CN105717553A - Calibration method for gravity gradient instrument of rotary accelerometer - Google Patents

Abstract

The invention discloses a method for calibrating a gravity gradiometer of a rotating accelerometer. Certain mass bodies are sequentially placed at four different positions outside the gravity gradiometer, and the gravitational field at the center of the gravity gradiometer is changed by changing the mass of the mass body. The changing gravitational field is sensed by gravity gradiometers. Filter and gradient demodulate the output signal of the gravity gradiometer to obtain the gravity gradient measurement result of the gravity gradiometer. The measurement results are calculated and compared with the theoretical value of the gravity gradient obtained by calculating the mass change of the mass body, and the zero position and scale coefficient of the two gravity gradient components of the gravity gradiometer are obtained. The invention can realize the gradient calibration of the gravity gradiometer of the rotation accelerometer.

Description

Calibration method of gravity gradiometer for rotating accelerometer

technical field

The invention relates to a gravity gradient calibration method of a rotational accelerometer gravity gradiometer, in particular to a method of changing the mass of a mass body to realize the gravity gradient calibration of a rotational accelerometer gravity gradiometer, and belongs to the technical field of precision measurement.

Background technique

High-precision gravity gradient measurement has very important application value and application prospects for the development of energy exploration, space science, earth science, geological science, and inertial navigation. Gravity gradient measurement has obvious advantages over gravity measurement. For information such as the shape, size and burial depth of geological structures, gravity gradient measurement can provide higher resolution, and is especially suitable for detecting and studying local geological structures and their details. At present, the gravity gradiometers with application prospects that are being studied abroad mainly include rotational accelerometer gravity gradiometers, superconducting gravity gradiometers, cold atom gravity gradiometers, satellite gravity gradiometers, etc. Among them, the technology of rotational accelerometer gravity gradiometers is the most Mature and the earliest commercial gravity gradiometer, and a lot of exploration work has been carried out; China began to pay attention to the application prospect of gravity gradiometer at the end of the last century, and many scientific research units cooperated to carry out related research, and branched out a number of different The research direction of the gravity gradiometer of the measurement principle, including the gravity gradiometer of the rotating accelerometer, the superconducting gravity gradiometer, the cold atom gravity gradiometer, the gravity gradiometer based on the micromechanical (MEMS) structure, and the satellite gravity gradiometer, among which the rotation Theoretical research on accelerometer gravity gradiometer is basically mature. Domestic scientific research institutes have developed a prototype of gravity gradiometer. Due to the sensor performance, stability of rotating structure, temperature control performance and other reasons, the resolution of gravity gradiometer is still low.

Gravity gradiometer is a kind of high-precision measuring instrument. It is very difficult to manufacture a gravity gradiometer with excellent performance. Even enterprises that can manufacture gravity gradiometer cannot carry out mass production. One of the important reasons is that the measuring components are difficult to mass produce, and Only a small number of qualified sensitive devices can be screened out from a large number of samples. In order to be able to measure a more accurate gravity gradient, the gravity gradiometer needs to be calibrated before use. At present, there are no relevant patents or literature published or published on the calibration method of the rotational accelerometer gravity gradiometer.

Contents of the invention

Technical problem: The present invention provides a simple, efficient, easy-to-implement, and important practical value calibration method for gravity gradiometers of rotational accelerometers.

Technical solution: The calibration method of the rotational accelerometer gravity gradiometer of the present invention comprises the following steps:

1) The operation before the gravity gradient calibration of the rotational accelerometer gravity gradiometer, the specific contents are as follows:

Establish the coordinate system of the gravity gradiometer as the northeast sky geographic coordinate system, denoted as OXYZ, and the origin O is the center of the rotating disk of the gravity gradiometer; at the initial moment, set the center of mass of the accelerometer A ₁ on the disk to be located in the positive direction of the X axis;

On the OXY plane of the gravity gradiometer coordinate system, set 4 mass body placement positions equidistant from the coordinate origin, position 1 is in the positive direction of the X and axis, position 2 is in the positive direction of the Y axis, and position 3 is in the line equation y=x , position 4 is on the line equation y=-x;

2) Place a mass body on a placement position, and perform gravity gradient demodulation on the output signal of the gravity gradiometer to obtain the gravity gradient component (Γ _yy -Γ _xx ) _1,1 ; then, based on the number of mass bodies placed last time , change the mass of the mass body at the placement position successively, and perform gravity gradient demodulation on the output signal of the gravity gradiometer, wherein the mass of the mass body placed each time is twice that of the previous one; follow the above operation for each placement position, and finally get:

Gravity gradient components at position 1 (Γ _yy -Γ _xx ) _1,1 , (Γ _yy -Γ _xx ) _1,2 , (Γ _yy -Γ _xx ) _1,4 ,..., (Γ _yy -Γ _xx ) _{1 ,2} ^n--1

Gravity gradient components at position 2 (Γ _yy -Γ _xx ) _2,1 , (Γ _yy -Γ _xx ) _2,2 , (Γ _yy -Γ _xx ) _2,4 , ..., (Γ _yy -Γ _xx ) _{2 ,2} ^n-1 ;

Gravity gradient components (Γ _xy ) _3,1 , (Γ _xy ) _3,2 , (Γ _xy ) _3,4 , ..., (Γ _xy ) _3,2 ^n-1 at position 3;

Gravity gradient components (Γ _xy ) _4,1 , (Γ _xy ) _4,2 , (Γ _xy ) _4,4 , ..., (Γ _xy ) _4,2 ^n-1 at position 4;

Among them, n is the ordinal number of gravity gradient demodulation. When placing the mass body for the first time, n is 1. Every time the mass body is changed, the ordinal number n increases by 1;

3) Calculate the zero position of the gravity gradient component (Γ _yy -Γ _xx ) of the gravity gradiometer according to the following formula:

${\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\frac{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}$

The zero position of the gravity gradient component (Γ _xy ) of the gravity gradiometer is calculated according to the following formula:

${\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\frac{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}$

Calculate the theoretical value of the gravity gradient component produced by the mass body to the center of the gravity gradiometer according to the following formula:

$\left\{\begin{array}{c}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; \&rho;</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; x</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; z</span>}\\ {<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; \&rho;</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; x</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; z</span>}\end{array}\right.$

Among them, (x, y, z) are the position coordinates of any point inside the mass body, (W _i , D _i , H _i ) are the coordinates of the center of mass of the mass body placed for the ith time, G is Newton’s gravitational constant, ρ is the density of the mass body, w, d, and h are the length, width, and height of the mass body respectively, Γ _xx is the spatial derivative of the gravitational acceleration component on the X-axis in the X-axis direction, and Γ _yy is the gravitational acceleration component on the Y-axis in the Y-axis direction The spatial derivative of Γ _xy is the spatial derivative of the gravitational acceleration on the X (Y) axis in the Y (X) axis direction;

4) According to the following formula, the gravity gradient components measured by the gravity gradiometer at position 1 with different masses are:

${<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>\frac{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}$

Perform linear fitting on the above formula to obtain a linear relationship between the mass of the mass and the gravity gradient value, and then calculate the scale coefficient of the gravity gradient component (Γ _yy -Γ _xx ) according to the following formula:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}}$

in is the theoretical value of the gravity gradient component The slope of the linear relationship obtained by linear fitting, Measure the gravity gradient component for the gravity gradiometer at position 1 The slope of the linear relationship obtained by linear fitting;

According to the following formula, the gravity gradient component measured by the gravity gradiometer when the number of different mass bodies in position 3 is obtained is: ${\left({\mathrm{\&Gamma;}}_{x\mathrm{the\; y}}\right)}_{2^{i-1}}^c=\frac{{\left({\mathrm{\&Gamma;}}_{x\mathrm{the\; y}}\right)}_{1,2^{i-1}}-{\left({\mathrm{\&Gamma;}}_{x\mathrm{the\; y}}\right)}_{2,2^{i-1}}}{2}$

Perform linear fitting on the above formula to obtain a linear relationship between the mass of the mass body and the gravity gradient value, and then calculate the scale coefficient of the gravity gradient component (Γ _xy ) according to the following formula:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}}$

in is the theoretical value of the gravity gradient component The slope of the linear relationship obtained by linear fitting, where, Measure the gravity gradient component for the gravity gradiometer at position 3 The slope of the linear relationship obtained from the linear fit.

Further, in the method of the present invention, the mass body is a cube with uniform density distribution.

Further, in the method of the present invention, in the step 2), the quality of the mass body at the placement position is increased by preparing a plurality of mass bodies with the same density and volume, and increasing the number of placed mass bodies.

In the present invention, certain mass bodies are sequentially placed on four different positions in the outer space of the gravity gradiometer, and the gravitational field at the center of the gravity gradiometer is changed by changing the quality of the mass body, and the changed gravitational field is sensitive to the gravity gradiometer, and then Filter and gradient demodulate the output signal of the gravity gradiometer to obtain the gravity gradient measurement result of the gravity gradiometer, compare the measurement result with the theoretical value of the gravity gradient, and obtain the zero position and scale coefficient of the two gravity gradient components of the gravity gradiometer.

Beneficial effect: compared with the prior art, the present invention has the following advantages:

The invention provides the calibration method of the gravity gradiometer of the rotational accelerometer for the first time. Usually, the calibration method of the gravity gradiometer is to fix the mass of the mass body, and it is realized by changing the distance from the center of mass of the mass body to the center of the gravity gradiometer. The distance between the center of the meter and the gravity gradient component is not a linear relationship, and the calibration error of the gravity gradient is relatively large; and the method of the present invention adopts the distance from the center of the fixed mass body to the center of the gravity gradient meter, and realizes gravity by changing the mass of the mass body. Gradient calibration, using this method can significantly reduce the gravity gradient distortion caused by the mass body at a short distance, and the linear relationship between the mass body mass and the gravity gradient component can be ensured within a certain range, which improves the gravity gradient calibration accuracy.

Description of drawings

Figure 1 is a schematic diagram of the mass body placement of the rotational accelerometer gravity gradiometer.

Fig. 2 is the corresponding relationship between the gravity gradient component (Γ _yy -Γ _xx ) measured by the gravity gradiometer and the number of mass bodies.

Fig. 3 is the corresponding relationship between the gravity gradient component (Γ _xy ) measured by the gravity gradiometer and the number of mass bodies.

detailed description

The present invention will be further described below in conjunction with embodiment and accompanying drawing.

1) The operation before the gravity gradient calibration of the rotational accelerometer gravity gradiometer, the specific contents are as follows:

Establish the coordinate system of the gravity gradiometer as the northeast sky geographic coordinate system, denoted as OXYZ, and the origin O is the center of the rotating disk of the gravity gradiometer; at the initial moment, set the center of mass of the accelerometer A ₁ on the disk to be located in the positive direction of the X axis;

On the OXY plane of the gravity gradiometer coordinate system, set 4 mass body placement positions equidistant from the coordinate origin, position 1 is in the positive direction of the X and axis, position 2 is in the positive direction of the Y axis, and position 3 is in the line equation y=x , position 4 is on the line equation y=-x;

2) Place a mass body on a placement position, and perform gravity gradient demodulation on the output signal of the gravity gradiometer to obtain the gravity gradient component (Γ _yy -Γ _xx ) _1,1 ; then, based on the number of mass bodies placed last time , change the mass of the mass body at the placement position successively, and perform gravity gradient demodulation on the output signal of the gravity gradiometer, wherein the mass of the mass body placed each time is twice that of the previous one; follow the above operation for each placement position, and finally get:

Gravity gradient components at position 1 (Γ _yy -Γ _xx ) _1,1 , (Γ _yy -Γ _xx ) _1,2 , (Γ _yy -Γ _xx ) _1,4 ,..., (Γ _yy -Γ _xx ) _{1 ,2} ^n--1

Gravity gradient components at position 2 (Γ _yy -Γ _xx ) _2,1 , (Γ _yy -Γ _xx ) _2,2 , (Γ _yy -Γ _xx ) _2,4 , ..., (Γ _yy -Γ _xx ) _{2 ,2} ^n-1 ;

Gravity gradient components (Γ _xy ) _3,1 , (Γ _xy ) _3,2 , (Γ _xy ) _3,4 , ..., (Γ _xy ) _3,2 ^n-1 at position 3;

Gravity gradient components (Γ _xy ) _4,1 , (Γ _xy ) _4,2 , (Γ _xy ) _4,4 , ..., (Γ _xy ) _4,2 ^n-1 at position 4;

Among them, n is the ordinal number of gravity gradient demodulation. When placing the mass body for the first time, n is 1. Every time the mass body is changed, the ordinal number n increases by 1;

3) Calculate the zero position of the gravity gradient component (Γ _yy -Γ _xx ) of the gravity gradiometer according to the following formula:

${\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\frac{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

The zero position of the gravity gradient component (Γ _xy ) of the gravity gradiometer is calculated according to the following formula:

${\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\frac{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Calculate the theoretical value of the gravity gradient component produced by the mass body to the center of the gravity gradiometer according to the following formula:

$\left\{\begin{array}{c}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; \&rho;</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; x</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; z</span>}\\ {<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; \&rho;</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; x</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; z</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Among them, (x, y, z) are the position coordinates of any point inside the mass body, (W _i , D _i , H _i ) are the coordinates of the center of mass of the mass body placed for the ith time, G is Newton’s gravitational constant, ρ is the density of the mass body, w, d, and h are the length, width, and height of the mass body respectively, Γ _xx is the spatial derivative of the gravitational acceleration component on the X-axis in the X-axis direction, and Γ _yy is the gravitational acceleration component on the Y-axis in the Y-axis direction The spatial derivative of Γ _xy is the spatial derivative of the gravitational acceleration on the X (Y) axis in the Y (X) axis direction;

4) Subtract the gravity gradient component (Γ _yy -Γ _xx ) _1,2 ^n-1 at position 1 and the gravity gradient component (Γ _yy -Γ _xx ) _2,2 ^n-1 at position 2 one by one and divide by 2 , to obtain the gravitational gradient components measured by the gravity gradiometer at position 1 with different mass bodies, namely:

${<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>\frac{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Perform linear fitting on the i gravity gradient components (Γ _yy -Γ _xx ) _1,2 ^i-1 measured by the gradiometer, and the linear relationship of the gravity gradient components (Γ _yy -Γ _xx ) obtained by design and calculation is:

${\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

in, are the slope and intercept of the linear relational expression of the measured value of the gravity gradient component (Γ _yy -Γ _xx ), respectively, and N is the number of mass bodies.

The theoretical gravity gradient component (Γ _yy -Γ _xx ) produced by the mass body at the same position to the center of the gravity gradiometer is calculated by using the theoretical calculation formula (3) of the gravity gradient component, and a linear fitting is performed on the calculated theoretical value of the gravity gradient Together, the linear fitting relational formula calculated by design is:

${\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

in, are the slope and intercept of the linear relational expression of the theoretical value of the gravity gradient component (Γ _yy -Γ _xx ), respectively, and N is the number of mass bodies.

The scale coefficient of the gravity gradient component (Γ _yy -Γ _xx ) is calculated according to the following formula:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Subtract the gravitational gradient component (Γ _xy ) _3,2 ^n-1 at position 3 and the gravitational gradient component (Γ _xy ) _4,2 ^n-1 at position 4 in one-to-one correspondence and divide by 2 to obtain the different mass body at position 3 The gravitational gradient components measured by the gravity gradiometer at the number of times are:

${<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>\frac{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

Linear fitting is carried out on the i gravity gradient components (Γ _xy ) _3,2 ^i-1 measured by the gradiometer, and the linear relationship formula of the gravity gradient components (Γ _xy ) obtained by design and calculation is:

${\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

in, are the slope and intercept of the linear relational expression of the gravity gradient component (Γ _xy ), respectively.

The theoretical calculation formula (3) of the gravity gradient component is used to calculate the theoretical gravity gradient component (Γ _xy ) generated by the mass body at the same position to the center of the gravity gradiometer, and the calculated theoretical value of the gravity gradient is linearly fitted, and the design calculation The obtained linear fitting relation is:

${\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

in, are the slope and intercept of the linear relational expression of the theoretical value of the gravity gradient component (Γ _xy ), respectively.

The scale coefficient of the gravity gradient component (Γ _xy ) is calculated according to the following formula:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

It should be understood that the above examples are only used to illustrate preferred implementations of the technical solutions of the present invention, and are not intended to limit the scope of the present invention. After reading the present invention, modifications and replacements of various equivalent forms of the present invention by those skilled in the art fall within the scope of protection defined by the claims of the present application.

Claims (3)

1. A calibration method for a gravity gradiometer of a rotary accelerometer is characterized by comprising the following steps:

1) the operation before gravity gradient calibration is carried out on the rotating accelerometer gravity gradiometer comprises the following specific contents:

establishing a gravity gradiometer coordinate system as a northeast geographic coordinate system, and recording the coordinate system as OXYZ, wherein an origin O is the center of a rotating disk of the gravity gradiometer; at the initial moment, an accelerometer A on the disc is set₁The center of mass of (2) is located in the positive direction of the X axis;

setting 4 mass body placing positions which are equidistant to a coordinate origin on an XY plane of a gravity gradiometer coordinate system, wherein the position 1 is in the positive direction of X and an axis, the position 2 is in the positive direction of Y axis, the position 3 is in the linear equation Y which is equal to X, and the position 4 is in the linear equation Y which is equal to X;

2) placing a mass body at a placing position, and performing gravity gradient demodulation on the output signal of the gravity gradiometer to obtain a gravity gradient component (_yy-_xx)_1,1(ii) a Then on the basis of the number of the mass bodies placed at the last time, the mass of the mass bodies at the placing positions is changed gradually, and the gravity gradient demodulation is carried out on the output signal of the gravity gradiometer, wherein the mass of the mass body placed at each time is twice of that of the mass body placed at the last time; for each placement position, according to the above operation, the following results are obtained:

gravity gradient component of position 1: (_yy-_xx)_1,1、(_yy-_xx)_1,2、(_yy-_xx)_1,4、……、(_yy-_xx)_1,2 ^n--1

Gravity gradient component of position 2: (_yy-_xx)_2,1、(_yy-_xx)_2,2、(_yy-_xx)_2,4、……、(_yy-_xx)_2,2 ^n-1；

Gravity gradient component of position 3: (_xy)_3,1、(_xy)_3,2、(_xy)_3,4、……、(_xy)_3,2 ^n-1；

Gravity gradient component of position 4: (_xy)_4,1、(_xy)_4,2、(_xy)_4,4、……、(_xy)_4,2 ^n-1；

Wherein n is the ordinal number of gravity gradient demodulation, n is 1 when the mass body is placed for the first time, and the ordinal number n is increased by 1 when the mass body is changed every time;

3) calculating the gravity gradient component of the gravity gradiometer according to the formula (_yy-_xx) Zero position of (2):

${\mathrm{\&Gamma;}}_{yy-xx}^{c0}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{{({\mathrm{\&Gamma;}}_{yy}-{\mathrm{\&Gamma;}}_{xx})}_{1,2^{i-1}}+{({\mathrm{\&Gamma;}}_{yy}-{\mathrm{\&Gamma;}}_{xx})}_{2,2^{i-1}}}{2}$

calculating the gravity gradient component of the gravity gradiometer according to the formula (_xy) Zero position of (2):

${\mathrm{\&Gamma;}}_{xy}^{c0}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{{\left({\mathrm{\&Gamma;}}_{xy}\right)}_{3,2^{i-1}}+{\left({\mathrm{\&Gamma;}}_{xy}\right)}_{4,2^{i-1}}}{2}$

calculating the gravity gradient component theoretical value generated by the mass body to the center of the gravity gradiometer according to the following formula:

$\left\{\begin{array}{c}{\left({\mathrm{\&Gamma;}}_{yy}-{\mathrm{\&Gamma;}}_{xx}\right)}_{2^{i-1}}^t=3G\mathrm{\&rho;}{\&Integral;}_{W_i-w/2}^{W_i+w/2}dx{\&Integral;}_{D_i-d/2}^{D_i+d/2}dy{\&Integral;}_{H_i-h/2}^{H_i+h/2}\frac{\left(y^2-x^2\right)}{{\left(x^2+y^2+z^2\right)}^{5/2}}dz\\ {\left({\mathrm{\&Gamma;}}_{xy}\right)}_{2^{i-1}}^t=3G\mathrm{\&rho;}{\&Integral;}_{W_i-w/2}^{W_i+w/2}dx{\&Integral;}_{D_i-d/2}^{D_i+d/2}dy{\&Integral;}_{H_i-h/2}^{H_i+h/2}\frac{xy}{{\left(x^2+y^2+z^2\right)}^{5/2}}dz\end{array}\right.$

wherein, (x, y, z) is the position coordinate of any point in the mass body, (W)_i,D_i,H_i) The mass center coordinate of the mass body is placed for the ith time, G is a Newton universal gravitation constant, rho is the density of the mass body, w, d and h are respectively the length, width and height of the mass body,_xxis the gravity acceleration component on the X axis in the X axis directionThe spatial derivative of (a) is determined,_yyis the spatial derivative of the gravitational acceleration component on the Y-axis in the Y-direction,_xyis the spatial derivative of the acceleration of gravity in the X (Y) axis in the direction of the Y (X) axis;

4) the gravity gradient component measured by the gravity gradiometer when the mass of different masses at the position 1 is obtained by calculation according to the following formula is:

${({\mathrm{\&Gamma;}}_{yy}-{\mathrm{\&Gamma;}}_{xx})}_{2^{i-1}}^c=\frac{{({\mathrm{\&Gamma;}}_{yy}-{\mathrm{\&Gamma;}}_{xx})}_{1,2^{i-1}}-{({\mathrm{\&Gamma;}}_{yy}-{\mathrm{\&Gamma;}}_{xx})}_{2,2^{i-1}}}{2}$

performing linear fitting on the above formula to obtain a linear relation formula of the mass body and the gravity gradient value, and then calculating according to the following formula to obtain the gravity gradient component (_yy-_xx) Scale factor of (c):

$K_{yy-xx}=\frac{K_{yy-xx}^t}{K_{yy-xx}^c}$

whereinAs theoretical values of gravity gradient componentsThe slope of the linear relation obtained by linear fitting,measuring gravity gradient components for a gravity gradiometer of position 1Linearly fitting to obtain the slope of a linear relation;

the gravity gradient component measured by the gravity gradiometer when the number of different masses at the position 3 is calculated according to the following formula is:

${\left({\mathrm{\&Gamma;}}_{xy}\right)}_{2^{i-1}}^c=\frac{{\left({\mathrm{\&Gamma;}}_{xy}\right)}_{1,2^{i-1}}-{\left({\mathrm{\&Gamma;}}_{xy}\right)}_{2,2^{i-1}}}{2}$

performing linear fitting on the above formula to obtain a linear relation formula of the mass body and the gravity gradient value, and then calculating according to the following formula to obtain the gravity gradient component (_xy) Scale factor of (c):

$K_{xy}=\frac{K_{xy}^t}{K_{xy}^c}$

whereinAs theoretical values of gravity gradient componentsLinearly fitting the slope of the resulting linear relationship, wherein,measuring the gradient component for a gravity gradiometer at position 3And linearly fitting the slope of the obtained linear relation.

2. The method for calibrating a gravity gradiometer of a rotary accelerometer according to claim 1 wherein the mass is a cube and the density distribution is uniform.

3. The calibration method for the gravity gradiometer of the rotary accelerometer according to claim 1 or 2, wherein in the step 2), the mass of the mass body at the placement position is increased by preparing a plurality of mass bodies with the same density and volume and increasing the number of the placed mass bodies.