CN103499845B - A kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation - Google Patents

A kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation Download PDF

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CN103499845B
CN103499845B CN201310403700.0A CN201310403700A CN103499845B CN 103499845 B CN103499845 B CN 103499845B CN 201310403700 A CN201310403700 A CN 201310403700A CN 103499845 B CN103499845 B CN 103499845B
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gravitation
operational amplifier
circuit
resistance
gradient
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CN201310403700.0A
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CN103499845A (en
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马存尊
李海兵
杨慧
马杰
韩军海
郭刚
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北京航天控制仪器研究所
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Abstract

The invention discloses a kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation.The Gradient of Gravitation that the present invention acts on gravity gradiometer by gravitation generation device exports expression formula, determine the most significant track of theoretical the Gradient of Gravitation change in a space, then the optimum optimization track that gravitation generation device is derived in theory moves, measure the Gradient of Gravitation that gravitation generation device each aspect on track causes, through signal storage and process, the Gradient of Gravitation of measurement is compared work with theoretical the Gradient of Gravitation value judge, obtain measuring accuracy and the resolution of gravity gradiometer.The present invention can carry out accuracy test, the parameter calibration of gravity gradiometer and calibrate for error, and has filled up the blank of domestic gradiometry.

Description

A kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation

Technical field

The present invention relates to a kind of method measuring the Gradient of Gravitation, particularly relate to a kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation, belong to field of measuring technique.

Background technology

Along with the development of science and technology, high precision navigation, earth physical prospecting, submarine accurately to move under water etc. and all have higher requirement to acquisition gravity field information.Gravity gradiometer is a kind of important gravity field information measuring technique and method.Compare gravity meter, gravity gradiometer has following advantage: gravity gradiometer overcomes the impact of the linear acceleration of gradiometry system motion carrier; The Precision Potential of gravity gradiometer is huge; Gravity gradiometer can carry out gravity tensor measurement.At present, external gravity gradiometer correlation technique is ripe, and the eighties in last century, gravity gradiometer dropped into civilian.And domestic relevant gravity gradiometer development is also in the development of theoretical analysis, engineering prototype, relevant measuring technique, method are also in the more original stage.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, provide a kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation, carried out the test of the Gradient of Gravitation by the movement of gravitation generation device on optimum optimization track, this measuring method is simple, and measuring accuracy is high.

Technical solution of the present invention is: a kind of gravity gradient instrument measurement method, and step is as follows:

(1) four accelerometers are distributed on the circular rotating members of single shaft gravity gradiometer, the sensitive axes of adjacent two accelerometers is mutually vertical, the sensitive axes direction of relative two accelerometers is contrary, the sensitive axes direction tangent circular rotating members of four accelerometers;

Wherein the coordinate of single shaft gravity gradiometer is sky, northeast geographic coordinate system, be designated as OXYZ, the center of circle of circular rotating members is the initial point O of coordinate system, and the rotational axis vertical of single shaft gravity gradiometer is in geoid surface, the radius of circular rotating members is r, and angular velocity of rotation is ω;

(2) gravitation generation device is arranged on apart from the space of circular rotating members center of circle 2m;

(3) theory calculate gravitation generation device acts on the Gradient of Gravitation of circular rotating members circle centre position, and computing formula is: Γ xx - Γ yy = 4 Gπρ R 3 l 5 ( x 2 - y 2 ) , Γ xy = 4 Gπρ R 3 l 5 xy ;

Wherein, Γ xx, Γ xy, Γ yythe gravity gradient tensor component of circular rotating members circle centre position, Γ xxfor the local derviation of gravitational acceleration component in X-axis of X-axis, Γ xythe local derviation of gravitational acceleration component in Y-axis of X-axis, Γ yybe the local derviation of gravitational acceleration component in Y-axis of Y-axis, G is Newton constant, and π is circular constant, and R is the radius of gravitation generation device, and ρ is the density of gravitation generation device, x, y, z are respectively the coordinate of gravitation generation device barycenter northeastward under sky geographic coordinate system:

(4) track of the Gradient of Gravitation to gravitation generation device calculated according to step (3) emulates the best mobile alignment obtaining gravitation generation device;

(5) single shaft gravity gradiometer is started, make gravitation generation device emulate along step (4) the best mobile alignment obtained to move, utilize the measurement of the Gradient of Gravitation measuring system obtain gravitation generation device act on circular rotating members circle centre position the Gradient of Gravitation change;

(6) the Gradient of Gravitation step (5) recorded and the Gradient of Gravitation of theory calculate compare, and calibrate the measuring accuracy of single shaft gravity gradiometer;

(7) after utilizing demarcation, single shaft gravity gradiometer carries out the Gradient of Gravitation measurement.

Described gravitation generation device is spheroid, and material is plumbous, and even density distributes.

When described step (4) emulates, the radius R of gravitation generation device gets 0.1m.

Angular range between described single shaft gravity gradiometer circular rotating members and the earth surface level is [-0.3 °, 0.3 °].

Described the Gradient of Gravitation measuring system is by four accelerating velocity meters, four I/V change-over circuits, two one-level amplifying circuits, second amplifying circuit, trap circuit, bandwidth-limited circuit, phase-sensitive detection circuit and low-pass filter circuit composition, four road current signals of four accelerometer generations convert four road voltage signals to respectively through four I/V change-over circuits, the two-way voltage signal often organizing accelerometer conversion carries out amplification respectively through an one-level amplifying circuit and processes for the anti-multiple-frequency modulation signal of offset voltage signal Semi-polarity, and two multiple-frequency modulation signals of same polarity are carried out addition amplification, second amplifying circuit carries out addition to the voltage signal that two one-level amplifying circuits export and amplifies, trap circuit carries out a frequency-doubled signal suppression to the voltage signal after second amplifying circuit amplification and again deducts a residual multiple-frequency modulation signal, bandwidth-limited circuit carries out bandpass filtering to the voltage signal that trap circuit exports, voltage signal after bandpass filtering eventually passes low-pass filter circuit filtering after carrying out phase sensitive detection by phase-sensitive detection circuit and obtains gradient tensor voltage signal.

Described I/V change-over circuit is by anti-phase scaling circuit, integrating circuit, voltage follower circuit and resistance R fcomposition, wherein the first operational amplifier A 1with resistance R f, electric capacity C oform anti-phase scaling circuit and realize the conversion of current signal to voltage signal, resistance R f, electric capacity C othe first operational amplifier A is connected on after parallel connection 1reverse input and output side between, the second operational amplifier A 2, resistance R 1form integrating circuit with electric capacity C, electric capacity C is connected on the second operational amplifier A 2reverse input end and output terminal between, resistance R 1be connected on the first operational amplifier A 1output terminal and the second operational amplifier A 2reverse input end between, the 3rd operational amplifier A 3, resistance R 2with resistance R 3composition voltage follower, resistance R 2be connected on the second operational amplifier A 2output terminal and the 3rd operational amplifier A 3reverse input end between, resistance R 3be connected on the 3rd operational amplifier A 3reverse input end and output terminal between, the 3rd operational amplifier A 3output terminal and the indirect resistance R of input current f, the first operational amplifier A 1, the second operational amplifier A 2with the 3rd operational amplifier A 3positive input ground connection.

Described bandwidth-limited circuit is by four operational amplifier A 4, A 5, A 6, A 7, 8 resistance R 4, R 5, R 6, R 7, R 8, R 9, R 10, R 11with two electric capacity C 1, C 2composition, resistance R 4the output of a termination trap circuit, another termination four-operational amplifier A 4reverse input end, resistance R 5be connected on four-operational amplifier A 4output terminal and reverse input end between, four-operational amplifier A 4output terminal connecting resistance R successively 6, R 7form the output of band-pass circuit, the 6th operational amplifier A 6positive input be connected on resistance R 6, R 7between, resistance R 9be connected on the 6th operational amplifier A 6reverse input end and output terminal between, resistance R 8be connected on the 5th operational amplifier A 5reverse input end and the 6th operational amplifier A 6output terminal between, resistance R 10be connected on the 6th operational amplifier A 6reverse input end and the 7th operational amplifier A 7output terminal between, electric capacity C 2be connected on the 5th operational amplifier A 5reverse input end and output terminal between, the 5th operational amplifier A 5output terminal connecting resistance R 7output terminal, electric capacity C 1be connected on the 7th operational amplifier A 7reverse input end and output terminal between, resistance R 11be connected on the 7th operational amplifier A 7reverse input end and the 5th operational amplifier A 5output terminal between, operational amplifier A 4, A 5, A 7positive input ground connection.

Described trap circuit is made up of operational amplification circuit A8, resistance R12, R13, R14 and bandwidth-limited circuit according to claim 3, between the output terminal that resistance R14 is connected on operational amplification circuit A8 and reverse input end, resistance R13 and bandwidth-limited circuit series connection are between the output terminal and reverse input end of operational amplification circuit A8, the output of the one termination second amplifying circuit of resistance R12, the reverse input end of another termination operational amplification circuit A8, the output of operational amplification circuit A8 is as the output of trap circuit.

The invention has the beneficial effects as follows: the Gradient of Gravitation that the present invention acts on gravity gradiometer by gravitation generation device exports expression formula, determine the most significant track of theoretical the Gradient of Gravitation change in a space, then the optimum optimization track that gravitation generation device is derived in theory moves, measure the Gradient of Gravitation that gravitation generation device each aspect on track causes, through signal storage and process, the Gradient of Gravitation of measurement is compared work with theoretical the Gradient of Gravitation value judge, obtain measuring accuracy and the resolution of gravity gradiometer.The present invention can carry out accuracy test, the parameter calibration of gravity gradiometer and calibrate for error, and has filled up the blank of domestic gradiometry.

Accompanying drawing explanation

Fig. 1 is measurement procedure figure of the present invention;

Fig. 2 is the position view of gravitation generation device in geographic coordinate system OXYZ;

Fig. 3 is gravity gradiometer measuring principle figure of the present invention;

Fig. 4 is the Gradient of Gravitation measuring system theory of constitution figure;

Fig. 5 is the theory of constitution figure of I/V conversion circuit;

Fig. 6 is the theory of constitution figure of bandwidth-limited circuit;

Fig. 7 is the theory of constitution figure of trap circuit.

Embodiment

As shown in Figure 1, performing step of the present invention is as follows:

(1) four accelerometers are distributed on the circular rotating members of single shaft gravity gradiometer, every two accelerometers form one group, often organize accelerometer symmetry to install, the sensitive axes of adjacent two accelerometers is mutually vertical, the sensitive axes direction of relative two accelerometers is contrary, the sensitive axes direction tangent circular rotating members of four accelerometers;

Wherein the coordinate of single shaft gravity gradiometer is sky, northeast geographic coordinate system, be designated as OXYZ, the center of circle of circular rotating members is the initial point O of coordinate system, and the rotational axis vertical of single shaft gravity gradiometer is in geoid surface, the radius of circular rotating members is r, and angular velocity of rotation is ω;

(2) gravitation generation device is arranged on apart from the space of circular rotating members center of circle 2m;

(3) theory calculate gravitation generation device acts on the Gradient of Gravitation of circular rotating members circle centre position, and computing formula is: Γ xx - Γ yy = 4 Gπρ R 3 l 5 ( x 2 - y 2 ) , Γ xy = 4 Gπρ R 3 l 5 xy ;

Wherein, Γ xx, Γ xy, Γ yythe gravity gradient tensor component of circular rotating members circle centre position, Γ xxfor the local derviation of gravitational acceleration component in X-axis of X-axis, Γ xythe local derviation of gravitational acceleration component in Y-axis of X-axis, Γ yybe the local derviation of gravitational acceleration component in Y-axis of Y-axis, G is Newton constant, and π is circular constant, and R is the radius of gravitation generation device, and ρ is the density of gravitation generation device, x, y, z are respectively the coordinate of gravitation generation device barycenter northeastward under sky geographic coordinate system, as shown in Figure 2;

(4) track of the Gradient of Gravitation to gravitation generation device calculated according to step (3) emulates the best mobile alignment obtaining gravitation generation device;

(5) single shaft gravity gradiometer is started, make gravitation generation device emulate along step (4) the best mobile alignment obtained to move, utilize the measurement of the Gradient of Gravitation measuring system obtain gravitation generation device act on circular rotating members circle centre position the Gradient of Gravitation change; During the barycenter relative coordinate initial point O place of gravitation generation device far point position n far away, the Gradient of Gravitation that gravitation generation device acts in gradiometry system is about 0, gravitation generation device barycenter in position 1,2,3 ..., n-1 time the Gradient of Gravitation measuring system the Gradient of Gravitation generation device that to export with the difference that exports of the Gradient of Gravitation measuring system during the n of position be this point act on the Gradient of Gravitation at initial point O place.

(6) the Gradient of Gravitation step (5) recorded and the Gradient of Gravitation of theory calculate compare, and calibrate the measuring accuracy of single shaft gravity gradiometer;

(7) after utilizing demarcation, single shaft gravity gradiometer carries out the Gradient of Gravitation measurement.

Embodiment:

As shown in Figure 3, its embodiment is as follows:

It is gravity gradiometer that the Gradient of Gravitation measures facility, and its model simplification is cylindrical, gets the radius r of gravity gradiometer, and it is gravitation generation device that the Gradient of Gravitation produces facility, and gravitation generation device is spherical, radius R, even material ρ.

Set up gravity gradiometer northeast sky geographic coordinate system OXYZ, turning axle OZ axle is perpendicular to geoid surface, and rotational speed is ω, and the plane of four accelerometer formations and the intersection point of turning axle are the initial point O of coordinate system; The coordinate signal of gravitation generation device in coordinate system OXYZ as shown in Figure 2.

From gravitational field concept, derivation gravitation generation device is on the impact of gradiometry system, and gravitation generation device barycenter acts on the gravitation at true origin O place when (x, y, z) puts:

g → = ( Gρ l ∫ ∫ ∫ Ω 1 x ′ 2 + y ′ 2 + z ′ 2 dx ′ dy ′ dz ′ ) · l → - - - ( 1 )

Do not add the expression formula provided after Integration Solving of derivation, gravitational acceleration distribution in each coordinate axis of gravity gradiometer coordinate system OXYZ:

g ( x ) = 4 πρG R 3 3 l 3 x i → , g ( y ) = 4 πρG R 3 3 l 3 y j → , g ( z ) = 4 πρG R 3 3 l 3 z k → - - - ( 2 )

Gravity gradient tensor is the gradient of gravitational acceleration, is expressed as Γ:

Γ = Γ xx Γ xy Γ xz Γ yx Γ yy Γ yz Γ zx Γ zy Γ zz = ▿ g ( x , y , z ) - - - ( 3 )

Gravitation generation device is at the gravity gradient tensor component of coordinate system OXYZ initial point:

Γ xx = 4 Gπρ R 3 3 l 5 ( 3 x 2 - l 2 ) Γ yy = 4 Gπρ R 3 3 l 5 ( 3 y 2 - l 2 ) Γ zz = 4 Gπρ R 3 3 l 5 ( 3 z 2 - l 2 ) Γ xy = Γ yx = 4 Gπρ R 3 l 5 xy Γ xz = Γ zx = 4 Gπρ R 3 l 5 xz Γ yz = Γ zy = 4 Gπρ R 3 3 l 5 yz - - - ( 4 )

Single shaft gravity gradiometer can only measure the gradient component Γ in circular rotating members plane xxyy, Γ xy, three axle gravity gradiometers could measure whole gradient component, and what discuss herein is single shaft gravity gradient instrument.By Newton second law, the Detection job of accelerometer 1 detects gravitational acceleration vector in space :

a → 1 = ( a → o - g → o ) + ω × r → · + 2 ω → e × ( ω → × r → ) + ω → × ( ω → × r → ) + ω → e × ( ω → e × r → ) - Γ · r → - - - ( 5 )

Wherein, the acceleration that to be circular rotating members circle centre position O point produce by the impact of the celestial body such as the earth, the sun; it is the terrestrial gravitation acceleration of circular rotating members circle centre position O point; it is the rotating angular acceleration of rotary part; the acceleration of Detection job relative to terrestrial coordinate system of accelerometer; it is the spin velocity of the earth.

According to gravity gradiometer measuring principle, the measurement equation of gravity gradiometer is by the combination of four accelerometer sense acceleration output shaft components, its expression formula:

( a → 1 · τ → 1 + a → 3 · τ → 3 ) - ( a → 2 · τ → 2 + a → 4 · τ → 4 ) 2 r = ( Γ xx - Γ yy ) sin 2 ( ωt ) - 2 Γ xy cos 2 ( ωt ) - - - ( 6 )

Wherein, it is the output shaft direction of accelerometer i.

By formula (4), formula (6), obtain:

( a → 1 · τ → 1 + a → 3 · τ → 3 ) - ( a → 2 · τ → 2 + a → 4 · τ → 4 ) 2 r = 4 Gπρ R 3 l 5 [ ( x 2 - y 2 ) sin 2 ( ωt ) - 2 xy cos 2 ( ωt ) ] - - - ( 7 )

According to concrete size, if gravitation generation device is circular, material is plumbous, and the radius R of gravitation generation device gets 0.1m, carries out theory calculate, determines the track that a Gradient of Gravitation is changed significantly, for the movement of gravitation generation device.

As shown in Figure 3, start gradiometry system, between the near point position (1), far point position (n) of optimum optimization track, get (2), (3) ... Deng n-2 location point, when gravitation generation device barycenter is in these, carry out the measurement of the Gradient of Gravitation.It should be noted that: approximate says, the gradient signal that the Gradient of Gravitation generation device of far point position causes is 0, and the major part in gravity gradiometer measuring-signal is steady state noise.So, gravitation generation device barycenter position (1), (2) ..., (n-1) time the Gradient of Gravitation that produces at initial point O place of the Gradient of Gravitation measuring system the Gradient of Gravitation generation device that to export with the difference that exports of the Gradient of Gravitation measuring system during position (n) be this position.

Simulating signal low-pass filtering is carried out in the output of the Gradient of Gravitation measuring system, suggestion filter cutoff frequency scope [0, ω/10 π]; Note E s, E cfor gravitation generation device k, a k ∈ (1,2 ... the n) sinusoidal component of the theoretical gradient value at place and cosine component, E ps, E pcfor gravitation generation device is at the sinusoidal component of the actual gradient value at a k place and cosine component.

E s = 4 Gπρ R 3 l k 5 ( x k 2 - y k 2 ) , E c = 4 Gπρ R 3 l k 5 ( - 2 x k y k )

E ps, E pcbe calculated as:

E ps=(E Sin) k-(E Sin) n;E pc=(E Cos) k-(E Cos) n

Wherein, x k, y k, l kthe position of gravitation generation device in the sky geographic coordinate system OXYZ of gravity gradiometer northeast; (E sin) k, (E sin) ngravitation generation device respectively k, a k ∈ (1,2 ... the gravity gradiometer measuring system sinusoidal component that n) place, n place cause exports, (E cos) k, (E cos) ngravitation generation device respectively k, a k ∈ (1,2 ... the gravity gradiometer measuring system cosine component that n) place, n place cause exports.

Setting gravitation generation device is positioned at a n place, the actual gradient of gradiometry system: E ps 1 = ( E Sin ) ni - ( E Sin ) nj ; E pc 1 = ( E Cos ) ni - ( E Cos ) nj . Wherein (E sin) ni, (E cos) nirepresent (E sin) k, (E cos) ni-th time measure, (E sin) nj, (E cos) njrepresent (E sin) k, (E cos) njth time measure. the Γ of the Gradient of Gravitation component xxyy,-2 Γ xymeasuring accuracy.To be positioned in real process k, a k ∈ (1,2 ... n) the Gradient of Gravitation component E that causes of the gravitation generation device at place ps, E pcwith theoretical the Gradient of Gravitation component E s, E ccompare, if then get E ps, E pcthat the Gradient of Gravitation of gravity gradiometer in self precision is measured.

As shown in Figure 4, the Gradient of Gravitation measuring system is by four accelerating velocity meters, four I/V change-over circuits, two one-level amplifying circuits, second amplifying circuit, trap circuit, bandwidth-limited circuit, phase-sensitive detection circuit and low-pass filter circuit composition, four road current signals of four accelerometer generations convert four road voltage signals to respectively through four I/V change-over circuits, the two-way voltage signal often organizing accelerometer conversion carries out amplification respectively through an one-level amplifying circuit and processes for the anti-multiple-frequency modulation signal of offset voltage signal Semi-polarity, and two multiple-frequency modulation signals of same polarity are carried out addition amplification, second amplifying circuit carries out addition to the voltage signal that two one-level amplifying circuits export and amplifies, trap circuit carries out a frequency-doubled signal suppression to the voltage signal after second amplifying circuit amplification and again deducts a residual multiple-frequency modulation signal, bandwidth-limited circuit carries out bandpass filtering to the voltage signal that trap circuit exports, voltage signal after bandpass filtering eventually passes low-pass filter circuit filtering after carrying out phase sensitive detection by phase-sensitive detection circuit and obtains gradient tensor voltage signal.

Concrete principle is as follows: the I of circuit of the present invention a, I b, I c, I dfour road electric currents are input as gravity gradiometer four acceierometer sensor output signals, and signal comprises a multiple-frequency modulation signal, two multiple-frequency modulation signals, DC bias signal and noise, and in the signal of every road, the amplitude of each component is identical, phase place is different.Four current input signals are become voltage signal by four I/V change-over circuit after-current signals and are amplified 50000 times, and direct current biasing component is deducted simultaneously; In A, B road voltage signal input first order inverting amplifier, a multiple-frequency modulation signal polarity wherein in A, B road is contrary, by a multiple-frequency modulation signal subtraction after first order amplifier, two multiple-frequency modulation signal polarities are identical, amplify 10 times by phase adduction after first order amplifier.Same A, B road, C, D road; Signal polarity after the amplification of two-way one-level is identical, passes in secondary see-saw circuit and sues for peace and amplify 2 times; Signal after secondary amplifies passes in a trap circuit, and object is a multiple-frequency modulation signal remaining in filtered signal and amplifies useful two multiple-frequency modulation signal 10 times; Signal after trap passes in bandwidth-limited circuit, and object makes two multiple-frequency modulation signals pass through and amplify 10 times, other frequency signals and noise filtering; Signal after band is logical passes in phase-sensitive detection circuit, and the signal after phase sensitive detection passes in low-pass filter circuit, and final output signal is just gravity gradient tensor signal.Because gravity gradient tensor is only contained in two frequency multiplication sinewave modulation signal, therefore this main circuit will eliminate DC component, frequency multiplication component sine waves, other higher hamonic waves and random noise, from two extremely faint frequency-doubled signals, detect gradient tensor signal.This circuit suppresses a multiple-frequency modulation signal greatly, amplifies two multiple-frequency modulation signals, effectively detects buried two frequency-doubled signal components in DC component, a frequency-doubled signal component.

As shown in Figure 5, I/V change-over circuit is by anti-phase scaling circuit, integrating circuit, voltage follower circuit and resistance R fcomposition, wherein the first operational amplifier A 1with resistance R f, electric capacity C oform anti-phase scaling circuit and realize the conversion of current signal to voltage signal, resistance R f, electric capacity C othe first operational amplifier A is connected on after parallel connection 1reverse input and output side between, the second operational amplifier A 2, resistance R 1form integrating circuit with electric capacity C, electric capacity C is connected on the second operational amplifier A 2reverse input end and output terminal between, resistance R 1be connected on the first operational amplifier A 1output terminal and the second operational amplifier A 2reverse input end between, the 3rd operational amplifier A 3, resistance R 2with resistance R 3composition voltage follower, resistance R 2be connected on the second operational amplifier A 2output terminal and the 3rd operational amplifier A 3reverse input end between, resistance R 3be connected on the 3rd operational amplifier A 3reverse input end and output terminal between, the 3rd operational amplifier A 3output terminal and the indirect resistance R of input current f, the first operational amplifier A 1, the second operational amplifier A 2with the 3rd operational amplifier A 3positive input ground connection.

As shown in Figure 6, bandwidth-limited circuit is by four operational amplifier A 4, A 5, A 6, A 7, 8 resistance R 4, R 5, R 6, R 7, R 8, R 9, R 10, R 11with two electric capacity C 1, C 2composition, resistance R 4the output of a termination trap circuit, another termination four-operational amplifier A 4reverse input end, resistance R 5be connected on four-operational amplifier A 4output terminal and reverse input end between, four-operational amplifier A 4output terminal connecting resistance R successively 6, R 7form the output of band-pass circuit, the 6th operational amplifier A 6positive input be connected on resistance R 6, R 7between, resistance R 9be connected on the 6th operational amplifier A 6reverse input end and output terminal between, resistance R 8be connected on the 5th operational amplifier A 5reverse input end and the 6th operational amplifier A 6output terminal between, resistance R 10be connected on the 6th operational amplifier A 6reverse input end and the 7th operational amplifier A 7output terminal between, electric capacity C 2be connected on the 5th operational amplifier A 5reverse input end and output terminal between, the 5th operational amplifier A 5output terminal connecting resistance R 7output terminal, electric capacity C 1be connected on the 7th operational amplifier A 7reverse input end and output terminal between, resistance R 11be connected on the 7th operational amplifier A 7reverse input end and the 5th operational amplifier A 5output terminal between, operational amplifier A 4, A 5, A 7positive input ground connection.

As shown in Figure 7, trap circuit is made up of operational amplification circuit A8, resistance R12, R13, R14 and band-pass circuit, between the output terminal that resistance R14 is connected on operational amplification circuit A8 and reverse input end, resistance R13 and band-pass circuit series connection are between the output terminal and reverse input end of operational amplification circuit A8, the output of the one termination second amplifying circuit of resistance R12, the reverse input end of another termination operational amplification circuit A8, the output of operational amplification circuit A8 is as the output of trap circuit.

The non-detailed description of the present invention is known to the skilled person technology.

Claims (6)

1. utilize gravity gradiometer to measure a method for the Gradient of Gravitation, it is characterized in that step is as follows:
(1) four accelerometers are distributed on the circular rotating members of single shaft gravity gradiometer, every two accelerometers form one group, often organize accelerometer symmetry to install, the sensitive axes of adjacent two accelerometers is mutually vertical, the sensitive axes direction of relative two accelerometers is contrary, the sensitive axes direction tangent circular rotating members of four accelerometers;
Wherein the coordinate of single shaft gravity gradiometer is sky, northeast geographic coordinate system, be designated as OXYZ, the center of circle of circular rotating members is the initial point O of coordinate system, and the rotational axis vertical of single shaft gravity gradiometer is in geoid surface, the radius of circular rotating members is r, and angular velocity of rotation is ω;
(2) gravitation generation device is arranged on apart from the space of circular rotating members center of circle 2m;
(3) theory calculate gravitation generation device acts on the Gradient of Gravitation of circular rotating members circle centre position, and computing formula is: Γ x x - Γ y y = 4 GπρR 3 l 5 ( x 2 - y 2 ) , Γ x y = 4 GπρR 3 l 5 x y ;
Wherein, Γ xx, Γ xy, Γ yythe gravity gradient tensor component of circular rotating members circle centre position, Γ xxfor the local derviation of gravitational acceleration component in X-axis of X-axis, Γ xythe local derviation of gravitational acceleration component in Y-axis of X-axis, Γ yybe the local derviation of gravitational acceleration component in Y-axis of Y-axis, G is Newton constant, and π is circular constant, and R is the radius of gravitation generation device, and ρ is the density of gravitation generation device, x, y, z are respectively the coordinate of gravitation generation device barycenter northeastward under sky geographic coordinate system:
(4) track of the Gradient of Gravitation to gravitation generation device calculated according to step (3) emulates the best mobile alignment obtaining gravitation generation device;
(5) single shaft gravity gradiometer is started, make gravitation generation device emulate along step (4) the best mobile alignment obtained to move, utilize the measurement of the Gradient of Gravitation measuring system obtain gravitation generation device act on circular rotating members circle centre position the Gradient of Gravitation change;
(6) the Gradient of Gravitation step (5) recorded and the Gradient of Gravitation of theory calculate compare, and calibrate the measuring accuracy of single shaft gravity gradiometer;
(7) after utilizing demarcation, single shaft gravity gradiometer carries out the Gradient of Gravitation measurement;
Described the Gradient of Gravitation measuring system is by four accelerometers, four I/V change-over circuits, two one-level amplifying circuits, second amplifying circuit, trap circuit, bandwidth-limited circuit, phase-sensitive detection circuit and low-pass filter circuit composition, four road current signals of four accelerometer generations convert four road voltage signals to respectively through four I/V change-over circuits, the two-way voltage signal often organizing accelerometer conversion carries out amplification respectively through an one-level amplifying circuit and processes for the anti-multiple-frequency modulation signal of offset voltage signal Semi-polarity, and two multiple-frequency modulation signals of same polarity are carried out addition amplification, second amplifying circuit carries out addition to the voltage signal that two one-level amplifying circuits export and amplifies, trap circuit carries out a multiple-frequency modulation signal suppressing to the voltage signal after second amplifying circuit amplification and again deducts a residual multiple-frequency modulation signal, bandwidth-limited circuit carries out bandpass filtering to the voltage signal that trap circuit exports, voltage signal after bandpass filtering eventually passes low-pass filter circuit filtering after carrying out phase sensitive detection by phase-sensitive detection circuit and obtains gradient tensor voltage signal,
Described I/V change-over circuit is by anti-phase scaling circuit, integrating circuit, voltage follower circuit and resistance R fcomposition, wherein the first operational amplifier A 1with resistance R f, electric capacity C oform anti-phase scaling circuit and realize the conversion of current signal to voltage signal, resistance R f, electric capacity C othe first operational amplifier A is connected on after parallel connection 1reverse input end and output terminal between, the second operational amplifier A 2, resistance R 1form integrating circuit with electric capacity C, electric capacity C is connected on the second operational amplifier A 2reverse input end and output terminal between, resistance R 1be connected on the first operational amplifier A 1output terminal and the second operational amplifier A 2reverse input end between, the 3rd operational amplifier A 3, resistance R 2with resistance R 3composition voltage follower circuit, resistance R 2be connected on the second operational amplifier A 2output terminal and the 3rd operational amplifier A 3reverse input end between, resistance R 3be connected on the 3rd operational amplifier A 3reverse input end and output terminal between, the 3rd operational amplifier A 3output terminal and the indirect resistance R of input current f, the first operational amplifier A 1, the second operational amplifier A 2with the 3rd operational amplifier A 3positive input ground connection.
2. a kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation according to claim 1, is characterized in that: described bandwidth-limited circuit is by four operational amplifier A 4, A 5, A 6, A 7, eight resistance R 4, R 5, R 6, R 7, R 8, R 9, R 10, R 11with two electric capacity C 1, C 2composition, resistance R 4the output terminal of a termination trap circuit, another termination four-operational amplifier A 4reverse input end, resistance R 5be connected on four-operational amplifier A 4output terminal and reverse input end between, four-operational amplifier A 4output terminal connecting resistance R successively 6, R 7form the output of bandwidth-limited circuit, the 6th operational amplifier A 6positive input be connected on resistance R 6, R 7between, resistance R 9be connected on the 6th operational amplifier A 6reverse input end and output terminal between, resistance R 8be connected on the 5th operational amplifier A 5reverse input end and the 6th operational amplifier A 6output terminal between, resistance R 10be connected on the 6th operational amplifier A 6reverse input end and the 7th operational amplifier A 7output terminal between, electric capacity C 2be connected on the 5th operational amplifier A 5reverse input end and output terminal between, the 5th operational amplifier A 5output terminal connecting resistance R 7output terminal, electric capacity C 1be connected on the 7th operational amplifier A 7reverse input end and output terminal between, resistance R 11be connected on the 7th operational amplifier A 7reverse input end and the 5th operational amplifier A 5output terminal between, operational amplifier A 4, A 5, A 7positive input ground connection.
3. a kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation according to claim 2, is characterized in that: described trap circuit is by operational amplification circuit A 8, resistance R 12, R 13, R 14form with bandwidth-limited circuit according to claim 2, resistance R 14be connected on operational amplification circuit A 8output terminal and reverse input end between, resistance R 13with bandwidth-limited circuit series connection at operational amplification circuit A 8output terminal and reverse input end between, resistance R 12the output terminal of a termination second amplifying circuit, another termination operational amplification circuit A 8reverse input end, operational amplification circuit A 8output as the output of trap circuit.
4. a kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation according to claim 1, it is characterized in that: described gravitation generation device is spheroid, material is plumbous, and even density distributes.
5. a kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation according to claim 1, is characterized in that: when described step (4) emulates, the radius R of gravitation generation device gets 0.1m.
6. a kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation according to claim 1, is characterized in that: the angular range between described single shaft gravity gradiometer circular rotating members and the earth surface level is [-0.3 °, 0.3 °].
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Families Citing this family (8)

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Publication number Priority date Publication date Assignee Title
CN103885019B (en) * 2014-02-28 2016-05-04 中国船舶重工集团公司第七一〇研究所 For two homogeneity range type magnetic field generation devices and the calibration steps of magnetometer calibration
CN104569496B (en) * 2014-12-26 2017-07-07 北京航天控制仪器研究所 A kind of method of use the Gradient of Gravitation testing acceleration score resolution
CN104597520B (en) * 2015-01-05 2017-03-29 中国船舶重工集团公司第七0七研究所 A kind of gravity gradiometer gravity gradient sensor input stimulus production method
CN104898176B (en) * 2015-06-10 2017-10-20 东南大学 A kind of rotating accelerometer gravity gradiometer gravity gradient demodulation method
CN105044798A (en) * 2015-06-29 2015-11-11 东南大学 Rotating accelerometer gravity gradiometer accelerometer scale factor feedback adjustment method
CN105717553B (en) * 2016-01-29 2018-01-16 东南大学 A kind of rotating accelerometer gravity gradiometer scaling method
CN106052694B (en) * 2016-07-11 2017-03-15 中南大学 Based on the method that gravitational vectors and its gradient tensor carry out locating and tracking to single moving object
CN110133735B (en) * 2019-05-16 2020-05-29 山东大学 Deep abnormal body boundary identification and step-by-step enhancement method, system, medium and equipment

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102608668A (en) * 2011-12-19 2012-07-25 华中科技大学 Gravity gradient measurement system and measurement method thereof

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
AUPS114702A0 (en) * 2002-03-18 2002-04-18 Bhp Billiton Innovation Pty Ltd Enhancement of sensors for airborne operation
CA2690893A1 (en) * 2006-11-20 2008-05-29 Technological Resources Pty Limited A gravity gradiometer

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102608668A (en) * 2011-12-19 2012-07-25 华中科技大学 Gravity gradient measurement system and measurement method thereof

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
Advances and Challenges in the development and deployment of gravity gradiometer systems;D.Difrancesco,et al.;《EGM 2007 International Workshop》;20071231;第1-6页 *
全张量重力梯度仪测量方程及误差分析;李海兵等;《东南大学学报(自然科学版)》;20100531;第40卷(第3期);第517-521页 *
星载硅微静电加速度计的设计与噪声分析;段光武;《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》;20120215(第2期);第71页第1-13行及图4.14 *
用于重力梯度仪标校的引力产生装置轨迹优化方法;马存尊等;《导航与控制》;20130831;第12卷(第3期);第40页第1栏第34行-第2栏第24行,第41页第1栏第13行-第2栏第25行,第42页第1栏第1行-第2栏第21行 *

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