CN108931824B - Error gain coefficient calibration method for gravity gradiometer of rotating accelerometer with movable base - Google Patents
Error gain coefficient calibration method for gravity gradiometer of rotating accelerometer with movable base Download PDFInfo
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Abstract
The invention discloses a method for calibrating error gain coefficients of a gravity gradiometer of a rotating accelerometer with a movable base. The calibration method can calibrate error gain coefficients caused by misalignment of accelerometer installation inside the gravity gradiometer, mismatch of accelerometer calibration coefficients, mismatch of circuits and the like. The calibration method is simple to operate and easy to implement.
Description
Technical Field
The invention relates to a method for calibrating an error coefficient of a gravity gradiometer of a rotating accelerometer with a movable base, belonging to the technical field of precision measurement.
Background
The dynamic base gravity gradient exploration is a low-cost and high-efficiency gravity gradient exploration method; is the most advanced gravity field exploration mode in the world at present. The gravity gradient data is widely applied to geological analysis, gravity field modeling, high-precision navigation, resource exploration and the like. The gravity gradiometer has extremely important national defense and civil values. At present, the gravity gradiometers researched at home and abroad mainly comprise cold atom gravity gradiometers, superconducting gravity gradiometers, MEMS gravity gradiometers and the like. The gravity gradiometers which have been put into commercial use abroad mainly include a rotary accelerometer gravity gradiometer and a rotary superconducting accelerometer gravity gradiometer. A gravity gradiometer model machine in China is under development.
During moving base gravity gradient exploration, due to the fact that installation errors of accelerometers in a gravity gradiometer exist, the first-order and high-order scale coefficients of the accelerometers are not matched, dynamic acceleration and angular jitter of a gravity gradiometer installation carrier are transmitted to the output of the gravity gradiometer, and measurement errors are caused. The invention provides a gravity gradiometer which can calibrate error gain coefficients caused by accelerometer installation errors in the gravity gradiometer, accelerometer scale coefficient mismatching and the like, can compensate gravity gradient measurement errors caused by carrier dynamic acceleration according to the calibrated error gain coefficients, and improves the measurement precision of the gravity gradiometer. There is no published literature to report the calibration of the error gain factor.
Disclosure of Invention
The technical problem is as follows: the invention provides the method for calibrating the error gain coefficient of the gravity gradiometer of the movable base rotating accelerometer, which can calibrate the error gain coefficient of the dynamic acceleration of a carrier, compensate the gravity gradient measurement error caused by the dynamic acceleration of the carrier, improve the measurement precision of the gravity gradiometer, and has simple operation and easy implementation.
The technical scheme is as follows: the invention discloses a method for calibrating an error gain coefficient of a gravity gradiometer of a rotating accelerometer with a movable base, which comprises the following steps:
(1) calibrating error gain coefficients of the gravity gradiometer respectively according to the following modes;
calibrating a first coefficient k of installation error of an accelerometerin/csAnd the gravity gradiometer scale factor kggi: during calibration, the gravity gradiometer is kept static, different detection masses are applied to the gravity gradiometer, different universal gravity gradient excitations are generated for the gravity gradiometer, the excitation of each detection mass to the gravity gradiometer and the output of the 1 st channel and the 2 nd channel of the gravity gradiometer are recorded, and N is used in total1The detection mass excites the gravity gradiometer and records N1Group data, N1Must be greater than or equal to 2, the data is substituted into the following equation, and k is calculatedin/csAnd kggi：
In the formula T1(1)，T2(1) Respectively representing the excitation of the 1 st and 2 nd channels of the gravity gradiometer by the 1 st detection mass, Gin(1)，Gcs(1) Respectively representing the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the action of the 1 st detection mass, T1(2)，T2(2) Respectively representing the excitation of the 2 nd detection mass to the 1 st channel and the 2 nd channel of the gravity gradiometer, Gin(2)，Gcs(2) Respectively representing the output of the 1 st channel and the 2 nd channel of the gravity gradiometer under the action of the 2 nd detection mass, T1(N1)，T2(N1) Respectively represent the Nth1Excitation of the 1 st and 2 nd channel of the gravity gradiometer by individual detection masses, Gin(N1)，Gcs(N1) Respectively represent the Nth1The output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the action of the detection mass;
represents the left inverse;
calibrating a second coefficient of accelerometer mounting errorDuring calibration, 2 times frequency acceleration is applied to the z-axis direction of the gravity gradiometer, namely
And recording the output of the 1 st channel of the gravity gradiometer under the action of the accelerationRepresenting the amplitude, G, of the 1 st applied 2-times frequency accelerationin(1) Shows the output of the 1 st channel of the gravity gradiometer under the action of the acceleration,
representing the amplitude, G, of the 2 nd applied 2-fold accelerationin(2) Representing the output of the 1 st channel of the gravity gradiometer under the acceleration action, and substituting the recorded 2 groups of experimental data into the following formula for calculation
Calibrating second-order nonlinear first coefficient of accelerometer
And second-order nonlinear second coefficient of accelerometer
During calibration, constant acceleration is applied to the x direction and the y direction of the gravity gradiometer at the same time, the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer are recorded, and N is applied in total2Recording N2 sets of experimental data, N, of the second different constant accelerations2Must be greater than or equal to 2, the experimental data is substituted into the following formula to calculate
And
in the formula (I), the compound is shown in the specification,
respectively representing the 1 st applied constant acceleration in the x direction and the 1 st applied constant acceleration in the y direction of the gravity gradiometer, Gin(1)，Gcs(1) Respectively showing the output of the 1 st channel and the 2 nd channel of the gravity gradiometer under the joint action of the two accelerations,
respectively representing the 2 nd applied constant acceleration in the x direction and the 2 nd applied constant acceleration in the y direction of the gravity gradiometer, Gin(2)，Gcs(2) Respectively showing the output of the 1 st channel and the 2 nd channel of the gravity gradiometer under the joint action of the two accelerations,
respectively represent the Nth direction of the x direction of the gravity gradiometer2Constant acceleration applied once and Nth direction in y direction2Constant acceleration of the secondary application, Gin(N2)，Gcs(N2) Respectively showing the output of the 1 st channel and the 2 nd channel of the gravity gradiometer under the joint action of the two accelerations,
represents the left inverse;
calibrating second-order nonlinear error third coefficient of accelerometer
During calibration, 1 frequency multiplication acceleration is applied to the direction of the z axis of the gravity gradiometer, namely
And recording the output of the 2 nd channel of the gravity gradiometer under the action of the acceleration,
representing the 1 st applied frequency multiplication acceleration amplitude G in the z-axis direction of the gravity gradiometercs(1) Representing the output of the 2 nd channel of the gravity gradiometer under the acceleration,representing the amplitude of the 1-time multiplied acceleration applied 2 nd time in the z-axis direction of the gravity gradiometer, Gcs(2) Representing the output of the 2 nd channel of the gravity gradiometer under the condition, and substituting the recorded 2 groups of experimental data into the following formula for calculation
Calibrating the fourth coefficient of the second-order nonlinear error of the accelerometer
And the fifth coefficient of second-order nonlinear error of accelerometerDuring calibration, the y-axis of the gravity gradiometer is subjected to a constant acceleration, i.e. the acceleration is constant
Simultaneously applying 3 times frequency acceleration to the z-axis direction of the gravity gradiometer, recording the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the combined action of the two accelerations, only changing the amplitude of the 3 times frequency acceleration applied to the z-axis direction of the gravity gradiometer, keeping the constant value acceleration applied to the y-axis direction of the gravity gradiometer unchanged, recording the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the combined action of the two accelerations, and recording to obtain 2 groupsData and substituting into the following formula to calculate
In the formula (I), the compound is shown in the specification,
represents an applied constant acceleration in the direction of the y-axis of the gravity gradiometer;
representing the amplitude, G, of the 1 st applied 3-times-frequency sinusoidal acceleration in the z-axis direction of the gravity gradiometerin(1)，Gcs(1) Respectively showing the output of the 1 st channel and the 2 nd channel of the gravity gradiometer under the joint action of the two accelerations,
representing the amplitude, G, of the 2 nd applied frequency-doubled sinusoidal acceleration of the gravity gradiometer in the z-axis directionin(2)，Gcs(2) The output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the combined action of the two accelerations are respectively shown.
Calibrating coupling first coefficient of accelerometer second-order nonlinear error and accelerometer installation error
Second coupling coefficient of second-order nonlinear error of accelerometer and installation error of accelerometer
During calibration, 3 times of frequency acceleration is applied to the y-axis direction of the gravity gradiometer, namely
The output of the 1 st channel and the 2 nd channel of the gravity gradiometer are recorded, acceleration is applied 2 times in total,2 sets of experimental data were recorded and,
representing the amplitude, G, of the 1 st applied 3-times-frequency sinusoidal acceleration in the y-axis direction of the gravity gradiometerin(1)，Gcs(1) Respectively representing the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the action of the acceleration,representing the amplitude, G, of the 2 nd applied frequency-doubled sinusoidal acceleration of the gravity gradiometer in the y-axis directionin(2)，Gcs(2) Respectively representing the output of the 1 st channel and the 2 nd channel of the gravity gradiometer under the acceleration action, and substituting the recorded 2 groups of experimental data into the following formula for calculation
(2) On the basis of the step (1), calibrating a sixth coefficient of the second-order nonlinear error of the accelerometer in the following way
During calibration, 1 frequency multiplication acceleration is applied to the y-axis direction of the gravity gradiometer, namely
Recording the output of the 2 nd channel of the gravity gradiometer, applying acceleration for 2 times in total, recording 2 groups of experimental data,
representing the amplitude of 1 multiplied sinusoidal acceleration applied at the 1 st time in the y-axis direction of the gravity gradiometer, Gcs (1) representing the output of the 2 nd channel of the gravity gradiometer under the action of the acceleration,
representing the amplitude, G, of the 1 st harmonic sinusoidal acceleration applied 2 nd time in the y-axis direction of the gravity gradiometercs(2) Representing the output of the 2 nd channel of the gravity gradiometer under the acceleration action, and substituting the recorded 2 groups of experimental data into the following formula for calculation
In the formula
Is the value calibrated in the step (1),is the value calibrated in step (1).
Furthermore, in the method, 4 accelerometers are arranged on a rotating disk inside the rotating accelerometer gravity gradiometer.
Furthermore, in the method, the direction of the sensitive axis of the accelerometer of the gravity gradiometer of the rotating accelerometer is consistent with the tangential direction of the rotating disk.
Furthermore, in the method of the present invention, the accelerometer installed inside the gravity gradiometer of the rotational accelerometer is a force-balanced accelerometer.
Further, in the method of the present invention, the output model of the accelerometer installed in the rotating accelerometer gravity gradiometer is:
in the formula K1Is the scaling factor of the accelerometer, K2，K4，K5，K6，K7，K8Respectively, the second order error coefficient of the accelerometer, IoutIs the output current of the accelerometer, aiIs an input axis square of an accelerometerTo a sensitive acceleration, aoIs the acceleration of the accelerometer in the direction of the output axis, apIs the acceleration of the accelerometer in the direction of the yaw axis.
When the gravity gradient exploration of the moving base is carried out, the dynamic acceleration of the carrier is transmitted to the output of the gravity gradiometer through the error gain coefficient of the gravity gradiometer, and the gravity gradient measurement error is generated. The error gain coefficient is caused by the installation error of an accelerometer inside the gravity gradiometer, mismatching of accelerometer scale coefficients, mismatching of circuits and the like. The method can calibrate the error gain coefficient of the dynamic acceleration of the carrier, thereby compensating the gravity gradient measurement error caused by the dynamic acceleration of the carrier and improving the measurement precision of the gravity gradiometer. The calibration method is simple to operate and easy to implement.
Has the advantages that: compared with the prior art, the invention has the following advantages:
the invention provides a calibration method of error gain coefficients of a gravity gradiometer of a rotary accelerometer for the first time. The calibration method can calibrate error gain coefficients caused by installation errors of the accelerometer in the gravity gradiometer of the rotating accelerometer, mismatch of the calibration coefficients of the accelerometer, mismatch of circuits and the like, can compensate gravity gradient measurement errors caused by acceleration of a carrier according to the calibrated error gain coefficients and carrier acceleration data, and improves the measurement precision of the gravity gradiometer. The calibration method is simple, efficient and easy to implement.
Drawings
FIG. 1 is a schematic view of the mounting of an accelerometer inside a rotary accelerometer gravity gradiometer.
Detailed Description
The invention is further described with reference to the following examples and the accompanying drawings.
The error model of the four-rotation accelerometer gravity gradiometer before demodulation is as follows:
in the formula kggiIs the scale factor, k, of a gravity gradiometerin/cs，
Is the error gain factor caused by the mounting misalignment of the accelerometer inside the gravity gradiometer,
is an error gain coefficient caused by the calibration coefficient of an accelerometer in the gravity gradiometer and circuit mismatching,
the error gain coefficient is caused by the misalignment of the installation error of the accelerometer in the gravity gradiometer and the mismatch of the scale coefficient of the accelerometer. a isx，ay，azThe acceleration of the gravity gradiometer in the x, y and z directions is obtained; t is1，T2Excitation of the 1 st channel and the 2 nd channel of the gravity gradiometer respectively; omega is the angular velocity of rotation of the accelerometer-mounted disk inside the gravity gradiometer. The output of the 1 st and 2 nd channels of the gravity gradiometer is ToutIn sin (2 Ω t), the amplitude of cos (2 Ω t) is demodulated. From the equation, the carrier acceleration ax，ay，azMiddle and low frequency part, can be obtained by an error gain coefficient kin/cs，
Transmitted to the output of the gravity gradiometer, causing gravity gradient measurement errors. k is a radical ofin/cs，
Is the error gain factor to be calibrated.
The invention discloses a method for calibrating an error gain coefficient of a gravity gradiometer of a rotating accelerometer with a movable base, which comprises the following steps:
(1) calibrating error gain coefficients of the gravity gradiometer respectively according to the following modes;
calibrating a first coefficient k of installation error of an accelerometerin/csAnd the gravity gradiometer scale factor kggi: when the calibration is carried out, the gravity gradiometer is kept still and is balancedApplying different detection masses, generating different gravitational gradient excitations to the gravity gradiometer, recording the excitation of each detection mass to the gravity gradiometer and the output of the 1 st and 2 nd channels of the gravity gradiometer, and totally using N1The detection mass excites the gravity gradiometer and records N1Group data, N1Must be greater than or equal to 2, the data is substituted into the following equation, and k is calculatedin/csAnd kggi：
In the formula T1(1)，T2(1) Respectively representing the excitation of the 1 st and 2 nd channels of the gravity gradiometer by the 1 st detection mass, Gin(1)，Gcs(1) Respectively representing the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the action of the 1 st detection mass, T1(2)，T2(2) Respectively representing the excitation of the 2 nd detection mass to the 1 st channel and the 2 nd channel of the gravity gradiometer, Gin(2)，Gcs(2) Respectively representing the output of the 1 st channel and the 2 nd channel of the gravity gradiometer under the action of the 2 nd detection mass, T1(N1)，T2(N1) Respectively represent the Nth1Excitation of the 1 st and 2 nd channel of the gravity gradiometer by individual detection masses, Gin(N1)，Gcs(N1) Respectively represent the Nth1The output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the action of the detection mass;
represents the left inverse;
calibrating a second coefficient of accelerometer mounting errorDuring calibration, 2 times frequency acceleration is applied to the z-axis direction of the gravity gradiometer, namely
And recordThe output of the 1 st channel of the gravity gradiometer under the action of the acceleration is used
Representing the amplitude, G, of the 1 st applied 2-times frequency accelerationin(1) Shows the output of the 1 st channel of the gravity gradiometer under the action of the acceleration,
representing the amplitude, G, of the 2 nd applied 2-fold accelerationin(2) Representing the output of the 1 st channel of the gravity gradiometer under the acceleration action, and substituting the recorded 2 groups of experimental data into the following formula for calculation
Calibrating second-order nonlinear first coefficient of accelerometer
And second-order nonlinear second coefficient of accelerometer
During calibration, constant acceleration is applied to the x direction and the y direction of the gravity gradiometer at the same time, the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer are recorded, and N is applied in total2Recording N2 sets of experimental data, N, of the second different constant accelerations2Must be greater than or equal to 2, the experimental data is substituted into the following formula to calculate
And
in the formula (I), the compound is shown in the specification,respectively representing the 1 st applied constant acceleration in the x direction and the 1 st applied constant acceleration in the y direction of the gravity gradiometer, Gin(1)，Gcs(1) Respectively showing the output of the 1 st channel and the 2 nd channel of the gravity gradiometer under the joint action of the two accelerations,
respectively representing the 2 nd applied constant acceleration in the x direction and the 2 nd applied constant acceleration in the y direction of the gravity gradiometer, Gin(2)，Gcs(2) Respectively showing the output of the 1 st channel and the 2 nd channel of the gravity gradiometer under the joint action of the two accelerations,
respectively represent the Nth direction of the x direction of the gravity gradiometer2Constant acceleration applied once and Nth direction in y direction2Constant acceleration of the secondary application, Gin(N2)，Gcs(N2) Respectively showing the output of the 1 st channel and the 2 nd channel of the gravity gradiometer under the joint action of the two accelerations,
represents the left inverse;
calibrating second-order nonlinear error third coefficient of accelerometer
During calibration, 1 frequency multiplication acceleration is applied to the direction of the z axis of the gravity gradiometer, namely
And recording the output of the 2 nd channel of the gravity gradiometer under the action of the acceleration,1 for the 1 st application in the z-axis direction of a gravity gradiometerAmplitude of frequency multiplication acceleration, Gcs(1) Representing the output of the 2 nd channel of the gravity gradiometer under the acceleration,
representing the amplitude of the 1-time multiplied acceleration applied 2 nd time in the z-axis direction of the gravity gradiometer, Gcs(2) Representing the output of the 2 nd channel of the gravity gradiometer under the condition, and substituting the recorded 2 groups of experimental data into the following formula for calculation
Calibrating the fourth coefficient of the second-order nonlinear error of the accelerometer
And the fifth coefficient of second-order nonlinear error of accelerometer
During calibration, the y-axis of the gravity gradiometer is subjected to a constant acceleration, i.e. the acceleration is constant
Applying 3 times frequency acceleration to the z-axis direction of the gravity gradiometer, recording the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the combined action of the two accelerations, only changing the amplitude of the 3 times frequency acceleration applied to the z-axis direction of the gravity gradiometer, keeping the constant value acceleration applied to the y-axis direction of the gravity gradiometer unchanged, recording the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the combined action of the two accelerations, recording to obtain 2 groups of data, substituting the data into the following formula to calculate
In the formula (I), the compound is shown in the specification,represents an applied constant acceleration in the direction of the y-axis of the gravity gradiometer; a isz3Ω(1) Representing the amplitude, G, of the 1 st applied 3-times-frequency sinusoidal acceleration in the z-axis direction of the gravity gradiometerin(1)，Gcs(1) Respectively showing the output of the 1 st channel and the 2 nd channel of the gravity gradiometer under the joint action of the two accelerations,
representing the amplitude, G, of the 2 nd applied frequency-doubled sinusoidal acceleration of the gravity gradiometer in the z-axis directionin(2)，Gcs(2) The output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the combined action of the two accelerations are respectively shown.
Calibrating coupling first coefficient of accelerometer second-order nonlinear error and accelerometer installation error
Second coupling coefficient of second-order nonlinear error of accelerometer and installation error of accelerometer
During calibration, 3 times of frequency acceleration is applied to the y-axis direction of the gravity gradiometer, namely
Recording the output of the 1 st channel and the 2 nd channel of the gravity gradiometer, applying acceleration for 2 times in total, recording 2 groups of experimental data,
representing the amplitude, G, of the 1 st applied 3-times-frequency sinusoidal acceleration in the y-axis direction of the gravity gradiometerin(1)，Gcs(1) Respectively representing the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the action of the acceleration,
representing the amplitude, G, of the 2 nd applied frequency-doubled sinusoidal acceleration of the gravity gradiometer in the y-axis directionin(2)，Gcs(2) Respectively representing the output of the 1 st channel and the 2 nd channel of the gravity gradiometer under the acceleration action, and substituting the recorded 2 groups of experimental data into the following formula for calculation
(2) On the basis of the step (1), calibrating a sixth coefficient of the second-order nonlinear error of the accelerometer in the following way
During calibration, 1 frequency multiplication acceleration is applied to the y-axis direction of the gravity gradiometer, namely
Recording the output of the 2 nd channel of the gravity gradiometer, applying acceleration for 2 times in total, recording 2 groups of experimental data,
representing the amplitude, G, of the 1 st applied frequency-doubled sinusoidal acceleration of the gravity gradiometer in the y-axis directioncs(1) Represents the output of the 2 nd channel of the gravity gradiometer under the action of the acceleration,
representing the amplitude, G, of the 1 st harmonic sinusoidal acceleration applied 2 nd time in the y-axis direction of the gravity gradiometercs(2) Representing the output of the 2 nd channel of the gravity gradiometer under the acceleration action, and substituting the recorded 2 groups of experimental data into the following formula for calculation
In the formula
Is the value calibrated in the step (1),
is the value calibrated in step (1).
To verify the scheme in the embodiment of the present invention, the following simulation analysis may be performed:
four-rotating accelerometer gravity gradiometer internal accelerometers are mounted as shown in figure 1, four accelerometers are mounted on a rotating disc, theoretically with the input axes of the accelerometers aligned in the tangential direction. Due to installation errors, the input axis of the accelerometer may deviate from the tangential direction. The input axis of the accelerometer deviates from the tangential direction, and the mounting error can be thetaY，θzAnd is described. The input and output model of the accelerometer inside the gravity gradiometer is as follows:
in the formula K1，K2，K4，K5，K6，K7，K8Are the 1 st, second order scaling coefficients of the accelerometer. The rotating frequency of the disk mounted with the rotating accelerometer of the gravity gradiometer simulated in the experiment is 0.25Hz, the corresponding angular frequency is omega which is 1.5708rad/s, and the radius of the rotating disk is 0.1 m. The amplification gain of the current-to-voltage conversion of the accelerometer inside the gravity gradiometer is lnA/v. The calibration coefficients and mounting error parameters of the accelerometers inside the simulated gravity gradiometer are listed in the following table:
the radius R of the rotating disk of the gravity gradiometer is 0.1m, and the rotating frequency omega is 1.5708 rad/s. Under the simulation parameters, the theoretical values of the error gain coefficient of the gravity gradiometer are as follows:
(1) calibration kin/csAnd kggi：
During calibration, the gravity gradiometer is kept static, different detection masses are applied to the gravity gradiometer, different universal gravity gradient excitations are generated for the gravity gradiometer, and the excitation of each detection mass to the gravity gradiometer and the corresponding output of the gravity gradiometer are recorded as calibrated experimental data. The excitation of the 1 st detection mass to the 1 st and 2 nd channels of the gravity gradiometer is denoted T1(1)，T2(1) The output of the 1 st and 2 nd channels of the gravity gradiometer under the action of the detection mass is represented as Gin(1)，Gcs(1). Using N in total1The gradiometer was excited for 9 proof masses and 9 sets of experimental data were recorded as shown in the table below.
Substituting the experimental data into the following formula, calculating kin/cs，
In the formula T1(1)，T2(1) Representing the excitation of the 1 st proof mass on the gravity gradiometer, Gin(1)，Gcs(1) Showing the output of the 1 st and 2 nd channels of the gravity gradiometer under the action of the 1 st proof mass. T is1(2)，T2(2) Represents the excitation of the 2 nd detection mass to the 1 st and 2 nd channels of the gravity gradiometer, Gin(2)，Gcs(2) Showing the output of the 1 st and 2 nd channels of the gravity gradiometer under the action of the 2 nd proof mass. T is1(9)，T2(9) Represents the excitation of the 9 th proof mass on the 1 st and 2 nd channels of the gravity gradiometer, Gin(9)，Gcs(9) To representOutputting the 1 st channel and the 2 nd channel of the gravity gradiometer under the action of the 9 th detection mass;indicating the left inverse. K is obtained by calculationggi＝4.165×10-4V/Eo，kin/cs＝3.437×10-6V/Eo。
(2) Calibration
During calibration, 2 times frequency acceleration is applied to the z-axis direction of the gravity gradiometer, namely
And recording the output of the gravity gradiometer under the acceleration action, and recording 2 groups of experimental data in total
Representing the amplitude, G, of the 1 st applied 2-times frequency accelerationin(1) Representing the output of the 1 st channel of the gravity gradiometer in this case,
representing the amplitude, G, of the 2 nd applied 2-fold accelerationin(2) Representing the output of the 1 st channel of the gravity gradiometer in this case.
The recorded 2 sets of experimental data were substituted into the following formula,
is calculated to obtain
(3) Calibration
And
during calibration, constant acceleration is applied to the x direction and the y direction of the gravity gradiometer at the same time, the constant acceleration of the x direction and the y direction of the gravity gradiometer and the corresponding output of the gravity gradiometer are recorded as data for calibration,
representing the constant acceleration, G, applied by the gravity gradiometer at the 1 st timein(1)，Gcs(1) Showing the output of the 1 st and 2 nd channels of the gravity gradiometer in this case. In the experiment, 2 times of different constant accelerations are applied in total, and the corresponding output of the gravity gradiometer is recorded, and the experimental data are shown in the following table.
| axcon(g) | aycon(g) | Gin(V) | Gcs(V) |
| 0.01 | 0.03 | 0.07798 | 0.1388 |
| 0.015 | 0.02 | -0.01015 | 0.1132 |
The experimental data were substituted into the following formula,
in the formula (I), the compound is shown in the specification,representing the constant acceleration, G, applied by the gravity gradiometer at the 1 st timein(1)，Gcs(1) Representing the output of the 1 st and 2 nd channels of the gravity gradiometer under the acceleration.
Representing the constant acceleration, G, applied by the gravity gradiometer at the 2 nd applicationin(2)，Gcs(2) Representing the output of the 1 st and 2 nd channels of the gravity gradiometer under the acceleration. Is calculated to obtain
(4) calibration
During calibration, 1 frequency multiplication acceleration is applied to the direction of the z axis of the gravity gradiometer, namely
And recording the output of the gravity gradiometer under the acceleration action, recording 2 groups of experimental data in total,
representing the 1 st applied frequency-doubled acceleration amplitude, Gcs(1) Representing the output of the 2 nd channel of the gravity gradiometer in this case,representing the 1 st applied frequency-doubled acceleration amplitude, Gcs(2) Representing the output of the 2 nd channel of the gravity gradiometer in this case. The experimental data recorded are as follows,
the recorded 2 sets of experimental data were substituted into the following formula,
is calculated to obtain
(5) CalibrationAnd
during calibration, the y-axis of the gravity gradiometer is subjected to a constant acceleration, i.e. the acceleration is constant
Meanwhile, 3 times frequency acceleration is applied to the direction of the z axis of the gravity gradiometer, the acceleration of the gravity gradiometer in the directions of the y axis and the z axis and the output of the gravity gradiometer are recorded as experimental data for calibration, the constant acceleration of the gravity gradiometer in the direction of the y axis is kept unchanged, the experiment is repeated, 2 groups of experimental data are recorded,
representing the constant acceleration of the gravity gradiometer in the y-axis direction;representing the magnitude, G, of the 1 st applied 3-fold frequency z-axis directional accelerationin(1)，Gcs(1) Respectively showing the 1 st and 1 st positions of the gravity gradiometer in this case,2-channel output.
Representing the magnitude, G, of the 2 nd applied 3-fold frequency z-axis directional accelerationin(2)，Gcs(2) The outputs of the 1 st and 2 nd channels of the gravity gradiometer in this case are shown separately.
The recorded 2 sets of experimental data were substituted into the following formula,
can calculate out
(6) CalibrationAnd
during calibration, 3 times of frequency acceleration is applied to the y-axis direction of the gravity gradiometer, namely
And recording the output of the gravity gradiometer, and recording 2 groups of experimental data in totalRepresents the amplitude of the 1 st applied y-axis direction 3 multiplied acceleration, Gin(1)，Gcs(1) Showing the output of the 1 st, 2 nd channel of the gravity gradiometer in this case.
Represents the amplitude of 3 multiplied accelerations in the y-axis direction, G, applied at the 2 nd timein(2)，Gcs(2) To representIn this case the output of the 1 st and 2 nd channels of the gravity gradiometer.
The recorded 2 sets of experimental data were substituted into the following formula,
can calculate out
(7) Calibration
During calibration, the gravity gradiometer applies 1-fold frequency acceleration in the y-axis direction, i.e. the acceleration is caused
Recording the amplitude of 1 frequency multiplication acceleration in the y-axis direction of the gravity gradiometer and the output of the corresponding gravity gradiometer as data for calibration, and recording 2 groups in total.
Denotes the amplitude, G, of the 1 st applied 1-fold acceleration in the y-axis directioncs(1) Representing the output of the 2 nd channel of the gravity gradiometer in this case.
Denotes the amplitude, G, of the 2 nd applied 1-fold acceleration in the y-axis directioncs(2) Representing the output of the 2 nd channel of the gravity gradiometer in this case.
2 sets of experimental numbers to be recorded, and previously calibrated
By substituting the following formula into the reaction mixture,
is calculated to
From the calibration results, kin/cs，
The calibration value is consistent with the theoretical value, and the experimental result proves that the calibration method provided by the invention can calibrate the error gain coefficient of the gravity gradiometer.
Claims (5)
1. A method for calibrating an error gain coefficient of a gravity gradiometer of a rotating accelerometer with a movable base is characterized by comprising the following steps:
(1) calibrating error gain coefficients of the gravity gradiometer respectively according to the following modes;
calibrating a first coefficient k of installation error of an accelerometerin/csAnd the gravity gradiometer scale factor kggi: during calibration, the gravity gradiometer is kept static, different detection masses are applied to the gravity gradiometer, different universal gravity gradient excitations are generated for the gravity gradiometer, the excitation of each detection mass to the gravity gradiometer and the output of the 1 st channel and the 2 nd channel of the gravity gradiometer are recorded, and N is used in total1The detection mass excites the gravity gradiometer and records N1Group data, N1Must be greater than or equal to 2, the data is substituted into the following equation, and k is calculatedin/csAnd kggi：
In the formula T1(1)，T2(1) Respectively representing the excitation of the 1 st and 2 nd channels of the gravity gradiometer by the 1 st detection mass, Gin(1)，Gcs(1) Respectively representing the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the action of the 1 st detection mass, T1(2)，T2(2) Respectively representing the excitation of the 2 nd detection mass to the 1 st channel and the 2 nd channel of the gravity gradiometer, Gin(2)，Gcs(2) Respectively representing the output of the 1 st channel and the 2 nd channel of the gravity gradiometer under the action of the 2 nd detection mass, T1(N1)，T2(N1) Respectively represent the Nth1Excitation of the 1 st and 2 nd channel of the gravity gradiometer by individual detection masses, Gin(N1)，Gcs(N1) Respectively represent the Nth1The output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the action of the detection mass;
represents the left inverse;
calibrating a second coefficient of accelerometer mounting error
During calibration, 2 times frequency acceleration is applied to the z-axis direction of the gravity gradiometer, namely az＝az2Ωsin2 Ω t, and recording the output of the 1 st channel of gravity gradiometer under the action of the acceleration by using az2Ω(1) The amplitude of the 1 st applied 2 x frequency acceleration is shown,
representing the output of the 1 st channel of the gravity gradiometer under the effect of the acceleration, az2Ω(2) Representing the magnitude of the 2 nd applied frequency doubled acceleration,
indicating gravity gradiometer under the effect of the accelerationThe output of 1 channel, the recorded 2 sets of experimental data are substituted into the following formula to calculate
Calibrating second-order nonlinear first coefficient of accelerometer
And second-order nonlinear second coefficient of accelerometer
During calibration, constant acceleration is applied to the x direction and the y direction of the gravity gradiometer at the same time, the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer are recorded, and N is applied in total2Recording N2 sets of experimental data, N, of the second different constant accelerations2Must be greater than or equal to 2, the experimental data is substituted into the following formula to calculate
And
in the formula, axcon(1)，aycon(1) Respectively represents the 1 st applied constant acceleration in the x direction and the 1 st applied constant acceleration in the y direction of the gravity gradiometer,
respectively representing the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the combined action of the two accelerations, axcon(2)，aycon(2) Respectively representThe 2 nd applied constant acceleration in the x-direction and the 2 nd applied constant acceleration in the y-direction of the gravity gradiometer,
respectively representing the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the combined action of the two accelerations, axcon(N2)，aycon(N2) Respectively represent the Nth direction of the x direction of the gravity gradiometer2Constant acceleration applied once and Nth direction in y direction2The rate of the second applied constant acceleration is,
respectively showing the output of the 1 st channel and the 2 nd channel of the gravity gradiometer under the joint action of the two accelerations,
represents the left inverse;
calibrating second-order nonlinear error third coefficient of accelerometer
During calibration, 1 frequency multiplication acceleration is applied to the direction of the z axis of the gravity gradiometer, namely az＝az1Ωsin Ω t, and recording the output of 2 nd channel of gravity gradiometer under the action of acceleration, az1Ω(1) Represents the amplitude of the 1 st applied frequency multiplication acceleration in the z-axis direction of the gravity gradiometer,
representing the output of channel 2 of the gravity gradiometer under the effect of this acceleration, az1Ω(2) Represents the amplitude of the 1 multiplied frequency acceleration applied at the 2 nd time in the z-axis direction of the gravity gradiometer,
representing the output of the 2 nd channel of the gravity gradiometer under the condition, and substituting the recorded 2 groups of experimental data into the following formula for calculation
Calibrating the fourth coefficient of the second-order nonlinear error of the accelerometer
And the fifth coefficient of second-order nonlinear error of accelerometer
During calibration, a constant acceleration, i.e. a, is applied in the y-axis direction of the gravity gradiometery＝ayconSimultaneously applying 3 times frequency acceleration to the z-axis direction of the gravity gradiometer, recording the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the combined action of the two accelerations, only changing the amplitude of the 3 times frequency acceleration applied to the z-axis direction of the gravity gradiometer, keeping the constant value acceleration applied to the y-axis direction of the gravity gradiometer unchanged, recording the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the combined action of the two accelerations, recording to obtain 2 groups of data, substituting the data into the following formula to calculate
In the formula, ayconRepresents an applied constant acceleration in the direction of the y-axis of the gravity gradiometer; a isz3Ω(1) Represents the amplitude of the 1 st applied 3-frequency-doubled sinusoidal acceleration in the z-axis direction of the gravity gradiometer,respectively representing the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the combined action of the two accelerations, az3Ω(2) Represents the amplitude of the 3 rd frequency multiplication sinusoidal acceleration applied at the 2 nd time in the direction of the z-axis of the gravity gradiometer,
respectively representing the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the joint action of the two accelerations;
calibrating coupling first coefficient of accelerometer second-order nonlinear error and accelerometer installation errorSecond coupling coefficient of second-order nonlinear error of accelerometer and installation error of accelerometer
During calibration, 3 times of frequency acceleration is applied to the y-axis direction of the gravity gradiometer, namely ay＝ay3Ωsin3 Ω t, recording the output of the 1 st channel and the 2 nd channel of the gravity gradiometer, applying 2 accelerations in total, recording 2 sets of experimental data, ay3Ω(1) Represents the amplitude of the 1 st applied 3-frequency-doubled sinusoidal acceleration in the y-axis direction of the gravity gradiometer,
respectively representing the output of the 1 st channel and the output of the 2 nd channel of the gravity gradiometer under the action of the acceleration, ay3Ω(2) Represents the amplitude of the 3 rd-time frequency sinusoidal acceleration applied at the 2 nd time in the y-axis direction of the gravity gradiometer,
respectively representing the output of the 1 st channel and the 2 nd channel of the gravity gradiometer under the acceleration action, and substituting the recorded 2 groups of experimental data into the following formula for calculation
(2) On the basis of the step (1), calibrating a sixth coefficient of the second-order nonlinear error of the accelerometer in the following way
During calibration, 1 frequency multiplication acceleration is applied to the y-axis direction of the gravity gradiometer, namely ay＝ay1Ωsin Ω t, recording the output of 2 nd channel of gravity gradiometer, applying 2 accelerations totally, recording 2 groups of experimental data, ay1Ω(1) Represents the amplitude of the 1 st applied frequency doubling sinusoidal acceleration in the y-axis direction of the gravity gradiometer at the 1 st time,
representing the output of the 2 nd channel of the gravity gradiometer under the effect of the acceleration, ay1Ω(2) Represents the amplitude of the 1-time frequency multiplication sinusoidal acceleration applied at the 2 nd time in the y-axis direction of the gravity gradiometer,representing the output of the 2 nd channel of the gravity gradiometer under the acceleration action, and substituting the recorded 2 groups of experimental data into the following formula for calculation
In the formula
Is the value calibrated in the step (1),
is the value calibrated in step (1).
2. The method for calibrating the error gain coefficient of the moving base rotary accelerometer gravity gradiometer of claim 1 wherein 4 accelerometers are mounted on a rotating disk inside the rotary accelerometer gravity gradiometer.
3. The method for calibrating the error gain coefficient of the moving base rotary accelerometer gravity gradiometer of claim 1 wherein the direction of the sensitive axis of the accelerometer of the rotary accelerometer gravity gradiometer is the same as the tangential direction of the rotating disk.
4. The method for calibrating the error gain coefficient of the moving base rotary accelerometer gravity gradiometer according to claim 1, 2 or 3, wherein the accelerometer mounted inside the rotary accelerometer gravity gradiometer is a force balanced accelerometer.
5. The method for calibrating the error gain coefficient of the gravity gradiometer of the mobile base rotary accelerometer according to claim 1, 2 or 3, wherein the output model of the accelerometer mounted on the gravity gradiometer of the rotary accelerometer is:
in the formula K1Is the scaling factor of the accelerometer, K2,K4,K5,K6,K7,K8Respectively, the second order error coefficient of the accelerometer, IoutIs the output current of the accelerometer, aiAcceleration sensitive to the direction of the input axis of the accelerometer, aoIs the acceleration of the accelerometer in the direction of the output axis, apIs the acceleration of the accelerometer in the direction of the yaw axis.
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