CN116500701A - Multi-parameter conversion fusion noise reduction method for gravity gradiometer grid measurement - Google Patents
Multi-parameter conversion fusion noise reduction method for gravity gradiometer grid measurement Download PDFInfo
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Abstract
The invention relates to a multi-parameter conversion fusion noise reduction method for gravity gradiometer grid measurement, which comprises the following steps: step 1, carrying out dynamic measurement of gravity gradient, obtaining gravity gradient measurement information and preprocessing to obtain gravity gradient data D uv 、D xy And step 2, completing the gravity gradient Γ in a tensor conversion mode uv Measurement signal sum Γ xy Measuring the interconversion of the signals; step 3, calculating errors in measurement of the original measurement data and the converted gravity gradient data respectively by using the repeated line measurement data; step 4, carrying out direct dynamic measurement on original gravity gradient measurement data obtained by a gravity gradiometer,and carrying out weighted fusion on the gravity gradient data obtained by tensor conversion to obtain the gravity gradient data after noise reduction. The invention can effectively improve the measuring precision of the instrument on the premise of not increasing the hardware of the instrument.
Description
Technical Field
The invention belongs to the technical field of gravity gradiometers, and particularly relates to a multi-parameter conversion fusion noise reduction method for grid measurement of a gravity gradiometer.
Background
Gravity gradient is defined as the spatial gradient of the gravity acceleration vector, i.e. the second derivative of the gravity position, characterizing the spatial rate of change of the gravity vector. In a geographic coordinate system, gravity vectorCan be decomposed into three components in x, y and z directions, each component having a gradient along a direction parallel to the coordinate axes. Thus, the gravity gradient tensor has a total of 3×3 components, as shown in fig. 1. Mathematically, the gravity gradient is expressed as:
wherein:
Γ—gravitational gradient tensor matrix at any spatial location outside the earth;
t-the gravitational potential function of the current position;
-a current location vector;
x, y and z-projections of the current position vector on three coordinate axes, wherein the coordinate system is usually selected as the northeast coordinate system;
Γ ij (i, j=x, y, z) -the gravity gradient tensor components, representing the gravity component g i Spatial rate of change in the j direction.
Gravity gradiometers are instruments for continuously measuring the tiny gravity gradient changes of the earth surface, and gravity gradiometers based on the measurement principle of a rotary accelerometer are the only practical near-surface dynamic gravity gradiometers so far. The gravity gradiometer main body instrument mainly comprises two key components of a gravity gradient sensor and an inertia stable platform. The gravity gradient sensor is mainly used for completing the measurement of the horizontal component of the gravity gradient tensor; the inertial stabilized platform is used for bearing the gravity gradient sensor, isolating the angular motion influence of the carrier for dynamic gravity gradient measurement, and providing a measurement coordinate system reference for the sensor. As shown in fig. 2, the gravity gradient measurement component as a core sensor modulates the gravity gradient tensor component to the frequency doubling position of the system rotation frequency by a mechanical rotation mode based on the accelerometer position differential measurement principle, and the relationship between the accelerometer output and the gravity gradient tensor component can be expressed as:
(a 1 +a 3 )-(a 2 +a 4 )＝2R(Γ xx -Γ yy )sin2ωt+4RΓ xy cos2ωt
in which a is i (i=1, 2,3, 4) is the output of four accelerometers, R is the distance of the accelerometer detection centroid to the center of rotation Γ xx 、Γ yy 、Γ xy Is the gravitational gradient tensor component in the rotation plane coordinate system, ω is the rotation angular velocity of the rotation device. To ensure that the signal to noise ratio of the two signal measurement output by the gravity gradient sensor is consistent, recordThe gravity gradient sensor is able to measure the gravity gradient tensor component Γ in the rotation plane coordinate system uv And Γ xy 。
Because of the process and performance level limitation of the core sensitive element accelerometer, the gravity gradiometer directly outputs signals under the dynamic measurement condition due to factors such as multi-loop installation errors and the like, and the gravity gradiometer has extremely low signal-to-noise ratio. In order to effectively extract a true gravity gradient signal in strong noise, a high-efficiency gravity gradient signal noise suppression method needs to be provided, and the gravity gradient signal processing precision is improved.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a multi-parameter conversion fusion noise reduction method for grid measurement of a gravity gradiometer.
The above object of the present invention is achieved by the following technical solutions:
the multi-parameter conversion fusion noise reduction method for the grid measurement of the gravity gradiometer is characterized by comprising the following steps of:
step 1, carrying out dynamic measurement of gravity gradient, obtaining gravity gradient measurement information and preprocessing to obtain gravity gradient data D uv 、D xy Andthe four data are represented as follows:
wherein,,and->Two-way gravity gradient Γ for developing repeated line measurements uv And Γ xy Identification data of-> Two-way gravity gradient Γ for carrying out only a single measurement uv And Γ xy Is a part of the identification data of the electronic device;
step 2, completing the gravity gradient Γ in a tensor conversion mode uv Measurement signal sum Γ xy Measuring the interconversion of the signals;
step 3, calculating errors in measurement of the original measurement and the converted gravity gradient data respectively by using the repeated line measurement data;
and step 4, carrying out weighted fusion on the original gravity gradient measurement data obtained by direct dynamic measurement of the gravity gradiometer and the gravity gradient data obtained by tensor conversion to obtain the gravity gradient data after noise reduction.
Further: the step 1 comprises the following steps:
firstly, installing a rotary accelerometer type gravity gradiometer on a mobile platform of an airplane, a ship and the like to finish starting up and system stabilization of the gravity gradiometer;
1.2, carrying out gravity gradient dynamic measurement by using a gravity gradiometer carried by a mobile platform such as an airplane, a ship and the like, wherein at least one repeated measuring line and a necessary checking line are needed in a measuring line planning requiring dynamic measurement for data offline processing;
1.3, carrying out necessary data processing on the gravity gradient measurement data of each measuring line and each checking line, wherein the data processing mainly comprises demodulation, vertical line motion compensation, horizontal angle motion compensation, self-gradient compensation and low-pass filtering, and carrying out gridding processing on the data after the low-pass filtering to obtain the gravity gradient measurement information after pretreatment.
Further, step 2 includes:
step 2.1, calculating to obtain a gravity gradient Γ uv Conversion of the Signal to Γ xy The operator of the signal comprises the following steps:
for gravity gradient Γ xy The two-dimensional Fourier transform of a signal can be expressed as
F in the formula xy Is the gravity gradient Γ xy The two-dimensional Fourier transform result of the signal, i is the imaginary unit, k x And k y Is the number of circles;
for fourier transforms, there are:
in the middle ofIs a fourier transform operator, ω is a number of circles, f (t) is any continuously-derivable function, and f' (t) is a derivative function of the function f (t);
this gives:
F xy ＝-k x k y F T (5)
f in the formula T Is the two-dimensional fourier result of the gravitational potential function;
the same principle is as follows:
F xx ＝-k x k x F T (6)
F yy ＝-k y k y F T (7)
f in the formula xx And F yy Is the gravity gradient Γ xx Signal sum Γ yy A two-dimensional fourier transform result of the signal;
combined type (8) and formula (9) and combinedThe method can obtain:
f in the formula uv Is the gravity gradient Γ uv A two-dimensional fourier transform result of the signal;
thereby obtaining the gravity gradient gamma in the frequency domain xy Signal sum Γ uv The conversion relation of the signals is as follows:
the conversion from frequency domain data to spatial domain data can be realized according to inverse fourier transform, specifically:
in the middle ofIs formed by gravity gradient gamma xy Gravity gradient Γ obtained by signal conversion uv A signal;
the process of formulas (5) to (12) is called gravity gradient frequency domain tensor conversion, abbreviated as:
in the middle ofIs formed by gravity gradient gamma xy Conversion of the Signal to Γ uv An operator of the signal;
the same can be obtained:
in the middle ofIs formed by gravity gradient gamma uv Gravity gradient Γ obtained by signal conversion xy Signal (I)>Is formed by gravity gradient gamma uv Conversion of the Signal to Γ xy An operator of the signal;
step 2.2, completing tensor conversion of the measured gravity gradient data according to the conversion operator obtained in step 2.1:
will actually measure gravity gradient data D uv 、D xy Andthe gravity gradient tensor conversion is completed respectively, specifically:
in E xy 、E uv 、And->Respectively from measured gravity gradient data D uv 、D xy 、/>And->And carrying out gravity gradient signal data of the completion of the gravity gradient tensor conversion.
Further, step 3 includes:
for raw measurement data, there are:
epsilon in uv And epsilon xy Is measured by gravity gradient raw material uv Signal sum Γ xy The measurement accuracy of the signal, m is the total point number in the repeated measurement area;
for the tensor-transformed gravity gradient data, there are:
in e uv And e xy Is measured by gravity gradient raw material uv Signal sum Γ xy Measuring essence of signalThe degree of the heat dissipation,and->The gravity gradient data in the corresponding direction is obtained by tensor conversion in the repeated measurement area.
Further, step 4 is:
in the middle ofAnd->Is the gravity gradient Γ after fusion uv Signal sum Γ xy Signal signal
The invention has the advantages and positive effects that:
1. the grid measurement multi-parameter combined noise suppression method for the gravity gradiometer can effectively improve the measurement accuracy of the instrument on the premise of not increasing the hardware of the instrument.
2. According to the multi-parameter conversion fusion method, the measured data of one component of the gravity gradient is converted into the data of the other component through the frequency domain method, the weighted fusion is carried out on the measured data of the other component of the gravity gradient, and the noise is uncorrelated by utilizing the fact that useful signals in the measured data of the same gravity gradient components obtained from two different measuring channels are completely identical, so that the measurement accuracy of the gravity gradient data after fusion is improved, and the noise reduction of the gravity gradient measured signals is realized.
Drawings
FIG. 1 is a gravity gradient tensor component schematic;
FIG. 2 is a schematic diagram of the principle of measurement of a rotary accelerometer type gravity gradient sensor;
FIG. 3 is a schematic illustration of an embodiment of the present inventionPreprocessed gravity gradient data D uv A schematic diagram;
FIG. 4 is the gravity gradient data D after preprocessing in an embodiment of the invention xy A schematic diagram;
FIG. 5 is a graph of Γ in an embodiment of the invention xy Obtained by signal conversionA signal schematic;
FIG. 6 is a graph of Γ in an embodiment of the invention uv Obtained by signal conversionA signal schematic;
FIG. 7 shows the gravity gradient Γ after noise reduction in an embodiment of the present invention uv A signal schematic;
FIG. 8 is a gravity gradient Γ after noise reduction in an embodiment of the present invention xy Schematic of the signal.
Detailed Description
The structure of the present invention will be further described by way of examples with reference to the accompanying drawings. It should be noted that the present embodiments are illustrative and not restrictive.
Referring to fig. 1-2, the invention is that the method comprises the following steps of
Step 1, carrying out dynamic measurement of gravity gradient, obtaining gravity gradient measurement information and preprocessing to obtain gravity gradient data D uv 、D xy And
firstly, installing a rotary accelerometer type gravity gradiometer on a mobile platform of an airplane, a ship and the like to finish starting up and system stabilization of the gravity gradiometer;
1.2, carrying out gravity gradient dynamic measurement by using a gravity gradiometer carried by a mobile platform such as an airplane, a ship and the like, wherein at least one repeated measuring line and a necessary checking line are needed in a measuring line planning requiring dynamic measurement for data offline processing;
1.3 carrying out necessary data processing on the gravity gradient measurement data of each measuring line and each checking line, wherein the data processing method mainly comprises demodulation, vertical line motion compensation, horizontal angle motion compensation, self-gradient compensation and low-pass filtering, and then carrying out gridding processing on the data after the low-pass filtering to obtain the gravity gradient measurement information after pretreatment.
In the case of performing measurement by the gravity gradiometer, one or a plurality of measurement lines are usually measured twice or more, which is called repeated line measurement. Two-way gravity gradient Γ to develop a repeated line measurement uv And Γ xy The data of the two measurements of the component are respectively recorded as And->Two-way gravity gradient Γ to perform only a single measurement uv And Γ xy The component data is recorded asGravity gradient data to be repeated for the same measurement +.>And->Gravity gradient data from single measurement alone are +.>Combining such that the combined gravity gradient data set D uv 、D xy Andgravity gradient data, all covering the whole area, are recorded as:
step 2, completing the gravity gradient Γ in a tensor conversion mode uv Measurement signal sum Γ xy Interconversion of measurement signals
The existing mature gravity gradient tensor conversion method mainly comprises two methods of a frequency domain and an equivalent source, wherein the tensor conversion method of the frequency domain is selected according to the scheme, and the specific implementation steps are as follows:
for gravity gradient Γ xy The two-dimensional Fourier transform of a signal can be expressed as
F in the formula xy Is the gravity gradient Γ xy The two-dimensional Fourier transform result of the signal, i is the imaginary unit, k x And k y Is the number of circles;
for fourier transforms, there are:
in the middle ofIs a fourier transform operator, ω is a number of circles, f (t) is any continuously-derivable function, and f' (t) is a derivative function of the function f (t);
this gives:
F xy ＝-k x k y F T (5)
f in the formula T Is the two-dimensional fourier result of the gravitational potential function;
the same principle is as follows:
F xx ＝-k x k x F T (6)
F yy ＝-k y k y F T (7)
f in the formula xx And F yy Is the gravity gradient Γ xx Signal sum Γ yy A two-dimensional fourier transform result of the signal;
combined type (6) and formula (7) and combinedThe method can obtain:
f in the formula uv Is the gravity gradient Γ uv A two-dimensional fourier transform result of the signal;
thereby obtaining the gravity gradient gamma in the frequency domain xy Signal sum Γ uv The conversion relation of the signals is as follows:
the conversion from frequency domain data to spatial domain data can be realized according to inverse fourier transform, specifically:
in the middle ofIs formed by gravity gradient gamma xy Signal signalThe gravity gradient Γ obtained by conversion uv A signal.
The process of formulas (5) to (12) is called gravity gradient frequency domain tensor conversion, abbreviated as:
in the middle ofIs formed by gravity gradient gamma xy Conversion of the Signal to Γ uv An operator of the signal.
The same can be obtained:
in the middle ofIs formed by gravity gradient gamma uv Gravity gradient Γ obtained by signal conversion xy Signal (I)>Is formed by gravity gradient gamma uv Conversion of the Signal to Γ xy An operator of the signal.
Will actually measure gravity gradient data D uv 、D xy Andthe gravity gradient tensor conversion is completed respectively, specifically:
in E xy 、E uv 、And->Respectively from measured gravity gradient data D uv 、D xy 、/>And->And carrying out gravity gradient signal data of the completion of the gravity gradient tensor conversion.
Step 3, calculating errors in measurement of original measurement and converted gravity gradient data respectively by using repeated line measurement data, wherein the original measurement data comprises:
epsilon in uv And epsilon xy Is measured by gravity gradient raw material uv Signal sum Γ xy The measurement accuracy of the signal, m, is the total number of points in the repeated measurement area.
For the tensor-transformed gravity gradient data, there are:
in e uv And e xy Is measured by gravity gradient raw material uv Signal sum Γ xy The accuracy of the measurement of the signal,and->The gravity gradient data in the corresponding direction is obtained by tensor conversion in the repeated measurement area.
Step 4, carrying out weighted fusion on original gravity gradient measurement data obtained by direct dynamic measurement of a gravity gradiometer and gravity gradient data obtained by tensor conversion to obtain noise-reduced gravity gradient data:
in the middle ofAnd->Is the gravity gradient Γ after fusion uv Signal sum Γ xy A signal.
Examples are as follows:
step 1, carrying out dynamic measurement of gravity gradient, obtaining gravity gradient measurement information and preprocessing to obtain gravity gradient data D uv 、D xy And
wherein the gravity gradient data D after pretreatment uv As shown in fig. 3; preprocessed gravity gradient data D xy As shown in fig. 4; whileAnd->Graphically and D uv And D xy Is substantially the same as D on the repeated line only uv And D xy Different.
Step 2, completing the gravity gradient Γ in a tensor conversion mode uv Measurement signal sum Γ xy Interconversion of measurement signals:
from Γ xy Obtained by signal conversionThe signals are shown in fig. 5; from Γ uv Signal conversion derived->The signals are shown in fig. 6.
Step 3, calculating errors in measurement of the original measurement and the converted gravity gradient data respectively by using the repeated line measurement data
The errors in the measurement of the gravity gradient data obtained from the formulas (14) and (15) are respectively: epsilon uv ＝25.2E，ε xy ＝23.6E，e uv ＝35.7E，e xy ＝37.2E。
Step 4, carrying out weighted fusion on original gravity gradient measurement data obtained by direct dynamic measurement of a gravity gradiometer and gravity gradient data obtained by tensor conversion to obtain noise-reduced gravity gradient data:
obtaining a gravity gradient Γ after noise reduction from equation (18) uv The signal data is shown in fig. 7; obtaining a gravity gradient Γ after noise reduction from equation (18) xy The signal data is shown in fig. 8.
Although the embodiments of the present invention and the accompanying drawings have been disclosed for illustrative purposes, those skilled in the art will appreciate that: various substitutions, changes and modifications are possible without departing from the spirit of the invention and the appended claims, and therefore the scope of the invention is not limited to the embodiments and the disclosure of the drawings.
Claims (5)
1. The multi-parameter conversion fusion noise reduction method for the grid measurement of the gravity gradiometer is characterized by comprising the following steps of:
step 1, carrying out dynamic measurement of gravity gradient, obtaining gravity gradient measurement information and preprocessing to obtain gravity gradient data D uv 、D xy Andthe four data are represented as follows:
wherein,,and->Two-way gravity gradient Γ for developing repeated line measurements uv And Γ xy Is provided with an identification data of (a), two-way gravity gradient Γ for carrying out only a single measurement uv And Γ xy Is a part of the identification data of the electronic device;
step 2, completing the gravity gradient Γ in a tensor conversion mode uv Measurement signal sum Γ xy Measuring the interconversion of the signals;
step 3, calculating errors in measurement of the original measurement data and the converted gravity gradient data respectively by using the repeated line measurement data;
and step 4, carrying out weighted fusion on the original gravity gradient measurement data obtained by direct dynamic measurement of the gravity gradiometer and the gravity gradient data obtained by tensor conversion to obtain the gravity gradient data after noise reduction.
2. The gravity gradiometer mesh measurement multi-parameter conversion fusion noise reduction method of claim 1, wherein step 1 comprises:
firstly, installing a rotary accelerometer type gravity gradiometer on a mobile platform of an airplane, a ship and the like to finish starting up and system stabilization of the gravity gradiometer;
1.2, carrying out gravity gradient dynamic measurement by using a gravity gradiometer carried by a mobile platform such as an airplane, a ship and the like, wherein at least one repeated measuring line and a necessary checking line are needed in a measuring line planning requiring dynamic measurement for data offline processing;
1.3, carrying out necessary data processing on the gravity gradient measurement data of each measuring line and each checking line, including demodulation, vertical line motion compensation, horizontal angle motion compensation, self-gradient compensation and low-pass filtering, and carrying out gridding processing on the low-pass filtered data to obtain the preprocessed gravity gradient measurement information.
3. The gravity gradiometer mesh measurement multi-parameter conversion fusion noise reduction method according to claim 1, wherein: the step 2 comprises the following steps:
step 2.1, calculating to obtain a gravity gradient Γ uv Conversion of the Signal to Γ xy The operator of the signal comprises the following steps:
for gravity gradient Γ xy The two-dimensional Fourier transform of a signal can be expressed as
Wherein F is xy Is the gravity gradient Γ xy The two-dimensional Fourier transform result of the signal, i is the imaginary unit, k x And k y Is the number of circles;
for fourier transforms, there are:
in the method, in the process of the invention,is a fourier transform operator, ω is a number of circles, f (t) is any continuously-derivable function, and f' (t) is a derivative function of the function f (t);
this gives:
F xy ＝-k x k y F T (5)
wherein F is T Is the two-dimensional fourier result of the gravitational potential function;
the same principle is as follows:
F xx ＝-k x k x F T (6)
F yy ＝-k y k y F T (7)
wherein F is xx And F yy Is the gravity gradient Γ xx Signal sum Γ yy A two-dimensional fourier transform result of the signal;
combined type (8) and formula (9) and combinedThe method can obtain:
wherein F is uv Is the gravity gradient Γ uv A two-dimensional fourier transform result of the signal;
thereby obtaining the gravity gradient gamma in the frequency domain xy Signal sum Γ uv The conversion relation of the signals is as follows:
the conversion from frequency domain data to spatial domain data can be realized according to inverse fourier transform, specifically:
in the method, in the process of the invention,is formed by gravity gradient gamma xy Gravity gradient Γ obtained by signal conversion uv A signal;
the process of formulas (5) to (12) is called gravity gradient frequency domain tensor conversion, abbreviated as:
in the method, in the process of the invention,is formed by gravity gradient gamma xy Conversion of the Signal to Γ uv An operator of the signal;
the same can be obtained:
in the method, in the process of the invention,is formed by gravity gradient gamma uv Gravity gradient Γ obtained by signal conversion xy Signal (I)>Is formed by gravity gradient gamma uv Conversion of the Signal to Γ xy An operator of the signal;
step 2.2, completing tensor conversion of the measured gravity gradient data according to the conversion operator obtained in step 2.1:
will actually measure gravity gradient data D uv 、D xy Andthe gravity gradient tensor conversion is completed respectively, specifically:
wherein E is xy 、E uv 、And->Respectively from measured gravity gradient data D uv 、D xy 、/>And->And carrying out gravity gradient signal data of the completion of the gravity gradient tensor conversion.
4. A gravity gradiometer mesh measurement multi-parameter conversion fusion noise reduction method according to claim 3, wherein: the step 3 comprises the following steps:
for raw measurement data, there are:
wherein ε uv And epsilon xy Is measured by gravity gradient raw material uv Signal sum Γ xy The measurement accuracy of the signal, m is the total point number in the repeated measurement area;
for the tensor-transformed gravity gradient data, there are:
in the formula e uv And e xy Is measured by gravity gradient raw material uv Signal sum Γ xy The accuracy of the measurement of the signal,andthe gravity gradient data in the corresponding direction is obtained by tensor conversion in the repeated measurement area.
5. The gravity gradiometer mesh measurement multi-parameter conversion fusion noise reduction method according to claim 4, wherein: the step 4 is as follows:
in the method, in the process of the invention,and->Is the gravity gradient Γ after fusion uv Signal sum Γ xy A signal.
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