CN109520486A - A kind of deviation of plumb line real-time computing technique based on horizontal tensor gravity gradient - Google Patents
A kind of deviation of plumb line real-time computing technique based on horizontal tensor gravity gradient Download PDFInfo
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Abstract
The invention discloses a kind of deviation of plumb line real-time computing techniques based on horizontal tensor gravity gradient, comprising the following steps: step 1 establishes the corresponding relationship model between gravity potential field and position deviation under cartesian coordinate system；Step 2 establishes the corresponding relationship model between gravity potential field and position deviation under standard spheroid body coordinate-system；Step 3, the mathematical model defined according to the deviation of plumb line derive the corresponding relationship between the deviation of plumb line and the horizontal tensor of gravity gradient in the way of coordinate system conversion.This method establishes the corresponding relationship between the horizontal tensor of gravity gradient and the deviation of plumb line, the deviation of plumb line is obtained in real time using the horizontal tensor data of the gravity gradient of gravity gradiometer real-time measurement, more conventional deviation of plumb line measurement method, this method may be implemented the deviation of plumb line and accurately calculate in real time, and without relying on astronomical and satellite navigation data, has autonomous measurement capability.
Description
Technical field
The present invention relates to gravimetric technique field, especially a kind of deviation of plumb line based on horizontal tensor gravity gradient is real
When calculation method.
Background technique
In geometry geodesic survey, it will be observed on data projection to the face and being counted as horizontal reference using the earth ellipsoid
It calculates.Plumb line direction on ellipsoid is defined as gravity direction, if the Mass Distribution of the earth is uniformly, on ellipsoid
The normal of each point is consistent with plumb line direction.However, the Mass Distribution of the earth is non-uniform, each point vertical on the earth ellipsoid
With normal direction there are deviation, the deviation of plumb line is exactly the difference between geoid vertical line and reference ellipsoid normal direction in line direction
Different, size and Orientation does not change with the Different Rule of point.In the special applications for having high dependency to the earth horizontal reference
In field, the influence to the deviation of plumb line is very sensitive.Such as: it, will using optical devices such as theodolites in ballistic missile transmitting
Known reference bearing passes to inertial guidance equipment on bullet, is needed at this time by the equipment such as theodolite reference ellipsoid method relative to the earth
Line accurately levels, and the foundation of leveling is that equipment optio binormal is overlapped with gravity direction.But due to the presence of the deviation of plumb line, this method is simultaneously
It cannot be guaranteed that required accurate leveling.In High Accuracy Inertial Navigation System, gravity deflection is important error source, adds gravity
Speed is entered in horizontal accelerometer by the Angles Projections, and integral forms horizontal velocity and location error.
Component of the deviation of plumb line on meridian plane is known as deviation of plumb line meridional component (north and south deviation of plumb line component), is denoted as ξ；
Component on prime plane is known as deviation of plumb line fourth of the twelve Earthly Branches tenth of the twelve Earthly Branches component, is denoted as η.The size of the deviation of plumb line is generally between 3 "~5 ", most
Big reachable 20 "~30 ".Currently, there are mainly four types of the methods of the calculating deviation of plumb line: astronomical geodesy method, gravity measurement side
Method, astrogravimetric method and GPS measurement method.Astronomical geodesy method is the direct measuring method defined under meaning, is needed
The static astronomical observation for a long time of each location point is realized, for country with a vast territory and area, this method
Although solving, more intensive deviation of plumb line precision is high, data are direct, and low efficiency, the practicability is poor,；Gravimetric Method is one
Kind indirect measurement method, the building of earth model is carried out according to global satellite, aviation, ocean and ground gravity data, thus
Difference on to the earth between different location geoid and ellipsoid model of globe solves the deviation of plumb line.This method needs
Data volume it is huge, it is higher for the location information required precision of measuring point, and the deviation of plumb line precision being calculated is relatively low,
Computational efficiency is very high；The characteristics of astrogravimetric is to combine two methods, two methods of having compromised；GPS technology is surveyed
Determine the deviation of plumb line, difference or the height anomaly that geoid must be obtained using measurement of the level technology are poor, also referred to as GPS level method.This
Kind method is limited vulnerable to landform.These four algorithms all cannot achieve the deviation of plumb line and calculate in real time, provide reality for inertial navigation system
When parameter.
For this purpose, we develop the theoretical method for carrying out deflection computation using the horizontal tensor of gravity gradient, realizes and hang down
Line deviation obtains in real time and independently, to meet latent device long-time independent navigation demand.
Summary of the invention
It is an object of the invention to avoid the deficiencies in the prior art, a kind of hanging down based on horizontal tensor gravity gradient is proposed
Line deviation real-time computing technique, algorithm cooperation gravity gradiometer measurement can export high-precision deviation of plumb line value, Jin Ershi in real time
Now the gravity disturbance of High Accuracy Inertial Navigation System is compensated, improves navigation accuracy.
The present invention solves its technical problem and adopts the following technical solutions to achieve:
A kind of deviation of plumb line real-time computing technique based on horizontal tensor gravity gradient, it is characterised in that: including following step
It is rapid:
Step 1 establishes the corresponding relationship model between gravity potential field and position deviation under cartesian coordinate system；
Step 2 establishes the corresponding relationship mould between gravity potential field and position deviation under standard spheroid body coordinate-system
Type；
Step 3, the mathematical model defined according to the deviation of plumb line derive the deviation of plumb line in the way of coordinate system conversion
With the corresponding relationship between the horizontal tensor of gravity gradient.
Moreover, the detailed process of the step 1 are as follows:
Establish an initial coordinate point P0, x coordinate direction direction north orientation, y-coordinate direction direction east orientation, and z coordinate direction
With P0Point vertical line direction is consistent, and is directed toward the earth's core；Other any point P in survey regioni, PiThe z coordinate direction of point and initial
Point P0Vertical direction it is parallel, and PiThe gravity direction of point is not consistent with the direction z, vector PiV is i point gravity giIn xz plane
On projection, and PiH is i point gravity giPart component gxiIn the projection of same plane；
P0Astronomical latitude at point is Φ0, ΔΦiIndicate PiThe direction V and PiThe angle in point z-axis direction, therefore, PiThe latitude of point
Degree are as follows:
Φi=Φ0+ΔΦi. (1)
-gxi=gisinΔΦi, it is believed that ΔΦi=sin ΔΦi, then have:
In the expression of the variation of the astronomical longitude of yz plane are as follows:
Equation (2) and (3) show P on geoid0And PiThe north orientation and east component generated at point, equally any
PkSimilar ΔΦ is obtained at pointkWith Δ ΛkExpression formula is obtained by the longitude and latitude relationship between two points:
Meanwhile
Wherein, ΦiAnd ΦkFor PiAnd PkThe latitude value of point is similar to equation (2) and equation (3), equation (4) and equation
(5) ΔΦ ini、ΔΛiAnd ΔΦk、ΔΛkRespectively in PiAnd PkNorth orientation and east component at point.
Moreover, indicating the true gravity potential field data of the earth with W:WithEquation (4) and
(5) simplify statement are as follows:
Moreover, the detailed process of the step 2 are as follows:
φ and λ indicate geodetic latitude under standard spheroid body and and geodetic longitude, U be gravity position under standard spheroid body, with
Equation (6) form of presentation similar with (7) will change under standard spheroid body are as follows:
Wherein, γiAnd γkBe in PiAnd PkTwo standard spheroid absolute gravity values at point, are subtracted using equation (6)
Equation (8) and utilization equation (7) subtract (9) and obtain,
Moreover, the detailed process of the step 3 are as follows:
Geodetic latitude and geodetic longitude are equal to the longitude and latitude under standard spheroid body, linear corresponding relation are as follows: φ=n φ-κ
With λ=n λ, κ value represents measurement point earth surface and standard spheroid surface along the difference in plumb line direction；
The mathematical expression that the deviation of plumb line defines are as follows:
Wherein, Φ and Λ is the longitude and latitude definition under astronomical coordinate system, and φ and λ are that the longitude and latitude under earth coordinates is fixed
Justice brings equation (11) and (12) into equation (10), then formula (10) changes are as follows:
Wherein, ξ i and ξ k, η i and η k indicate the deviation of plumb line at Pi and Pk point in equation (13) and (14)；
Within the scope of 0.5 ° 0.5 ° of X, the normal gravity under two coordinate systems is equal, therefore gk=γk, gi=γi, side
Journey (13) and (14) then change are as follows:
From formula (15) and (16), using gravity the direction x and y component as intermediate variable, derive that vertical line is inclined
Corresponding relationship between difference and gravity gradient, introduces new expression formula:
Δ W=W-U (17)
Obtain following simplified formula:
The horizontal component W of gravity gradientΔAnd WxyCaused by being the curvature effect of the earth, their passes between the deviation of plumb line
System is direct, specific expression formula are as follows:
Formula (18) and (19) are converted, establish and introduce a new coordinate system reflection gravity gradient horizontal component
With the corresponding relationship between deviation of plumb line variation, to realize the real-time calculating of the deviation of plumb line,
Coordinate conversion is carried out according to new coordinate reference system, using arbitrary point i and k line direction as n axis, with its vertical line
Axis of orientation as s axis, the data of this two observation points are transformed into new coordinate-system, specific mapping mode is such as
Under:
Then corresponding coordinate transformation result is
Then gravity gradient value under new coordinate system are as follows:
The horizontal tensor of new gravity gradient established under new coordinate system, it is horizontal with the gravity gradient under original coordinate system
It establishes when relationship between tensor and is carried out under two continuous azimuth condions of measurement point i and k, therefore utilize this coordinate
Conversion regime is as intermediate variable link, to obtain new equation expression formula；
It is desirable to then have to being integrated on the left of equation (22)
Such as fruit dot PiAnd PkThe distance between it is close if, by second dervative Wns variation regard as one it is linear, therefore
The integral expression of equation (23) then becomes:
Wherein, Nik=nk-niTo represent point PiAnd PkThe distance between；
It carries out effectively merging to convert then having according to the integral result of (23) and equation (21),
Wsk-Wsi=-(Wxk-Wxi)sinαik+(Wyk-Wyi)cosαik (25)
Similar situation, the expansion formula under earth coordinates are as follows:
Usk-Usi=-(Uxk-Uxi)sinαik+(Uyk-Uyi)cosαik (26)
The difference that equation (25) subtracts (26), G are represented using new variable formulaik/ g=Δ υik, and it is expressed as two
Level variable of the point Pi and Pk on the direction n, obtains following expression:
Then had according to the analysis result of the deviation of plumb line:
Gik/ g=(ξk-ξi)sinαik-(ηk-ηi)cosαik (28)
And corresponding Δ WnsIt may be calculated
Wherein, Δ WΔ=WΔ-UΔWith Δ Wxy=Wxy-Uxy, wherein WΔAnd WxyIt can be measured by gravity gradiometer,
And UΔAnd UxyIt is that gravity gradient value under earth coordinates can use formula and be solved, brings equation (30) into equation (29)
Then have afterwards
It brings equation (31) into equation (28), obtains the corresponding pass between the final deviation of plumb line and the horizontal tensor of gravity gradient
System:
From formula (32), the gravity gradient Horizontal component values and observed quantity point of each measurement point can be accurately analyzed
Corresponding relationship between the deviation of plumb line is realized that the deviation of plumb line is realized using the formula and is calculated.
The advantages and positive effects of the present invention are:
This method establishes the corresponding relationship between the horizontal tensor of gravity gradient and the deviation of plumb line, real-time using gravity gradiometer
The horizontal tensor data of the gravity gradient of measurement obtain the deviation of plumb line in real time, more conventional deviation of plumb line measurement method, and this method can be with
It realizes that the deviation of plumb line accurately calculates in real time, and without relying on astronomical and satellite navigation data, has autonomous measurement capability.
Detailed description of the invention
Fig. 1 is corresponding relationship of any observation point between astronomic coordinate system；
Fig. 2 is that x and y converts to form new coordinate system to n and s coordinate.
Specific embodiment
The invention will be further described with reference to the accompanying drawing and by specific embodiment, and following embodiment is descriptive
, it is not restrictive, this does not limit the scope of protection of the present invention.
A kind of deviation of plumb line real-time computing technique based on horizontal tensor gravity gradient, establishes gravity under different coordinate-systems
Linear relationship between gradient and longitude and latitude carries out the deviation of plumb line as datum mark using the deviation of plumb line of 2~3 known points
Iterative solution.
Detailed process is as follows:
It is defined according to the deviation of plumb line it is found that the essence of the deviation of plumb line is exactly that (cartesian coordinate and standard are ellipse for different coordinates
Spherical coordinate system) under normal direction difference.
Under cartesian coordinate system, it is assumed that any one initial coordinate point P0, wherein it is directed toward north orientation, y in x coordinate direction
Coordinate direction direction east orientation, and z coordinate direction and P0Point vertical line direction is consistent, and is directed toward the earth's core.Therefore, have separately in survey region
Outer any point Pi, its z is oriented parallel to P0The z coordinate axis direction of point, xiIt is oriented parallel to P0The astronomical meridian plane of point is cut
Line, the two point between physical relationship it is as shown in Figure 1.It is assumed that PiThe z coordinate direction of point and initial point P0Vertical direction it is flat
Row, and PiThe gravity direction of point is not consistent with the direction z.In Fig. 1, vector PiV is i point gravity giProjection in xz plane,
And PiH is i point gravity giPart component gxiIn the projection of same plane.
P0Astronomical latitude at point is Φ0, ΔΦiIndicate PiThe direction V and PiThe angle in point z-axis direction, therefore, PiThe latitude of point
Degree are as follows:
Φi=Φ0+ΔΦi. (1)
According to Fig. 1 ,-gxi=gisinΔΦi；ΔΦ under actual conditionsiIt is very small, it is approximately considered ΔΦi=sin
ΔΦi, then have:
Also there is same characteristic in the direction y, in the expression of the variation of the astronomical longitude of yz plane are as follows:
Equation (2) and (3) show P on geoid0And PiThe north orientation and east component generated at point, equally any
PkSimilar ΔΦ is obtained at pointkWith Δ ΛkExpression formula is obtained by the longitude and latitude relationship between two points:
Meanwhile
Wherein, ΦiAnd ΦkFor PiAnd PkThe latitude value of point is similar to equation (2) and equation (3), equation (4) and equation
(5) ΔΦ ini、ΔΛiAnd ΔΦk、ΔΛkRespectively in PiAnd PkNorth orientation and east component at point.
In order to more simply clearly state these formula, the true gravity potential field data of the earth are indicated with W, are then provided as follows
Definition:WithSo equation (4) and (5) can be stated with following formula:
Under standard spheroid body coordinate-system, we establish corresponding between same similar gravity potential field and position deviation
Relationship, wherein φ and λ indicate geodetic latitude under standard spheroid body and and geodetic longitude, U be gravity position under standard spheroid body,
The form of presentation similar with equation (6) and (7) will change under standard spheroid body are as follows:
Wherein, γiAnd γkBe in PiAnd PkTwo standard spheroid absolute gravity values at point, are subtracted using equation (6)
Equation (8) and utilization equation (7) subtract (9) and obtain,
According to the definition of the deviation of plumb line: the deviation of plumb line is exactly normal direction and study plot under geoid coordinate system
It is ellipse approximatively to think that geodetic latitude and geodetic longitude are equal to standard herein for the deviation of normal direction under ball spheroid coordinate-system
Longitude and latitude under sphere, there are certain linear corresponding relations between them in fact: φ=n φ-κ and λ=n λ, therein main
Difference is exactly κ value, it represents measurement point earth surface and standard spheroid surface along the difference in plumb line direction.In practical application
In, the two concepts are not distinguished, this value can be ignored under normal circumstances.
The mathematical expression that the deviation of plumb line defines are as follows:
Wherein, Φ and Λ is the longitude and latitude definition under astronomical coordinate system, and φ and λ are that the longitude and latitude under earth coordinates is fixed
Justice brings equation (11) and (12) into equation (10), then formula (10) changes are as follows:
Wherein, ξ i and ξ k, η i and η k indicate the deviation of plumb line at Pi and Pk point in equation (13) and (14).
It consults literature various to show, within the scope of 0.5 ° 0.5 ° of X, it is believed that the normal gravity under two coordinate systems
It is approximately equal, therefore gk=γk, gi=γi.Equation (13) and (14) then change are as follows:
From formula (15) and (16), it can be seen that the deviation of plumb line is related to x the and y directional derivative of gravity position.Currently,
There is no instrument the two components can be accurately measured come, therefore, can only using gravity the direction x and y component in
Between variable, derive the corresponding relationship between the deviation of plumb line and gravity gradient, introduce new expression formula:
Δ W=W-U (17)
Obtain following simplified formula:
The horizontal component W of gravity gradientΔAnd WxyCaused by being the curvature effect of the earth, their passes between the deviation of plumb line
System is direct, specific expression formula are as follows:
In order to find out the inner link between the horizontal tensor of gravity gradient and the deviation of plumb line, formula (18) and (19) are carried out
Conversion establishes and introduces the corresponding pass between a new coordinate system reflection gravity gradient horizontal component and deviation of plumb line variation
System, to realize the real-time calculating of the deviation of plumb line, the new coordinate system of introducing is as shown in Figure 2.
Coordinate conversion is carried out according to new coordinate reference system, using arbitrary point i and k line direction as n axis, with its vertical line
Axis of orientation as s axis, the data of this two observation points are transformed into new coordinate-system, specific mapping mode is such as
Under:
Then corresponding coordinate transformation result is
Then gravity gradient value under new coordinate system are as follows:
The horizontal tensor of new gravity gradient established under new coordinate system, it is horizontal with the gravity gradient under original coordinate system
It establishes when relationship between tensor and is carried out under two continuous azimuth condions of measurement point i and k, therefore utilize this coordinate
Conversion regime is as intermediate variable link, to obtain new equation expression formula.It is desirable to being accumulated on the left of equation (22)
Point, then have
Such as fruit dot PiAnd PkThe distance between it is close if, we approximate can regard second dervative Wns variation as one
Linear, therefore the integral expression of equation (23) then becomes:
Wherein, Nik=nk-niTo represent point PiAnd PkThe distance between.According to the integral result of (23) and equation (21)
It carries out effectively merging to convert then having,
Wsk-Wsi=-(Wxk-Wxi)sinαik+(Wyk-Wyi)cosαik (25)
Similar situation, the expansion formula under earth coordinates are as follows:
Usk-Usi=-(Uxk-Uxi)sinαik+(Uyk-Uyi)cosαik (26)
The difference that equation (25) subtracts (26), G are represented using new variable formulaik/ g=Δ υik, and it is expressed as two
Level variable of the point Pi and Pk on the direction n.Then available following expression:
Then had according to the analysis result of the deviation of plumb line:
Gik/ g=(ξk-ξi)sinαik-(ηk-ηi)cosαik (28)
And corresponding Δ WnsIt may be calculated
Wherein, Δ WΔ=WΔ-UΔWith Δ Wxy=Wxy-Uxy.Wherein, WΔAnd WxyIt can be measured by gravity gradiometer,
And UΔAnd UxyIt is that gravity gradient value under earth coordinates can use formula and be solved.Then bring equation (30) into equation
(29) then have after
Equation (31) is brought into equation (28) then between the available final deviation of plumb line and the horizontal tensor of gravity gradient
Corresponding relationship:
The corresponding relationship between the deviation of plumb line and the horizontal tensor of gravity gradient is derived in the way of coordinate system conversion, from
In formula (32), the gravity gradient Horizontal component values and observed quantity point that we can analyze each measurement point clear and accurately hang down
Corresponding relationship between line deviation may be implemented the deviation of plumb line using the formula and realize calculating.
Although disclosing the embodiment of the present invention and attached drawing for the purpose of illustration, those skilled in the art can be managed
Solution: do not departing from the present invention and spirit and scope of the appended claims in, various substitutions, changes and modifications be all it is possible,
Therefore, the scope of the present invention is not limited to the embodiment and attached drawing disclosure of that.
Claims (5)
1. a kind of deviation of plumb line real-time computing technique based on horizontal tensor gravity gradient, it is characterised in that: the following steps are included:
Step 1 establishes the corresponding relationship model between gravity potential field and position deviation under cartesian coordinate system；
Step 2 establishes the corresponding relationship model between gravity potential field and position deviation under standard spheroid body coordinate-system；
Step 3, the mathematical model defined according to the deviation of plumb line, by coordinate system conversion in the way of derive the deviation of plumb line with again
Corresponding relationship between the horizontal tensor of force gradient.
2. the deviation of plumb line real-time computing technique according to claim 1 based on horizontal tensor gravity gradient, feature exist
In: the detailed process of the step 1 are as follows:
Establish an initial coordinate point P0, x coordinate direction direction north orientation, y-coordinate direction direction east orientation, and z coordinate direction and P0Point
Vertical line direction is consistent, and is directed toward the earth's core；Other any point P in survey regioni, PiThe z coordinate direction of point and initial point P0's
Vertical direction is parallel, and PiThe gravity direction of point is not consistent with the direction z, vector PiV is i point gravity giThrowing in xz plane
Shadow, and PiH is i point gravity giPart component gxiIn the projection of same plane；
P0Astronomical latitude at point is Φ0, ΔΦiIndicate PiThe direction V and PiThe angle in point z-axis direction, therefore, PiThe latitude of point
Are as follows:
Φi=Φ0+ΔΦi. (1)
-gxi=gisinΔΦi, it is believed that ΔΦi=sin ΔΦi, then have:
In the expression of the variation of the astronomical longitude of yz plane are as follows:
Equation (2) and (3) show P on geoid0And PiThe north orientation and east component generated at point, equally in any PkPoint
Place obtains similar ΔΦkWith Δ ΛkExpression formula is obtained by the longitude and latitude relationship between two points:
Meanwhile
Wherein, ΦiAnd ΦkFor PiAnd PkThe latitude value of point is similar to equation (2) and equation (3), in equation (4) and equation (5)
ΔΦi、ΔΛiAnd ΔΦk、ΔΛkRespectively in PiAnd PkNorth orientation and east component at point.
3. the deviation of plumb line real-time computing technique according to claim 2 based on horizontal tensor gravity gradient, feature exist
In: the true gravity potential field data of the earth are indicated with W:WithEquation (4) and (5) simplify statement
Are as follows:
4. the deviation of plumb line real-time computing technique according to claim 3 based on horizontal tensor gravity gradient, feature exist
In: the detailed process of the step 2 are as follows:
φ and λ indicate geodetic latitude under standard spheroid body and and geodetic longitude, U is gravity position under standard spheroid body, with equation
(6) form of presentation similar with (7) will change under standard spheroid body are as follows:
Wherein, γiAnd γkBe in PiAnd PkTwo standard spheroid absolute gravity values at point, subtract equation using equation (6)
(8) and (9) are subtracted using equation (7) to obtain,
5. the deviation of plumb line real-time computing technique according to claim 4 based on horizontal tensor gravity gradient, feature exist
In: the detailed process of the step 3 are as follows:
Geodetic latitude and geodetic longitude are equal to the longitude and latitude under standard spheroid body, linear corresponding relation are as follows: φ=n φ-κ and λ
=n λ, κ value represents measurement point earth surface and standard spheroid surface along the difference in plumb line direction；
The mathematical expression that the deviation of plumb line defines are as follows:
Wherein, Φ and Λ is the longitude and latitude definition under astronomical coordinate system, and φ and λ are the longitude and latitude definition under earth coordinates, will
Equation (11) and (12) bring equation (10) into, then formula (10) changes are as follows:
Wherein, ξ i and ξ k, η i and η k indicate the deviation of plumb line at Pi and Pk point in equation (13) and (14)；
Within the scope of 0.5 ° 0.5 ° of X, the normal gravity under two coordinate systems is equal, therefore gk=γk, gi=γi, equation
(13) then change with (14) are as follows:
From formula (15) and (16), using gravity the direction x and y component as intermediate variable, derive the deviation of plumb line with
Corresponding relationship between gravity gradient introduces new expression formula:
Δ W=W-U (17)
Obtain following simplified formula:
The horizontal component W of gravity gradientΔAnd WxyCaused by being the curvature effect of the earth, their relationships between the deviation of plumb line are straight
It connects, specific expression formula are as follows:
Formula (18) and (19) are converted, a new coordinate system reflection gravity gradient horizontal component is established and introduce and hung down
Corresponding relationship between line change of error, thus realize the real-time calculating of the deviation of plumb line,
Coordinate conversion is carried out according to new coordinate reference system, the side using arbitrary point i and k line direction as n axis, with its vertical line
To axis as s axis, the data of this two observation points are transformed into new coordinate-system, specific mapping mode is as follows:
Then corresponding coordinate transformation result is
Then gravity gradient value under new coordinate system are as follows:
The horizontal tensor of new gravity gradient established under new coordinate system, with the horizontal tensor of gravity gradient under original coordinate system
Between relationship when establish and carry out under two continuous azimuth condions of measurement point i and k, therefore converted using this coordinate
Mode is as intermediate variable link, to obtain new equation expression formula；
It is desirable to then have to being integrated on the left of equation (22)
Such as fruit dot PiAnd PkThe distance between it is close if, regard second dervative Wns variation as linear, a therefore equation
(23) integral expression then becomes:
Wherein, Nik=nk-niTo represent point PiAnd PkThe distance between；
It carries out effectively merging to convert then having according to the integral result of (23) and equation (21),
Wsk-Wsi=-(Wxk-Wxi)sinαik+(Wyk-Wyi)cosαik (25)
Similar situation, the expansion formula under earth coordinates are as follows:
Usk-Usi=-(Uxk-Uxi)sinαik+(Uyk-Uyi)cosαik (26)
The difference that equation (25) subtracts (26), G are represented using new variable formulaik/ g=Δ υik, and it is expressed as two point Pi
With level variable of the Pk on the direction n, following expression is obtained:
Then had according to the analysis result of the deviation of plumb line:
Gik/ g=(ξk-ξi)sinαik-(ηk-ηi)cosαik (28)
And corresponding Δ WnsIt may be calculated
Wherein, Δ WΔ=WΔ-UΔWith Δ Wxy=Wxy-Uxy, wherein WΔAnd WxyIt can be measured by gravity gradiometer, and UΔ
And UxyIt is that gravity gradient value under earth coordinates can use formula and be solved, equation (30) is brought into after equation (29) then
Have
It brings equation (31) into equation (28), obtains the corresponding relationship between the final deviation of plumb line and the horizontal tensor of gravity gradient:
From formula (32), the gravity gradient Horizontal component values and observed quantity point vertical line of each measurement point can be accurately analyzed
Corresponding relationship between deviation is realized that the deviation of plumb line is realized using the formula and is calculated.
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110188510A (en) * | 2019-06-25 | 2019-08-30 | 佛山智异科技开发有限公司 | A kind of Bei Xian mechanism gravity characteristic equivalent simulation method |
| CN110238848A (en) * | 2019-05-30 | 2019-09-17 | 埃夫特智能装备股份有限公司 | The calculation method of gravitational vectors under a kind of robot coordinate system |
| CN111578968A (en) * | 2020-06-17 | 2020-08-25 | 中国人民解放军63660部队 | Novel plumb line deviation correction method |
| CN112729288A (en) * | 2020-12-23 | 2021-04-30 | 北京机电工程研究所 | Gravity gradient-terrain heterogeneous data matching navigation positioning system |
| CN112762924A (en) * | 2020-12-23 | 2021-05-07 | 北京机电工程研究所 | Navigation positioning method based on gravity gradient-terrain heterogeneous data matching |
| CN113251995A (en) * | 2021-05-18 | 2021-08-13 | 中国科学院云南天文台 | Method for obtaining all-weather astronomical longitude and latitude indirect measurement value |
| CN114089432A (en) * | 2021-11-10 | 2022-02-25 | 中国地质大学（北京） | Frequency domain method for inverting marine gravity gradient by using satellite altimetry data |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20100121623A1 (en) * | 2008-11-12 | 2010-05-13 | Terra Nova Sciences Llc | Methods and systems for constructing and using a subterranean geomechanics model spanning local to zonal scale in complex geological environments |
| CN102608668A (en) * | 2011-12-19 | 2012-07-25 | 华中科技大学 | Gravity gradient measurement system and measurement method thereof |
| CN103076640A (en) * | 2013-01-17 | 2013-05-01 | 中国科学院测量与地球物理研究所 | Method for inverting earth gravitational field by using variance-covariance diagonal tensor principle |
| CN103163562A (en) * | 2013-02-01 | 2013-06-19 | 中国科学院测量与地球物理研究所 | Satellite gravity gradient retrieval method based on filtering principle |
| CN105044795A (en) * | 2015-05-29 | 2015-11-11 | 中国船舶重工集团公司第七0七研究所 | Method for reducing measurement error of rotating accelerometer gravity gradiometer by using fiber optic gyroscope |
| US20180372499A1 (en) * | 2017-06-25 | 2018-12-27 | Invensense, Inc. | Method and apparatus for characterizing platform motion |
-
2019
- 2019-01-02 CN CN201910000427.4A patent/CN109520486B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20100121623A1 (en) * | 2008-11-12 | 2010-05-13 | Terra Nova Sciences Llc | Methods and systems for constructing and using a subterranean geomechanics model spanning local to zonal scale in complex geological environments |
| CN102608668A (en) * | 2011-12-19 | 2012-07-25 | 华中科技大学 | Gravity gradient measurement system and measurement method thereof |
| CN103076640A (en) * | 2013-01-17 | 2013-05-01 | 中国科学院测量与地球物理研究所 | Method for inverting earth gravitational field by using variance-covariance diagonal tensor principle |
| CN103163562A (en) * | 2013-02-01 | 2013-06-19 | 中国科学院测量与地球物理研究所 | Satellite gravity gradient retrieval method based on filtering principle |
| CN105044795A (en) * | 2015-05-29 | 2015-11-11 | 中国船舶重工集团公司第七0七研究所 | Method for reducing measurement error of rotating accelerometer gravity gradiometer by using fiber optic gyroscope |
| US20180372499A1 (en) * | 2017-06-25 | 2018-12-27 | Invensense, Inc. | Method and apparatus for characterizing platform motion |
Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110238848A (en) * | 2019-05-30 | 2019-09-17 | 埃夫特智能装备股份有限公司 | The calculation method of gravitational vectors under a kind of robot coordinate system |
| CN110188510A (en) * | 2019-06-25 | 2019-08-30 | 佛山智异科技开发有限公司 | A kind of Bei Xian mechanism gravity characteristic equivalent simulation method |
| CN111578968A (en) * | 2020-06-17 | 2020-08-25 | 中国人民解放军63660部队 | Novel plumb line deviation correction method |
| CN112729288A (en) * | 2020-12-23 | 2021-04-30 | 北京机电工程研究所 | Gravity gradient-terrain heterogeneous data matching navigation positioning system |
| CN112762924A (en) * | 2020-12-23 | 2021-05-07 | 北京机电工程研究所 | Navigation positioning method based on gravity gradient-terrain heterogeneous data matching |
| CN112762924B (en) * | 2020-12-23 | 2023-07-14 | 北京机电工程研究所 | Navigation positioning method based on gravity gradient-topography heterologous data matching |
| CN112729288B (en) * | 2020-12-23 | 2023-07-14 | 北京机电工程研究所 | Gravity gradient-topography heterologous data matched navigation positioning system |
| CN113251995A (en) * | 2021-05-18 | 2021-08-13 | 中国科学院云南天文台 | Method for obtaining all-weather astronomical longitude and latitude indirect measurement value |
| CN114089432A (en) * | 2021-11-10 | 2022-02-25 | 中国地质大学（北京） | Frequency domain method for inverting marine gravity gradient by using satellite altimetry data |
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