration, and can determine the fluctuating and fluctuation of Mars geoid.Therefore, Mars gravitational field fine structure research is
The demand of planetary science, geoscience, astrophysics, astronomy, space science etc..
By taking the earth as an example, in NASA Jet Propulsion Laboratory (NASA's JPL) and German Potsdam earth science research
The GRACE terrestrial gravitation double star of the heart (GFZ) joint research and development is dedicated to long wave gravity field signal in the precise measurement earth.GRACE-A
(Tom) and GRACE-B (Jerry) is designed as nearly circle, proximal pole and low rail double star, passes through high rail GPS (Global Positioning
System, global positioning system) satellite precise measurement satellite orbital position and orbital velocity, be based on K-band range-measurement system
(KBR) high-precision sensing interstellar distance, using star accelerometer (ACC) obtain nonconservative force (atmospheric drag, solar light pressure,
Terrestrial radiation pressure, track and gesture stability power etc.) information realization earth gravitational field inverting.
Based on the outstanding contribution and successful experience of current GRACE earth satellite gravity measurement plan, NASA's jet
Promoting Experiment room (NASA-JPL) has successfully implemented moonik gravity measurement plan GRAIL in 2011, it is intended to establish high
Precision lunar gravity model.GRAIL-A (Ebb) and GRAIL-B (Flow) moon double star are using SSO (Sun Synchronous Orbit), nearly circle, low rail and same
Rail design.GRAIL-A/B double star is based on Ka wave band lunar gravity range-finding system (LGRS) precise measurement interstellar distance, utilizes depth
Satellite orbit is continuously tracked in empty tracking network (DSN), senses satellite by Inertial Measurement Unit, sun sensor and star tracker
3 d pose passes observation signal back earth station using X-band radio science beacon (RSB) in real time.
Since NASA has succeeded in sending up first Mars probes Mariner-4, Mars on November 28th, 1964
Gravity field model building relies primarily on orbit perturbation observation data.Mars gravity field model refers to a series of Mars gravitational potential coefficients
Set.Up to now, international numerous scientific research institutions have used Conventional gravity measuring technique to carry out and have goed deep into and extensive Mars
The research demonstration that gravity field model is established.
Different from pervious gravity field measurement orbit perturbation technology, future, Martian satellite gravimetric technique not only will be in fire
Talent scout surveys and plays an important role in the works, and directly determines that the optimal trajectory design of Mars probes steps on fiery lander with manned
The optimum option of position.In view of current Earth satellite gravity survey plan GRACE's and moonik gravity measurement plan GRAIL
Outstanding performance and outstanding contribution, how to further increase Mars gravitational field inversion accuracy is those skilled in the art's urgent need to resolve
One of problem.
Summary of the invention
Technology of the invention solves the problems, such as: a kind of method for overcoming the deficiencies of the prior art and provide celestial body gravitational field inverting
With system and processor, high-precision, fast inversion with realization to celestial body gravitational field.
In order to solve the above-mentioned technical problem, the invention discloses a kind of methods of celestial body gravitational field inverting, comprising:
Obtain the crucial load data of celestial body；Wherein, the crucial load data, comprising: velocity error, track position between star
Set error and nonconservative force error；
Half numerical value composition error model is constructed according to the crucial load data；Wherein, the half numerical value composition error mould
Type is velocity error, orbital position error and the relevant mathematical model of nonconservative force error between the star；
According to the rank error variance and the half numerical value composition error model determined by substar error, celestial body gravity is carried out
Field inverting.
In the method for above-mentioned celestial body gravitational field inverting, the crucial load data for obtaining celestial body, comprising:
Pass through velocity error between satellite borne laser interfeerometry ranging instrument acquisition star；
Orbital position error is obtained by ground Deep Space Network；
Nonconservative force error is obtained without towing control system by spaceborne.
In the method for above-mentioned celestial body gravitational field inverting, further includes:
Obtain substar error；
The rank error variance determined according to substar error.
In the method for above-mentioned celestial body gravitational field inverting, the rank error variance determined according to substar error, comprising:
According to longitude λMWith latitude φMUniform grid partition is carried out to celestial body surface, by substar error delta ηM(φM,λM)
Average interpolation is at lattice point；
To the substar error delta η after differenceM(φM,λM) determined according to spherical function expansion, and according to spherical function expansion result
The rank error variance.
In the method for above-mentioned celestial body gravitational field inverting, the substar error delta η to after differenceM(φM,λM) according to ball
Functional expansion, and the rank error variance is determined according to spherical function expansion result, comprising:
According to such as following formula (1), to the substar error delta η after the differenceM(φM,λM) according to spherical function expansion:
Wherein,Indicate the coefficient of spherical function expansion；The order of l expression spherical function expansion；L indicates celestial body
The theoretical order of gravitational field inverting；The expansion number of m expression spheric function；P indicates association Legendre function；
It enables:
Wherein,
Wherein,Indicate spheric function；Qm(λM) indicate SIN function or cosine function；
According to above formula (1), (2), (3) and (4), rank error variance is determined
In the method for above-mentioned celestial body gravitational field inverting, the half numerical value composition error model is as follows:
Wherein, δ NcIndicate geoid error；RMIndicate celestial body mean radius；θMIt indicates to correspond to laser interference ranging
The interstellar distance ρ of instrumentM12Huo Xinjiao；The product of GM expression gravitational constant G and celestial body mass M；rMIndicate centroid of satellite to star
The distance at body center；Velocity error between expression star；ΔtMIndicate the sampling interval；LmaxIndicate the reason of celestial body gravitational field inverting
By maximum order；δrMIndicate orbital position error；δfMIndicate nonconservative force error；
Wherein,
In the method for above-mentioned celestial body gravitational field inverting, rank error variance and institute that the basis is determined by substar error
Half numerical value composition error model is stated, the inverting of celestial body gravitational field is carried out, comprising:
According to above-mentioned formula (5), the calculation result of (6) and (7), the inverting of celestial body gravitational field is carried out.
In the method for above-mentioned celestial body gravitational field inverting,
Longitude λMRange are as follows: 0 °~360 °, latitude φMRange are as follows: -90 °~90 °.
Correspondingly, the invention also discloses a kind of systems of celestial body gravitational field inverting, comprising:
Module is obtained, for obtaining the crucial load data of celestial body；Wherein, the crucial load data, comprising: fast between star
Spend error, orbital position error and nonconservative force error；
Model construction module, for constructing half numerical value composition error model according to the crucial load data；Wherein, described
Half numerical value composition error model is velocity error, orbital position error and the relevant mathematical modulo of nonconservative force error between the star
Type；
Inverting module, for according to the rank error variance and the half numerical value composition error mould determined by substar error
Type carries out the inverting of celestial body gravitational field.
Correspondingly, the invention also discloses a kind of processors characterized by comprising the processor is used for:
Obtain the crucial load data of celestial body；Wherein, the crucial load data, comprising: velocity error, track position between star
Set error and nonconservative force error；
Half numerical value composition error model is constructed according to the crucial load data；Wherein, the half numerical value composition error mould
Type is velocity error, orbital position error and the relevant mathematical model of nonconservative force error between the star；
According to the rank error variance and the half numerical value composition error model determined by substar error, celestial body gravity is carried out
Field inverting.
The invention has the following advantages that
The method of celestial body gravitational field inverting of the present invention, based on velocity error, orbital position error and Fei Bao between star
It keeps power error and constructs half numerical value composition error model, realized based on the half numerical value composition error model to celestial body gravitational field
Inverting, inversion accuracy are 10 times or more of the inversion accuracy of traditional celestial body survey plan, and celestial body gravitational field inversion accuracy is high, resolves
Speed is fast, low to computer performance requirement, and error model physical meaning is clear, is easy to carry out celestial body gravitational field error analysis.
Detailed description of the invention
Fig. 1 is a kind of celestial body measuring principle figure in the embodiment of the present invention；
Fig. 2 is a kind of step flow chart of the method for celestial body gravitational field inverting in the embodiment of the present invention；
Fig. 3 is a kind of based on velocity error, orbital position error and nonconservative force error shadow between star in the embodiment of the present invention
Loud Mars-SST Mars accumulates geoid error contrast schematic diagram；
Fig. 4 is a kind of accumulative the earth level of the Mars-SST based on tachometric survey precision between different stars in the embodiment of the present invention
Face accuracy comparison schematic diagram；
Fig. 5 is a kind of accumulative the earth level of the Mars-SST based on different orbital position measurement accuracy in the embodiment of the present invention
Face accuracy comparison schematic diagram；
Fig. 6 is a kind of accumulative the earth level of the Mars-SST based on different nonconservative force measurement accuracy in the embodiment of the present invention
Face accuracy comparison schematic diagram；
Fig. 7 is a kind of based on different synthesis precisions (speed, orbital position and nonconservative force between star) in the embodiment of the present invention
Mars-SST add up geoid accuracy comparison schematic diagram.
Specific embodiment
To make the object, technical solutions and advantages of the present invention clearer, public to the present invention below in conjunction with attached drawing
Embodiment is described in further detail.
The present invention has carried out the exploratory technicism of Martian satellite gravity measurement plan in future Mars-SST by taking Mars as an example
Card research.Mars-SST-A/B Mars gravity double star is expected based between satellite borne laser interfeerometry ranging instrument (ILRS) high-acruracy survey star
Speed (is similar to next-generation earth satellite gravity measurement plan GRACEFollow-On), passes through the deep-space network of earth station
(DSN) accurate and double star orbital position and orbital velocity (being similar to moonik gravity measurement plan GRAIL), benefit is continuously tracked
(present satellites gravity measurement is similar to the spaceborne nonconservative force for acting on double star without towing control system (DFCS) real-time compensation
Plan GOCE.Therefore, it is at least above based on Martian satellite gravity measurement plan in future Mars-SST inverting Mars gravitational field precision
Utilize 10 times of inversion accuracy of traditional mars exploration plan.
Future, the scientific goal of Mars-SST Mars gravity double star plan was as follows: accurate Drawing Mars static state and time-varying gravity
, it understands the mass flow and climatic stratigraphy of Mars in depth, detects the earth's crust and internal structure of Mars, study the atmosphere of Mars
Dynamics.The basic principle of Mars-SST Mars gravitational field inverting is as follows: being based on Mars gravitational potential coefficient and Satellite Observations
(speed, the orbital position of ground Deep Space Network, the nonconservative force without towing control system, star are quick between the star of laser interference range finder
The 3 d pose etc. of sensor (SCA)) transformational relation construct moonscope equation；It is accurately resolved by least square method (LSM)
Moonscope equation, to obtain Mars gravitational potential coefficient.The successful implementation of international mars exploration plan provides simultaneously to us
Opportunities and challenges.Therefore, we need to use for reference the successful experience of existing Mars probes as far as possible, push Mars in future to defend as early as possible
The successful implementation of star gravity plan, and then drive related discipline (planetary science, geoscience, astrophysics, astronomy etc.)
Fast development.Based on the above reasons, the present invention focuses primarily on Mars- in future using novel half numerical value composition error modelling
The research demonstration of SST Martian satellite gravity measurement crucial load precision index matching relationship in the works.
The invention proposes be based on half numerical value composition error modelling accurately and quickly inverting Mars-SST Mars gravitational field
New technology, and accurately and quickly 400 rank Mars-SST Mars gravitational fields of inverting.
Referring to Fig.1, a kind of celestial body measuring principle figure in the embodiment of the present invention is shown.Wherein, OM-XMYMZMIt indicates with star
The constitution heart is the coordinate system of origin, θMIndicate the interstellar distance ρ for corresponding to laser interference range finderM12Huo Xinjiao, rM1It indicates
Distance of the mass center of Mars-SST-A satellite to celestial body center, rM2Indicate the mass center of Mars-SST-B satellite to celestial body center away from
From,Indicate the interstellar distance of Mars-SST-A and Mars-SST-B,Indicate the speed of Mars-SST-A satellite,
Indicate the speed of Mars-SST-B satellite.
Referring to Fig. 2, a kind of step flow chart of the method for celestial body gravitational field inverting in the embodiment of the present invention is shown.At this
In embodiment, the method for the celestial body gravitational field inverting, comprising:
Step 201, the crucial load data of celestial body is obtained.
In the present embodiment, the crucial load data can specifically include: velocity error between star, orbital position error and
Nonconservative force error.
Preferably, velocity error between star can be obtained by satellite borne laser interfeerometry ranging instrument；It is obtained by ground Deep Space Network
Orbital position error；Nonconservative force error is obtained without towing control system by spaceborne.
Step 202, half numerical value composition error model is constructed according to the crucial load data.
In the present embodiment, the half numerical value composition error model is velocity error, orbital position error between the star
Mathematical model relevant with nonconservative force error.
Step 203, it according to the rank error variance and the half numerical value composition error model determined by substar error, carries out
Celestial body gravitational field inverting.
In the present embodiment, the method for determination of rank error variance, which can be such that, obtains substar error；It is missed according to substar
The rank error variance that difference determines.
Preferably, the mode of the rank error variance determined according to substar error can be such that according to longitude λMAnd latitude
φMUniform grid partition is carried out to celestial body surface, by substar error delta ηM(φM,λM) average interpolation is at lattice point；To difference
Substar error delta η afterwardsM(φM,λM) according to spherical function expansion, and according to spherical function expansion result determine the rank error side
Difference.Wherein, longitude λMMay range from: 0 °~360 °, latitude φMMay range from: -90 °~90 °.
It is specific:
According to such as following formula (1), to the substar error delta η after the differenceM(φM,λM) according to spherical function expansion:
Wherein,Indicate the coefficient of spherical function expansion；The order of l expression spherical function expansion；L indicates celestial body
The theoretical order of gravitational field inverting；The expansion number of m expression spheric function；P indicates association Legendre function.
It enables:
Wherein,
Wherein,Indicate spheric function；Qm(λM) indicate SIN function or cosine function.
According to above formula (1), (2), (3) and (4), rank error variance is determined
In the preferred embodiment of the present invention, the expression formula of the half numerical value composition error model can be such that
Wherein, δ NcIndicate geoid error；RMIndicate celestial body mean radius；θMIt indicates to correspond to laser interference ranging
The interstellar distance ρ of instrumentM12Huo Xinjiao；The product of GM expression gravitational constant G and celestial body mass M；rMIndicate centroid of satellite to star
The distance at body center；Velocity error between expression star；ΔtMIndicate the sampling interval；LmaxIndicate the reason of celestial body gravitational field inverting
By maximum order；δrMIndicate orbital position error；δfMIndicate nonconservative force error.
Wherein,
Preferably, the inverting of celestial body gravitational field can be carried out according to above-mentioned formula (5), the calculation result of (6) and (7).
In the present embodiment, the method to the celestial body gravitational field inverting based on half numerical value composition error model is given
Verifying.
Referring to Fig. 3, show a kind of based on velocity error between star, orbital position error and non-conservative in the embodiment of the present invention
The Mars-SST Mars that power error influences accumulates geoid error contrast schematic diagram.
As shown in figure 3, line 1 indicates the 110 rank Mars weights that NASA Jet Propulsion Laboratory (NASA-JPL) is announced
Force field model MRO110C；At 110 ranks, accumulation geoid precision is 3.641m.Line 2, line 3, line 4 and line 5 respectively indicate
Velocity error, the orbital position error of ground Deep Space Network, nothing are dragged between the star of laser interference range finder based on Mars-SST double star
Drag the nonconservative force error of control system and the 400 ranks accumulation Mars geoid error of comprehensive crucial load error inverting.
Comparative study result is as follows:
(1) at 400 ranks, velocity error, orbital position error and nonconservative force are missed between the star based on Mars-SST double star
The accumulation Mars geoid error that difference does not influence is 5.013 × 10-1m、5.021×10-1M and 5.316 × 10-1m.Base
Known to accordance in Fig. 2 middle line 2, line 3 and line 4: based on crucial load error model (speed, orbital position and Fei Bao between star
Keep power) efficiently and quickly estimation Mars gravitational field precision is reliable respectively；Meanwhile crucial load precision index (speed between star,
Orbital position and nonconservative force) it is mutually matched.
(2) at 400 ranks, the composition error model inversion based on Mars-SST double star key load accumulates Mars the earth water
Quasi- surface error is 8.798 × 10-1m.By Fig. 2 middle line 1 and the comparison of line 5 it is found that being based on Mars-SST double star plan inverting Mars
The more existing MRO110C Mars gravity field model precision of gravitational field precision is at least 10 times high.
(3) the crucial load error model of the synthesis for estimating accumulation Mars geoid error that the present invention constructs
(half numerical value composition error model) is correctly, to be conducive to establish next-generation high-precision and high-space resolution Mars gravitational field mould
Type.
Referring to Fig. 4, it is tired to show a kind of Mars-SST based on tachometric survey precision between different stars in the embodiment of the present invention
Count geoid accuracy comparison schematic diagram.
As shown in figure 4, line 1 indicates MRO110C Mars gravity field model precision；At 110 ranks, add up Mars the earth level
Face precision is 3.641m.Line 2, line 3 and line 4 respectively indicate velocity error between the different stars based on satellite borne laser interfeerometry ranging instrument
(10-6m/s、10-7M/s and 10-8M/s) 400 rank Mars-SST of inverting adds up Mars geoid precision.Comparative study result
It is as follows:
(1) at 400 ranks, based on velocity error 10 between satellite borne laser interfeerometry ranging instrument star-6M/s inverting adds up Mars the earth
Level surface precision is 5.013m, is based respectively on velocity error 10 between star-7M/s and 10-8M/s inverting adds up Mars geoid
Precision improves 10 times and 100 times.If velocity error is designed to 10 between satellite borne laser interfeerometry ranging instrument star-6M/s, due to star
Between tachometric survey precision it is lower, therefore Mars gravitational field inversion accuracy can not by substance improve；Conversely, if Mars-SST is bis-
Star uses tachometric survey precision 10 between higher star-8The development difficulty of m/s, satellite borne laser interfeerometry ranging instrument will increase.
(2) satellite borne laser interfeerometry ranging instrument is the key that improve one of Mars gravity field model precision load.Measuring principle
As follows: transmission uses double-frequency laser signal between first, Mars-SST-A/B star；The laser that second, Mars-SST satellite reception arrive
The laser signal that signal and local overstable oscillation device generate carries out Frequency mixing processing；Third, phase signal be sent back to the earth with
Track station.The development and application of satellite borne laser interfeerometry ranging instrument are not only the main flow direction of DSN-SST-LL observation mode in future, and
It and is the important means for constructing next-generation high-precision Mars gravitational field figure.
(3) it combines Mars gravitational field inversion accuracy and crucial load develops difficulty, satellite borne laser interfeerometry ranging instrument star
Between velocity error 10-7M/s is more preferably selecting for Mars-SST double star plan.
Referring to Fig. 5, it is tired to show a kind of Mars-SST based on different orbital position measurement accuracy in the embodiment of the present invention
Count geoid accuracy comparison schematic diagram.
As shown in figure 5, line 1 indicates MRO110C Mars gravity field model precision；At 110 ranks, add up Mars the earth level
Face precision is 3.641m.Line 2, line 3 and line 4 respectively indicate different orbital position error (350m, 35m based on ground Deep Space Network
And 3.5m) inverting 400 rank Mars-SST add up Mars geoid precision.Result of study is as follows:
(1) at 400 ranks, based on the 3.5m inverting of orbit measurement precision add up Mars geoid precision be 5.021 ×
10-2M is based respectively on orbit measurement precision 35m and 350m inverting and adds up Mars geoid precision for 10 times and 100 of reduction
Times.When Mars-SST double star is designed as higher orbit determination accuracy 3.5m, although Mars gravitational field inversion accuracy is conducive to certain journey
Degree improves, but since the Development Techniques to ground Deep Space Network are more demanding, will affect the successful implementation of Mars-SST plan.
Conversely, lower orbital position measurement accuracy 350m will be unfavorable for the promotion of Mars gravity field model precision.
It (2) is inverting high-precision and high-space resolution to the Precise Orbit measurement of Mars-SST double star based on ground Deep Space Network
The key factor of Mars gravitational field.At present satellite borne laser interference H_2O maser instrument and without towing control system measurement accuracy it is basic
It is able to satisfy the demand of Mars gravitational field inversion accuracy.However, current track measurement accuracy is slightly lower relative to other crucial load.Cause
This, the orbit measurement precision improvement of ground Deep Space Network is to establish next-generation high-precision and high spatial resolution Mars gravity field model
Urgent need.
(3) orbit observation precision of weighing the advantages and disadvantages and implementing plan possibility, Mars-SST double star use ground Deep Space Network rail
Road measurement accuracy 35m is more excellent.
Referring to Fig. 6, it is tired to show a kind of Mars-SST based on different nonconservative force measurement accuracy in the embodiment of the present invention
Count geoid accuracy comparison schematic diagram.
As shown in fig. 6, line 1 indicates MRO110C Mars gravity field model precision；At 110 ranks, add up Mars the earth level
Face precision is 3.641m.Line 2, line 3 and line 4 respectively indicate based on without towing control system different nonconservative force errors (3 ×
10-10m/s2、3×10-11m/s2With 3 × 10-12m/s2) inverting 400 rank Mars-SST add up Mars geoid precision.Research
As a result as follows:
(1) at 400 ranks, it is based on nonconservative force error 3 × 10-11m/s2Inverting adds up Mars geoid precision
5.316×10-1M utilizes nonconservative force error 3 × 10-12m/s2Inverting adds up Mars geoid precision and improves 10 times, leads to
Cross nonconservative force error 3 × 10-10m/s2Inverting, which adds up Mars geoid precision, reduces by 10 times.When without towing control system
Nonconservative force be designed to low measurement accuracy 3 × 10-10m/s2When, Mars gravitational field inversion accuracy will lost to a certain degree；
If conversely, using higher nonconservative force precision 3 × 10-12m/s2When, the technical difficulty of no towing controlling system design will
Largely increase.
(2) the spaceborne measuring principle without towing control system is as follows: detecting Mars gravitational field based on Mars-SST double star
Period utilizes the nonconservative force that gravity double star is acted on without towing control system real-time compensation.Since areographic low-heat is led
Rate, low thermal diffusivity and low specific heat capacity, as Mars-SST double star orbit altitude gradually decreases, Mars radiation pressure is in gradually increase
Trend.Since martian atmosphere is leaner, although the atmospheric drag for acting on Mars-SST double star is relatively small, the sun
The negative effect of wind pressure and cosmic ray pressure is very important.Therefore, based on spaceborne without towing control system to the essence of nonconservative force
Really compensation is the substantive key factor for improving Mars gravitational field inversion accuracy.
(3) in short, weighing the advantages and disadvantages, the nonconservative force accuracy Design of Mars-SST Mars gravity double star plan is 3 × 10- 11m/s2It is more excellent.
Referring to Fig. 7, show in the embodiment of the present invention it is a kind of based on different synthesis precisions (speed between star, orbital position and
Nonconservative force) Mars-SST add up geoid accuracy comparison schematic diagram.
As shown in fig. 7, line 1 indicates MRO110C Mars gravity field model precision；At 110 ranks, add up Mars the earth level
Face precision is 3.641m.Line 2, line 3 and line 4 are respectively indicated using half numerical value composition error model, are surveyed based on satellite borne laser interference
Distance meter, ground Deep Space Network, the crucial load error of the difference without towing control system are (1.: speed 10 between star-6M/s, orbital position
350m and nonconservative force 3 × 10-10m/s2；2.: speed 10 between star-7M/s, orbital position 35m and nonconservative force 3 × 10-11m/s2；
3.: speed 10 between star-8M/s, orbital position 3.5m and nonconservative force 3 × 10-12m/s2) inverting 400 rank Mars-SST add up Mars
Geoid precision.Result of study is as follows:
(1) at 400 ranks, (1.: speed 10 between star based on crucial loaded matching precision index-6M/s, orbital position 350m
With nonconservative force 3 × 10-10m/s2) inverting add up Mars geoid precision be 8.798m.When using crucial loaded matching essence
Spend index (2.: speed 10 between star-7M/s, orbital position 35m and nonconservative force 3 × 10-11m/s2；3.: speed 10 between star-8m/s、
Orbital position 3.5m and nonconservative force 3 × 10-12m/s2), will be improved by adding up Mars geoid inversion accuracy by 10 times and 100
Times.
(2) crucial loaded matching accuracy Design speed 10 between star of Mars-SST Mars gravity double star plan-7M/s, rail
Road position 35m and nonconservative force 3 × 10-11m/s2It is more excellent.
In conclusion the method for celestial body gravitational field inverting of the present invention, is missed based on velocity error, orbital position between star
Difference and nonconservative force error construct half numerical value composition error model, are realized based on the half numerical value composition error model to star
The inverting of the weight field of force, inversion accuracy are 10 times or more of the inversion accuracy of traditional celestial body survey plan, celestial body gravitational field inverting essence
Degree is high, computing speed is fast, low to computer performance requirement, and error model physical meaning is clear, is easy to carry out celestial body gravitational field mistake
Difference analysis.
Based on the above embodiment, the embodiment of the invention also discloses a kind of systems of celestial body gravitational field inverting, comprising: obtains
Module, for obtaining the crucial load data of celestial body；Wherein, the crucial load data, comprising: velocity error, track between star
Location error and nonconservative force error.Model construction module, for being constructed according to the crucial load data, half numerical value is comprehensive to be missed
Differential mode type；Wherein, the half numerical value composition error model is velocity error, orbital position error and nonconservative force between the star
The relevant mathematical model of error.Inverting module, for according to the rank error variance and half numerical value determined by substar error
Composition error model carries out the inverting of celestial body gravitational field.
Based on the above embodiment, the embodiment of the invention also discloses a kind of processor, the processor is used for: obtaining star
The crucial load data of body；Wherein, the crucial load data, comprising: velocity error between star, orbital position error and non-conservative
Power error；Half numerical value composition error model is constructed according to the crucial load data；Wherein, the half numerical value composition error model
For velocity error, orbital position error and the relevant mathematical model of nonconservative force error between the star；It is missed according to by substar
The rank error variance and the half numerical value composition error model that difference determines, carry out the inverting of celestial body gravitational field.
For device embodiment, since it is corresponding with embodiment of the method, so be described relatively simple, correlation
Place referring to embodiment of the method part explanation.
Various embodiments are described in a progressive manner in this explanation, the highlights of each of the examples are with its
The difference of his embodiment, the same or similar parts between the embodiments can be referred to each other.
The above, optimal specific embodiment only of the invention, but scope of protection of the present invention is not limited thereto,
In the technical scope disclosed by the present invention, any changes or substitutions that can be easily thought of by anyone skilled in the art,
It should be covered by the protection scope of the present invention.
The content that description in the present invention is not described in detail belongs to the well-known technique of professional and technical personnel in the field.
Claims (6)
1. a kind of method of celestial body gravitational field inverting characterized by comprising
Obtain the crucial load data of celestial body；Wherein, the crucial load data, comprising: velocity error, orbital position miss between star
Difference and nonconservative force error；
Half numerical value composition error model is constructed according to the crucial load data；Wherein, the half numerical value composition error model is
Velocity error, orbital position error and the relevant mathematical model of nonconservative force error between the star；
According to the rank error variance and the half numerical value composition error model determined by substar error, it is anti-to carry out celestial body gravitational field
It drills；
Wherein, the crucial load data for obtaining celestial body, comprising:
Pass through velocity error between satellite borne laser interfeerometry ranging instrument acquisition star；
Orbital position error is obtained by ground Deep Space Network；
Nonconservative force error is obtained without towing control system by spaceborne；
Wherein, the rank error variance determined according to substar error, comprising:
According to longitude λMWith latitude φMUniform grid partition is carried out to celestial body surface, by substar error delta ηM(φM,λM) average
It is interpolated at lattice point；
To the substar error delta η after differenceM(φM,λM) according to spherical function expansion, and according to the determination of spherical function expansion result
Rank error variance；
Wherein, the substar error delta η to after differenceM(φM,λM) according to spherical function expansion, and according to spherical function expansion knot
Fruit determines the rank error variance, comprising:
According to such as following formula (1), to the substar error delta η after the differenceM(φM,λM) according to spherical function expansion:
Wherein,Indicate the coefficient of spherical function expansion；The order of l expression spherical function expansion；L indicates celestial body gravity
The theoretical order of field inverting；The expansion number of m expression spheric function；P indicates association Legendre function；
It enables:
Wherein,
Wherein,Indicate spheric function；Qm(λM) indicate SIN function or cosine function；
According to above formula (1), (2), (3) and (4), rank error variance is determined
Wherein, the half numerical value composition error model is as follows:
Wherein, δ NcIndicate geoid error；RMIndicate celestial body mean radius；θMIt indicates to correspond to laser interference range finder
Interstellar distance ρM12Huo Xinjiao；The product of GM expression gravitational constant G and celestial body mass M；rMIndicate centroid of satellite into celestial body
The distance of the heart；Velocity error between expression star；ΔtMIndicate the sampling interval；LmaxIndicate the theory of celestial body gravitational field inverting most
Big order；δrMIndicate orbital position error；δfMIndicate nonconservative force error；
Wherein,
2. the method for celestial body gravitational field inverting according to claim 1, which is characterized in that further include:
Obtain substar error；
The rank error variance determined according to substar error.
3. the method for celestial body gravitational field inverting according to claim 1, which is characterized in that the basis is by substar error
Determining rank error variance and the half numerical value composition error model carry out the inverting of celestial body gravitational field, comprising:
According to above-mentioned formula (5), the calculation result of (6) and (7), the inverting of celestial body gravitational field is carried out.
4. the method for celestial body gravitational field inverting according to claim 1, which is characterized in that
Longitude λMRange are as follows: 0 °~360 °, latitude φMRange are as follows: -90 °~90 °.
5. a kind of system of the celestial body gravitational field inverting of the method for celestial body gravitational field inverting described in claim 1, special
Sign is, comprising:
Module is obtained, for obtaining the crucial load data of celestial body；Wherein, the crucial load data, comprising: speed is missed between star
Difference, orbital position error and nonconservative force error；
Model construction module, for constructing half numerical value composition error model according to the crucial load data；Wherein, the half
Being worth composition error model is velocity error, orbital position error and the relevant mathematical model of nonconservative force error between the star；
Inverting module, for according to the rank error variance and the half numerical value composition error model determined by substar error, into
Planetary gravitational field inverting.
6. a kind of processor of the method for celestial body gravitational field inverting described in claim 1 characterized by comprising institute
Processor is stated, is used for:
Obtain the crucial load data of celestial body；Wherein, the crucial load data, comprising: velocity error, orbital position miss between star
Difference and nonconservative force error；
Half numerical value composition error model is constructed according to the crucial load data；Wherein, the half numerical value composition error model is
Velocity error, orbital position error and the relevant mathematical model of nonconservative force error between the star；
According to the rank error variance and the half numerical value composition error model determined by substar error, it is anti-to carry out celestial body gravitational field
It drills.
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