CN106646644B - Determine that two steps of geoid integrate anti-solution based on limit aviation vector gravitational - Google Patents
Determine that two steps of geoid integrate anti-solution based on limit aviation vector gravitational Download PDFInfo
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Abstract
Determining that two steps of geoid integrate anti-solution based on limit aviation vector gravitational the present invention relates to a kind of, technical characteristics are to include：It is theoretical based on the horizontal boundary values of broad sense, on enroute altitude band limit aviation disturbing potential is calculated using band limit aviation vector gravitational；Using inverse Poisson integral models, sea disturbance position will be limited with band on limit aviation disturbing potential downward continuation to sea, is obtained, and geoid will be converted into limit sea disturbance position by Bruns formula.Reasonable design of the present invention provides new solution to calculate geoid based on aviation vector gravitational, realizes the computing function that aviation vector gravitational determines geoid, and acquired geoid precision meets engineering application demand.
Description
Technical field
It is especially a kind of to be determined based on band limit aviation vector gravitational the invention belongs to airborne vector gravimetry technical field
Two steps of geoid integrate anti-solution.
Background technology
Airborne vector gravimetry technology is using aircraft as carrier, with inertial navigation system and global navigation satellite positioning system
It unites as sensor and obtains the inertial acceleration information than force information and carrier respectively, pass through the joints such as coordinate conversion and filtering
Calculate the vector gravitational in aviation height.Geoid is a closed surface for representing the figure of the earth, be defined as with entirely
Ball without the best closely sealed terrestrial gravitation equipotential surface of the static mean sea level of tide, while be also can reflect earth's internal structure with it is close
Spend the physical surface of distribution characteristics.Determine that geoid is one of main purpose of airborne vector gravimetry.
Currently, determine that the research of geoid is to use to be similar to astronmical leveling principle based on aviation vector gravitational, by
Survey line section integral converts the horizontal component of vector gravitational to the disturbing potential on course line, by disturbing potential downward continuation to big ground water
Behind quasi- face, then undulation of the geoid calculated using Bruns formula, still, obtained by the above method is level surface relative to the earth,
It needs to be only geoid after adding benchmark, it is difficult to meet the needs of engineering application.
Invention content
It is determined greatly based on band limit aviation vector gravitational it is an object of the invention to overcome the deficiencies of the prior art and provide a kind of
Two steps of ground-level integrate anti-solution, realize that aviation vector gravitational determines the computing function of geoid and the earth of acquisition
Level surface precision meets engineering application demand.
The present invention solves existing technical problem and following technical scheme is taken to realize：
It is a kind of to determine that two steps of geoid integrate anti-solution based on limit aviation vector gravitational, include the following steps：
Step 1 is based on the horizontal boundary values theory of broad sense, using band limit aviation vector gravitational calculating with limit boat on enroute altitude
Empty disturbing potential；
Step 2, using inverse Poisson integral models, by the band obtained in step 1 limit aviation disturbing potential downward continuation to extra large
On face, band limit sea disturbance position is obtained, and geoid will be converted into limit sea disturbance position by Bruns formula.
It is as follows that the step 1 calculates the formula with limit aviation disturbing potential：
In formula：Tb(r, θ, λ) is band limit aviation disturbing potential, and r calculates the earth's core at point to diameter for aviation, and θ and λ are aviation meters
The colatitude and longitude at point are calculated, b is band limit order, and GM is Gravitational coefficient of the Earth, and R is earth radius, and L is far field truncation funcation
Maximum order, l are the reference to gravitational field model order removed, Cn(H,ψ0) it is band limit aviation Vector operation band limit aviation disturbing potential
Far field truncation funcation, H is aviation height, ψ0It is integral radius, Tn(θ, λ) is the Laplace harmonic functions of disturbing gravity position, π
It is pi, N is measuring point number in integral radius,WithRespectively band limit aviation vector gravitational measuring point j
North-south component and thing component,It is north-south component and thing point with limit aviation vector gravitational measuring point j
Amount calculates the integral kernel function with limit aviation disturbing potential, ψjIt is that aviation measuring point and aviation calculate spherical angle between point away from Δ σjIt is
Integrate unit area.
Further, the north-south component of the band limit aviation vector gravitational measuring point j and thing component calculate band limit aviation disturbance
The integral kernel function of positionCalculation formula be：
θ in formulajAnd λjIt is the colatitude and longitude at aviation measuring point j, Pn(cosψj) it is Legendre function.
Further, the far field truncation funcation C of the band limit aviation Vector operation band limit aviation disturbing potentialn(H,ψ0) calculating
Formula is：
R in formulanm(ψ0) be Legendre function integral function, be expressed as：
Further, the inverse Poisson integral models of the step 2 are：
In formula：Tb(R, θ ', λ ') is the band limit sea disturbance position of point, (θ ', λ ') be respectively point colatitude and
Longitude, Kb(R, ψ, r) is the kernel function of Poisson integral models, and calculation formula is：
Inverse Poisson integral models are to carrying out processing of inverting after Poisson integral model discretizations, and calculation formula is such as
Under：
Tb(R)=(ATA)-1ATTb(r)
In formula：Tb(R) it is the expression matrix with limit sea disturbance position, Tb(r) it is the expression matrix with limit aviation disturbing potential, A
It is the expression matrix of Poisson integral models.
Further, formula of the step 2 based on Bruns formula calculating geoid is：
In formula：Nb(R, θ, λ) is geoid, and γ is normal gravity.
The advantages and positive effects of the present invention are：
The present invention is first depending on the horizontal boundary values theory of broad sense, is calculated with limit aviation disturbance based on band limit aviation vector gravitational
Position；Then according to inverse Poisson integral models, band limit sea disturbance position is obtained based on band limit disturbing potential downward continuation, and pass through
Bruns formula calculate geoid, provide new solution to calculate geoid based on aviation vector gravitational, lead to
Experimental verification is crossed, the precision of the geoid obtained using this method can meet the needs of engineer application.
Description of the drawings
Fig. 1 a are 2km band limit aviation disturbing gravities north and south horizontal component schematic diagram；
Fig. 1 b are 2km band limit aviation disturbing gravity thing horizontal component schematic diagrames；
Fig. 2 is geoid schematic diagram；
Fig. 3 is the difference value schematic diagram of geoid and standard value that the present invention obtains.
Specific implementation mode
The embodiment of the present invention is further described below in conjunction with attached drawing.
The present invention is a kind of new method calculating geoid based on aviation vector gravitational data, and main includes in following
Hold：It is theoretical according to the horizontal boundary values of broad sense, band limit aviation disturbing potential is calculated based on band limit aviation vector gravitational；According to inverse Poisson
Integral model obtains band limit sea disturbance position based on band limit disturbing potential downward continuation, and calculates the earth level by Bruns formula
Face.
To make the objectives, technical solutions, and advantages of the present invention more comprehensible, it develops simultaneously embodiment pair below in conjunction with attached drawing
The content of present invention elaborates.
Use the air strips limit aviation vector gravitational north and south of global 2160 order of high-order gravity field model EGM2008 simulation calculations
Horizontal componentWith thing horizontal componentAs basic data, the flying height of the aviation vector gravitational is 2000 meters, area
The latitude in domain is 36 ° to 41 °, and longitude is 247 ° to 252 °, and resolution ratio is 2.0 '.In order to simulate airborne vector gravimetry data
The error of handling result, to the band limit aviation vector gravitational horizontal component introduce respectively observation error white noise error (σ=±
3mGal).As shown in table 1：
Table 1 is with limit aviation horizontal component statistical form/mGal
2km bands limit aviation disturbing gravity north and south horizontal component and 2km band limit aviation disturbances is set forth in Fig. 1 a and Fig. 1 b
Gravity thing horizontal component.
In order to check effectiveness of the invention, corresponding geoid N is calculated based on EGM2008 gravity field modelsb
(R, θ, λ), zoning are 38 ° to 39 °, and longitude is 249 ° to 250 °, and resolution ratio is 2.0 '.
2 geoid of table statistics/centimetre
| Type | Minimum value | Maximum value | Average value | Standard deviation | Middle error | Number |
| Geoid | -46.516 | 50.115 | 2.878 | 19.533 | 19.744 | 900 |
Fig. 2 gives geoid schematic diagram.
Using the present invention calculate this aviation vector gravitational data calculate geoid the specific steps are：
Step 1 is based on the horizontal boundary values theory of broad sense, using band limit aviation vector gravitational calculating with limit boat on enroute altitude
Empty disturbing potential, specific formula for calculation are：
In formula：Tb(r, θ, λ) is band limit aviation disturbing potential, and r calculates the earth's core at point to diameter for aviation, and θ and λ are aviation meters
The colatitude and longitude at point are calculated, b is band limit order, and GM is Gravitational coefficient of the Earth, and R is earth radius, and L is far field truncation funcation
Maximum order, l are the reference to gravitational field model order removed, Cn(H,ψ0) it is band limit aviation Vector operation band limit aviation disturbing potential
Far field truncation funcation, H is aviation height, ψ0It is integral radius, Tn(θ, λ) is the Laplace harmonic functions of disturbing gravity position, π
It is pi, N is measuring point number in integral radius,WithRespectively band limit aviation vector gravitational measuring point j
North-south component and thing component,It is north-south component and thing point with limit aviation vector gravitational measuring point j
Amount calculates the integral kernel function with limit aviation disturbing potential, ψjIt is that aviation measuring point and aviation calculate spherical angle between point away from Δ σjIt is
Integrate unit area.
Wherein, north-south component and thing component with limit aviation vector gravitational measuring point j calculate the product with limit aviation disturbing potential
Pyrene functionCalculation formula be：
θ in formulajAnd λjIt is the colatitude and longitude at aviation measuring point j, Pn(cosψj) it is Legendre function.
Wherein, the far field truncation funcation C of aviation disturbing potential is limited with limit aviation Vector operation bandn(H,ψ0) calculation formula be：
R in formulanm(ψ0) be Legendre function integral function, be expressed as：
Step 2 is based on inverse Poisson integral models, and the band obtained in step 1 is limited aviation disturbing potential downward continuation to sea
On face, band limit sea disturbance position is obtained, and geoid will be converted into limit sea disturbance position by Bruns formula, specifically
Calculation formula is：
Poisson integral models are：
In formula：Tb(R, θ ', λ ') is the band limit sea disturbance position of point, (θ ', λ ') be respectively point colatitude and
Longitude, Kb(R, ψ, r) is the kernel function of Poisson integral models, and calculation formula is：
Inverse Poisson integral models are to carrying out processing of inverting after Poisson integral model discretizations, and calculation formula is such as
Under：
Tb(R)=(ATA)-1ATTb(r)
In formula：Tb(R) it is the expression matrix with limit sea disturbance position, Tb(r) it is the expression matrix with limit aviation disturbing potential, A
It is the expression matrix of Poisson integral models.
Based on Bruns formula calculate geoid formula be：
In formula：Nb(R, θ, λ) is geoid, and γ is normal gravity.
By step 2 result of calculation compared with the geoid of standard, statistics such as following table：
Table 3 based on two steps integrate the geoid of anti-solution compared with standard value statistical form/centimetre
| Minimum value | Maximum value | Average value | Standard deviation | Middle error | Number | |
| Fiducial value | -13.856 | 10.875 | -1.085 | 5.274 | 5.384 | 900 |
Fig. 3 gives the difference value of geoid and standard value that anti-solution is integrated based on two steps, passes through table 3 and Fig. 3
As can be seen that in 2000 meters of aviation height, integrates anti-solution using two steps and be based on (σ=± 3mGal) containing white noise error
Band limit aviation vector gravitational calculate geoid precision be 5.384 centimetres, fully meet engineering application requirement.
It is emphasized that embodiment of the present invention is illustrative, without being restrictive, therefore packet of the present invention
Include the embodiment being not limited to described in specific implementation mode, it is every by those skilled in the art according to the technique and scheme of the present invention
The other embodiment obtained, also belongs to the scope of protection of the invention.
Claims (5)
1. a kind of determining that two steps of geoid integrate anti-solution based on limit aviation vector gravitational, it is characterised in that including with
Lower step：
Step 1 is based on the horizontal boundary values theory of broad sense, is disturbed using band limit aviation vector gravitational calculating with aviation is limited on enroute altitude
Dynamic position；
Step 2, using inverse Poisson integral models, the band obtained in step 1 is limited into aviation disturbing potential downward continuation to sea
On, band limit sea disturbance position is obtained, and geoid will be converted into limit sea disturbance position by Bruns formula；
It is as follows that the step 1 calculates the formula with limit aviation disturbing potential：
In formula：Tb(r, θ, λ) is band limit aviation disturbing potential, and r calculates the earth's core at point to diameter for aviation, and θ and λ are that aviation calculates point
The colatitude and longitude at place, b are band limit orders, and GM is Gravitational coefficient of the Earth, and R is earth radius, and L is the maximum of far field truncation funcation
Order, l are the reference to gravitational field model order removed, Cn(H,ψ0) it is to limit the remote of aviation disturbing potential with limit aviation Vector operation band
Area's truncation funcation, H are aviation height, ψ0It is integral radius, Tn(θ, λ) is the Laplace harmonic functions of disturbing gravity position, and π is round
Frequency, N are measuring point numbers in integral radius,WithSouth respectively with limit aviation vector gravitational measuring point j
Northern component and thing component,It is north-south component and thing component meter with limit aviation vector gravitational measuring point j
Calculate the integral kernel function with limit aviation disturbing potential, ψjIt is that aviation measuring point and aviation calculate spherical angle between point away from Δ σjIt is integral
Unit area.
2. according to claim 1 determine that two steps of geoid integrate anti-solution based on limit aviation vector gravitational,
It is characterized in that：The north-south component and thing component of the band limit aviation vector gravitational measuring point j is calculated with limit aviation disturbing potential
Integrate kernel functionCalculation formula be：
θ in formulajAnd λjIt is the colatitude and longitude at aviation measuring point j, Pn(cosψj) it is Legendre function.
3. according to claim 1 determine that two steps of geoid integrate anti-solution based on limit aviation vector gravitational,
It is characterized in that：The far field truncation funcation C of the band limit aviation Vector operation band limit aviation disturbing potentialn(H,ψ0) calculation formula
For：
R in formulanm(ψ0) be Legendre function integral function, be expressed as：
4. according to claim 1 determine that two steps of geoid integrate anti-solution based on limit aviation vector gravitational,
It is characterized in that：The inverse Poisson integral models of the step 2 are：
In formula：Tb(R, θ ', λ ') is the band limit sea disturbance position of point, and (θ ', λ ') is the colatitude and longitude of point respectively,
Kb(R, ψ, r) is the kernel function of Poisson integral models, and calculation formula is：
Inverse Poisson integral models are to carrying out processing of inverting after Poisson integral model discretizations, and calculation formula is as follows：
Tb(R)=(ATA)-1ATTb(r)
In formula：Tb(R) it is the expression matrix with limit sea disturbance position, Tb(r) it is with the expression matrix for limiting aviation disturbing potential, A is
The expression matrix of Poisson integral models.
5. according to claim 1 determine that two steps of geoid integrate anti-solution based on limit aviation vector gravitational,
It is characterized in that：The step 2 based on Bruns formula calculate geoid formula be：
In formula：Nb(R, θ, λ) is geoid, and γ is normal gravity.
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| CN108415879B (en) * | 2018-01-19 | 2021-04-06 | 中国人民解放军92859部队 | Aviation gravity least square downward continuation analysis method based on upward continuation |
| CN108594319A (en) * | 2018-05-11 | 2018-09-28 | 中国人民解放军61540部队 | A kind of Downward Continuation of Airborne Gravity Data method and system |
| CN110161582B (en) * | 2019-05-24 | 2020-05-12 | 中国地质科学院 | Gravity conversion method and system combining air data and ground data |
| CN112949049B (en) * | 2021-02-08 | 2021-11-30 | 中国人民解放军92859部队 | Method for calculating gravity anomaly low-order radial derivative by using band-limiting thought |
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