CN112180457A - Method and system for calibrating gradiometer by adopting high-precision ground gravity data - Google Patents
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Abstract
The invention relates to a method and a system for calibrating gradiometers by adopting high-precision ground gravity data, which are used for obtaining gravity gradient data at a satellite orbit calculated by ground data by adopting a local gravity field optimization mode aiming at an area with high-precision gravity data and uniform distribution on the ground, and estimating a scale factor of satellite gravity gradient observation data by comparing a calculation value and an observation value of gravity gradient in a measurement broadband when a gravity gradient measurement satellite passes through the area, thereby calibrating and calculating the gravity gradient observation value.
Description
Technical Field
The invention relates to the technical field of geodetic surveying, in particular to an external calibration method and system for a gravity gradient observation value in a satellite gravity gradient measurement observation platform.
Background
The GOCE satellite is an earth gravity field detection satellite transmitted by the European space Bureau, and a carried high-precision electrostatic gravity gradiometer is formed by three pairs of 6 accelerometers in orthogonal direction symmetry, can directly measure the second derivative of the earth gravity value, and has the characteristics of high precision and high sensitivity.
Since a low-orbit satellite is easily affected by a complex space environment at an orbit, a critical load gravity gradiometer carried by the satellite needs to be calibrated. The calibration of the observation data includes a pre-flight calibration, an internal calibration and an external calibration. During the flight of the satellite, the operating environment is not ideal. In this process, systematic deviations in the observed data, typically manifested as misalignment of the accelerometer to the readings, i.e., a mismatch of the deviation and the scale factor, occur. Therefore, in the later data calibration process, the scale factor and the deviation are used as reference and evaluation criteria.
The calibration before flight is the test calibration of the load before the satellite is launched to run, and belongs to the field of ground test. The internal calibration converts the observed value of the gravity gradiometer three-direction accelerometer into a Common Mode (CM) and a Differential Mode (DM), and performs quality control on data output. Typically, the frequency of internal calibration is once a month. And the external calibration adopts an independent data source to calibrate the observation data, and the coordinate transformation is carried out on the external data and then the external data is compared with the observation data to obtain a deviation value. Common external calibration methods are: and calibrating based on the earth gravity field model and calibrating the satellite observation data by utilizing satellite tracking.
In the prior art, data calibration is mainly realized by a calibration method using an earth gravity field model and a method for calibrating observation data of a satellite tracking satellite. In the two methods:
the calibration method using the earth gravity field model is that a known gravity field model is used for generating a gravity gradient, and the calculated value is compared with an observed value actually measured by a gravity gradiometer to obtain a deviation value. The drawbacks of this method are: known gravity field models are many, such as an OSU91A model, an EGM96 model, a CG03C model, an EGM2008 model, and the like, and with scale factors and deviations as reference standards, different models achieve different calibration accuracies, and data generated by a gravity field model alone cannot meet a better accuracy requirement, and in practical application, other various types of data such as satellite height measurement data and ground gravity data need to be combined.
The satellite tracking satellite observation data calibration means that the gravity gradient is used for measuring observation data obtained by a satellite tracking satellite device carried by a satellite, the reference frame conversion is carried out on the observation data of the satellite tracking satellite device based on the star image instrument reference frame to obtain observation data based on the gravity gradiometer reference frame, and the observation data is compared with a satellite gravity gradient observation value to obtain a deviation value. The drawbacks of this method are: the satellite tracking satellite calibration method is divided into a high-low satellite tracking mode and a low-low satellite tracking mode, and a high-precision GPS-GLONASS satellite-borne receiver carried by the satellite tracking satellite calibration method provides position information, so that satellite gravity gradient data can be calibrated by using satellite tracking satellite observation data. Since high-low satellite tracking satellite data is more sensitive to low-order gravitational fields, this method has the advantage of low-order parts of the earth gravitational field model (below 30 th order); for the middle and high order parts (30-120 orders) of the earth gravity field model, the calibration effect of the method is poor.
Disclosure of Invention
Based on the above-mentioned state of the art, the main object of the present invention is to: and carrying out external calibration on the satellite gravity observation data by using the high-precision ground gravity data. In order to avoid the above-listed two prior art limited constraints on the gravity field model and the satellite-borne GPS, the method uses high-precision ground gravity data to calibrate the satellite gravity observation data.
To achieve the above object, according to one aspect of the present invention, there is provided a method for calibrating a gradiometer using high-precision ground gravity data, comprising the steps of:
acquiring gravity observation data of a satellite to be calibrated in a selected area;
constructing model gravity data;
filtering the gravity observation data and the model gravity data;
carrying out coordinate transformation on the model gravity data after filtering processing to obtain model gravity data for calculation;
and calculating to obtain calibration parameters by utilizing the gravity observation data after the filtering processing and the model gravity data for calculation.
Furthermore, the gravity observation data of the satellite to be calibrated is a satellite gravity observation value when the gravity gradient measurement satellite passes through the selected area.
Furthermore, the model gravity data is obtained by combining ground gravity data with a gravity field model and performing data residual error substitution.
Further, the filtering process includes performing segmentation processing on the model gravity data and the gravity observation data, performing interpolation operation on each data segment, and performing fast fourier analysis on the data segments to determine fourier coefficients of the two groups of data.
Further, the coordinate transformation comprises the step of converting a local north-pointing coordinate system where the model gravity data are located into a ground-fixed coordinate system, then converting the local north-pointing coordinate system into an inertial coordinate system, and finally converting the inertial coordinate system into data under a gravity gradiometer reference frame.
Further, the calculating the calibration parameter includes:
performing calibration calculation on the gravity observation data after the filtering processing and model gravity data used for calculation to obtain an error value v;
the calibration parameter x is calculated by using the following calculation formula of the error value v:
v=Ax-L
wherein the content of the first and second substances,n is the number of observed values in a calibration period, ysIs the satellite observation, y' is the observation long period term, and t is time.
According to another aspect of the present invention, there is provided a system for calibrating a gradiometer using high accuracy ground gravity data, comprising:
a data acquisition module: acquiring gravity observation data of a satellite to be calibrated in a selected area;
a model construction module: constructing model gravity data;
a filtering processing module: filtering the gravity observation data and the model gravity data;
a coordinate transformation module: carrying out coordinate transformation on the model gravity data after filtering processing to obtain model gravity data for calculation;
a calibration parameter calculation module: and calculating to obtain calibration parameters by utilizing the gravity observation data after the filtering processing and the model gravity data for calculation.
Furthermore, the gravity observation data of the satellite to be calibrated is a satellite gravity observation value when the gravity gradient measurement satellite passes through the selected area.
Furthermore, the model gravity data is obtained by combining ground gravity data with a gravity field model and performing data residual error substitution.
Further, the filtering process includes performing segmentation processing on the model gravity data and the gravity observation data, performing interpolation operation on each data segment, and performing fast fourier analysis on the data segments to determine fourier coefficients of the two groups of data.
Further, the coordinate transformation comprises the step of converting a local north-pointing coordinate system where the model gravity data are located into a ground-fixed coordinate system, then converting the local north-pointing coordinate system into an inertial coordinate system, and finally converting the inertial coordinate system into data under a gravity gradiometer reference frame.
Further, the calculating the calibration parameter includes:
performing calibration calculation on the gravity observation data after the filtering processing and model gravity data used for calculation to obtain an error value v;
the calibration parameter x is calculated by using the following calculation formula of the error value v:
v=Ax-L
wherein the content of the first and second substances,n is the number of observed values in a calibration period, ysIs the satellite observation, y' is the observation long period term, and t is time.
In summary, the present invention provides a method and a system for calibrating a gradiometer by using high-precision ground gravity data, wherein a local gravity field optimization method is adopted for an area on the ground where the high-precision gravity data are uniformly distributed to obtain gravity gradient data at a satellite orbit calculated by the ground data, and when a gravity gradient measurement satellite passes through the area, a scale factor of the satellite gravity gradient observation data is estimated by comparing a calculation value and an observation value of a gravity gradient in a measurement bandwidth, so as to calibrate and calculate a gravity gradient observation value.
Drawings
FIG. 1 is a flow chart of a method of the present invention for calibrating a gradiometer using high accuracy ground gravity data;
FIG. 2 is a flow chart of a process for building model gravity data;
fig. 3 is a schematic diagram of the implementation process of coordinate transformation.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings in conjunction with the following detailed description. It should be understood that the description is intended to be exemplary only, and is not intended to limit the scope of the present invention. Moreover, in the following description, descriptions of well-known structures and techniques are omitted so as to not unnecessarily obscure the concepts of the present invention.
The technical solution of the present invention will be described in detail below with reference to the accompanying drawings. According to an embodiment of the present invention, there is provided a method for calibrating a gradiometer using high-precision ground gravity data, the method having a flow chart as shown in fig. 1, including the steps of:
s1: and acquiring the gravity observation data of the satellite to be calibrated in the selected area. And intercepting a satellite gravity observation value when the gravity gradient measurement satellite passes through the area as satellite gravity observation data to be calibrated according to the selected area range of the ground gravity data. Considering that the effective measurement bandwidth of the gravity gradiometer mounted on a gravity gradiometer is 5mHZ-0.1HZ, the size of the selected detection region should be close to the range of 12 ° × 12 °, corresponding to the region through which the distance of flight of the satellite 200s (5mHZ) passes.
And S2, constructing model gravity data. The process of constructing the model gravity data is shown in the flowchart in fig. 2, and the model gravity data is obtained by combining the ground gravity data with the gravity field model and performing data residual transformation. Selecting an area with flat terrain and large ground gravity point distribution density, and obtaining gravity data of actual measurement points, namely a ground gravity observation value, which is set as g, by using a ground gravity observation instrument, such as an absolute gravimeter FG-5m. Selecting a reference gravity field model, such as EGM2008 (truncation to 300 orders), calculating according to the coordinates of the selected area to obtain model data of the selected area under the gravity field model, namely a model gravity observation value, and setting the model data as gm', thereby obtaining a gravity observed value residual error delta g at the real measuring point coordinate of the selected aream:
Δgm=gm-gm′
Defining the gravity data of the point to be corrected as g, carrying out interpolation fitting on the residual error of the real measuring point of the selected area to obtain delta g, replacing the delta g into the point to be corrected to obtain the gravity data of the grid coordinate of the point to be corrected as gmerge=Δg+g,gmergeIs the model gravity data.
And S3, filtering the gravity observation data and the model gravity data. Considering the on-orbit variation characteristic of the gravity gradient value, before the data sequence is applied to calibration calculation, the data sequence needs to be filtered, the model gravity data and the gravity observation data of the satellite are processed in a segmented mode, interpolation operation is carried out on each data segment respectively, then fast Fourier analysis is carried out on the data segments, and Fourier coefficients of the two groups of data are determined. Specifically, the following expression may be employed:
where f (k) may be expanded using fourier coefficients, it may be written as:
wherein, TNN is the observed value number of the data segment g (t).
And S4, carrying out coordinate transformation on the model gravity data after the filtering processing to obtain model gravity data for calculation. The gravity observation of the satellite is represented in a gravity Gradiometer Reference Frame (GRF), and the gravity gradient observation calculated by using the gravity field model is generally in a local north-oriented coordinate system (LNOF), so that coordinate transformation is required in the calibration verification process, as shown in fig. 3: the local north-seeking coordinate system is converted into a ground-fixed coordinate system, then is converted into an inertial coordinate system, and finally is converted into data under a gravity gradiometer reference frame, wherein the conversion model is as follows:
VGRF=RVLNOFRT
wherein, VGRFIs observed data under a reference frame of the gravity gradiometer, R is a transformation matrix,
wherein the content of the first and second substances,is a transformation matrix for transforming a local north-seeking coordinate system into a ground-fixed coordinate system,for the transformation matrix of the earth-fixed coordinate system into the inertial coordinate system,and converting the inertial coordinate system into a conversion matrix of the reference frame of the gravity gradiometer.
wherein the content of the first and second substances,and λ are the instantaneous longitude and latitude of the satellite center of mass, respectively. Because the transformation under different coordinate frames is completed based on the Euler angle parameters, in practical application, the Euler angle is influenced by the common influence of the time difference, nutation and rotation. In the above formula, P1As a time-of-arrival transformation matrix, R2、R3Are euler transformation matrix parameters.
wherein q is1、q2、q3、q4The earth-fixed coordinate system EFRF is converted into four elements of an inertial coordinate system IRF.
wherein q1, q2, q3 and q4 are four elements of an inertial coordinate system IRF converted into a reference frame of a gravity gradiometer GRF, and Q, R, T respectively represents conversion matrixes of three Euler angles. The four-element conversion expressions are uniform, see above.
And S5, calculating to obtain calibration parameters by using the gravity observation data after the filtering processing and the model gravity data for calculation. Comparing the satellite gravity observation value with a ground gravity gradient model calculated by a gravity field model, and adopting the following calibration formula:
where E is an expected value, y is an observed gravity value of an actual measurement point, and in the present embodiment, y is a data entry obtained by coordinate conversion of the model gravity data obtained in step S2sIs the satellite observation, Δ y is the bias, y' is the long period term of the observation, T is time, T is the mean orbital period, ak、bkAre fourier transform coefficients.
The above equation is simplified as:
y(t)=λ·ys(t)+Δy
wherein y (t) is satellite observation data with scale factor and deviation, and ground gravity model data ys' (t) is substituted into the above equation to obtain the reference observation for calculating the calibration parameter:
y'(t)=λ·ys'(t)+Δy
the error of the calibration data from the actual observed data is:
v=y'(t)-y(t)=λ·ys'(t)+Δy-y(t)
further, it is possible to obtain:
v=Ax-L
wherein the content of the first and second substances,n is the number of observed values in a calibration period, x is a calibration parameter matrix, and the external calibration parameters x are solved to be scale factors and deviation, so that data calibration is obtained.
According to another embodiment of the present invention, there is provided a system for calibrating a gradiometer using high accuracy ground gravity data, the system comprising:
a data acquisition module: acquiring gravity observation data of a satellite to be calibrated in a selected area;
a model construction module: constructing model gravity data;
a filtering processing module: filtering the gravity observation data and the model gravity data;
a coordinate transformation module: carrying out coordinate transformation on the model gravity data after filtering processing to obtain model gravity data for calculation;
a calibration parameter calculation module: and calculating to obtain calibration parameters by utilizing the gravity observation data after the filtering processing and the model gravity data for calculation.
Wherein each module in the system is configured to implement each step corresponding to the method for calibrating a gradiometer using high accuracy ground gravity data. And will not be described in detail herein.
In summary, the present invention relates to a method and a system for calibrating a gradiometer by using high-precision ground gravity data, wherein a local gravity field optimization method is adopted for an area on the ground where the high-precision gravity data are uniformly distributed to obtain gravity gradient data at a satellite orbit calculated from the ground data, and when a gravity gradient measurement satellite passes through the area, a scale factor of the satellite gravity gradient observation data is estimated by comparing a calculation value and an observation value of a gravity gradient in a measurement bandwidth, so as to calibrate and calculate a gravity gradient observation value. Through the technical scheme provided by the invention, the problem that the data generated by only using the gravity field model cannot meet better precision requirements can be effectively solved, and the problems of terrain constraint, poor high-order effect on the gravity model and the like are avoided.
It is to be understood that the above-described embodiments of the present invention are merely illustrative of or explaining the principles of the invention and are not to be construed as limiting the invention. Therefore, any modification, equivalent replacement, improvement and the like made without departing from the spirit and scope of the present invention should be included in the protection scope of the present invention. Further, it is intended that the appended claims cover all such variations and modifications as fall within the scope and boundaries of the appended claims or the equivalents of such scope and boundaries.
Claims (12)
1. A method for calibrating a gradiometer using high accuracy ground gravity data, comprising the steps of:
acquiring gravity observation data of a satellite to be calibrated in a selected area;
constructing model gravity data;
filtering the gravity observation data and the model gravity data;
carrying out coordinate transformation on the model gravity data after filtering processing to obtain model gravity data for calculation;
and calculating to obtain calibration parameters by utilizing the gravity observation data after the filtering processing and the model gravity data for calculation.
2. The method according to claim 1, wherein the gravity observation data of the satellite to be calibrated is a satellite gravity observation value when the gravity gradiometric satellite passes through the selected area.
3. The method of claim 1, wherein the model gravity data is obtained by data residual substitution of ground gravity data in combination with a gravity field model.
4. The method of claim 1, wherein the filtering process comprises segmenting the model gravity data and the gravity observation data, performing an interpolation operation on each data segment, and performing a fast fourier analysis on the data segments to determine fourier coefficients of the two sets of data.
5. The method of claim 1, wherein the coordinate transformation comprises transforming a local north-pointing coordinate system in which the model gravity data is located into a geostationary coordinate system, then into an inertial coordinate system, and finally into data under a gravity gradiometer frame of reference.
6. The method of claim 1, wherein said calculating calibration parameters comprises:
performing calibration calculation on the gravity observation data after the filtering processing and model gravity data used for calculation to obtain an error value v;
the calibration parameter x is calculated by using the following calculation formula of the error value v:
v=Ax-L
7. A system for calibrating a gradiometer using high accuracy ground gravity data, comprising:
a data acquisition module: acquiring gravity observation data of a satellite to be calibrated in a selected area;
a model construction module: constructing model gravity data;
a filtering processing module: filtering the gravity observation data and the model gravity data;
a coordinate transformation module: carrying out coordinate transformation on the model gravity data after filtering processing to obtain model gravity data for calculation;
a calibration parameter calculation module: and calculating to obtain calibration parameters by utilizing the gravity observation data after the filtering processing and the model gravity data for calculation.
8. The system according to claim 7, wherein the gravity observation data of the satellite to be calibrated is a satellite gravity observation value of a GOCE satellite passing through the selected area.
9. The system of claim 7, wherein the model gravity data is obtained by data residual substitution of ground gravity data in combination with a gravity field model.
10. The system of claim 7, wherein the filtering process comprises performing a segmentation process on the model gravity data and the gravity observation data, performing an interpolation operation on each data segment, and performing a fast fourier analysis on the data segments to determine fourier coefficients of the two sets of data.
11. The system of claim 7, wherein the coordinate transformation comprises transforming the local north-seeking coordinate system in which the model gravity data is located into a geostationary coordinate system, then into an inertial coordinate system, and finally into data under a gravity gradiometer frame of reference.
12. The system of claim 7, wherein said calculating calibration parameters comprises:
performing calibration calculation on the gravity observation data after the filtering processing and model gravity data used for calculation to obtain an error value v;
the calibration parameter x is calculated by using the following calculation formula of the error value v:
v=Ax-L
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