Airborne gravity gradient measurement data multi-source error modeling method

Abstract

The application belongs to the technical field of aviation gravity measurement, and particularly relates to a multi-source error modeling method for aviation gravity gradient measurement data, which comprises the following steps: constructing a transformation matrix of a measurement coordinate system and a carrier coordinate system; correcting the transformation matrix to obtain an error-containing transformation matrix; converting a gravity gradient tensor in the carrier coordinate system into a gravity gradient tensor in the measurement coordinate system by using the error-containing transformation matrix; converting vibration error from the carrier coordinate system to the measurement coordinate system by using the error-containing transformation matrix; calculating self-gradient error by mapping based on the mass distribution of each part of the airplane; describing measurement system random noise by using a Gaussian white noise model; and adding the gravity gradient tensor in the measurement coordinate system, the vibration error in the measurement coordinate system, the self-gradient error and the measurement system random noise to obtain a multi-source error model. The method can effectively detect weak noise interference, the approximation degree of the output result to the actual measurement data is high, and the aviation gravity gradient measurement precision is greatly improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of airborne gravity measurement, and particularly relates to a multi-source error modeling method for airborne gravity gradient measurement data. BACKGROUND

[0002] Airborne gravity gradient measurement is widely used in geological exploration, resource survey and other fields by detecting the unevenness of the gravity field. The measurement accuracy of the gravity gradient tensor, as the core measurement parameter, directly determines the reliability of the exploration results.

[0003] In the prior art, the gravity gradient measurement signal is easily disturbed by various noises, including self-gradient caused by the quality of the carrier itself, flight vibration, attitude deviation and measurement system noise. These error sources are coupled into the measurement data through different mechanisms, and are difficult to effectively separate and correct.

[0004] The existing error processing methods are mostly designed for a single error source, lack of systematic analysis of the coupling mechanism of multi-source errors, resulting in insufficient robustness of the error model, inability to accurately adapt to different flight attitudes and quality distribution changes, and limited detection capability for weak noise, which seriously affects the accuracy of the measurement data. SUMMARY

[0005] The embodiment of the application provides a multi-source error modeling method for airborne gravity gradient measurement data, which solves the problem that the existing model is mostly designed for a single error source, resulting in insufficient robustness of the error model and inability to accurately adapt to different flight attitudes and quality distribution changes.

[0006] According to the multi-source error modeling method for airborne gravity gradient measurement data provided by the embodiment of the application, the following steps are included:

[0007] A transformation matrix of the measurement coordinate system and the carrier coordinate system is constructed;

[0008] The difference between the attitude angle measured by the navigation unit and the real attitude angle of the aircraft is used to correct the transformation matrix to obtain an error-containing transformation matrix;

[0009] The gravity gradient tensor in the carrier coordinate system is converted into the gravity gradient tensor in the measurement coordinate system by using the error-containing transformation matrix;

[0010] The vibration error is converted from the carrier coordinate system to the measurement coordinate system by using the error-containing transformation matrix;

[0011] The self-gradient error is calculated by mapping based on the mass distribution of each part of the aircraft;

[0012] A Gaussian white noise model is used to describe the random noise of the measurement system;

[0013] Add the gravity gradient tensor in the measurement coordinate system, the vibration error in the measurement coordinate system, the self-gradient error and the measurement system random noise to obtain a multi-source error model.

[0014] Further, the transformation matrix is obtained by multiplying a rotation matrix of the yaw angle, a rotation matrix of the roll angle and a rotation matrix of the pitch angle.

[0015] Further, the difference between the attitude angle measured by the navigation unit and the real attitude angle of the aircraft is used to correct the transformation matrix to obtain an error-containing transformation matrix, including:

[0016] Convert the difference from the carrier coordinate system to the measurement coordinate system as an attitude error amount;

[0017] Decompose the attitude error amount into an x-direction error component, a y-direction error component and a z-direction error component;

[0018] Add the roll angle in the transformation matrix to the x-direction error component, add the pitch angle to the y-direction error component and add the yaw angle to the z-direction error component.

[0019] Further, based on the mass distribution of each part of the aircraft, the self-gradient error is calculated by mapping, including: decomposing the aircraft into a plurality of cuboid components, calculating the initial coordinates of the center of gravity of each cuboid component;

[0020] After the initial coordinates of the center of gravity are transformed by the transformation matrix, the transformed coordinates of the center of gravity are obtained;

[0021] According to the transformed coordinates of the center of gravity, the boundary of each cuboid component is calculated;

[0022] In the boundary range, the gravity gradient tensor component generated by each cuboid component at the observation point is calculated;

[0023] Superimpose the gravity gradient tensor components of all cuboid components to obtain the self-gradient error.

[0024] Further, in the boundary range, the gravity gradient tensor component generated by each cuboid component at the observation point is calculated, and the formula used is:

[0025] ,

[0026] is the gravity gradient tensor component of the first cuboid component, is the direction index, is the gravitational constant, is the density of each cuboid component, is the mass of the first cuboid component, , and For the first The length, width, and height of each cuboid component. , and For the first The transformed centroid coordinates of each cuboid component Let be the volume of the cuboid component.

[0027] Furthermore, the vibration error is converted into a gravity gradient form by coupling the vibration acceleration with the installation error angle of the gravity gradient sensor and then using a three-dimensional spatial derivative operator.

[0028] Compared with the prior art, this application has at least the following beneficial effects:

[0029] The multi-source error model proposed in this application is adaptable to different carrier attitude and mass distribution change scenarios, and its robustness and stability are significantly improved. It can effectively detect weak noise interference, and the output results have a high degree of approximation to the actual measurement data, which greatly improves the accuracy of airborne gravity gradient measurement. It can be directly applied to the error correction of airborne gravity gradient measurement system and has strong practicality. Attached Figure Description

[0030] Figure 1 A flowchart illustrating the multi-source error modeling method for airborne gravity gradient measurement data provided in this application embodiment;

[0031] Figure 2 This is a schematic diagram showing the approximate decomposition of an aircraft into multiple cuboid components, as provided in an embodiment of this application. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0033] During the measurement process, airborne gravity gradient measurement systems generate error sources such as self-gradient error, attitude error, and vibration error due to factors such as aircraft weight, air turbulence, engine vibration, and attitude angle measurement errors. This application constructs a multi-source error model by coupling the error sources with the gravity gradient tensor, thereby achieving accurate error correction of the measurement data.

[0034] See Figure 1 As shown in the embodiment of this application, a multi-source error modeling method for airborne gravity gradient measurement data includes:

[0035] S1 constructs the transformation matrix between the measurement coordinate system and the carrier coordinate system;

[0036] Based on yaw angle (the angle of rotation about the z-axis) , pitch angle (angle of rotation around the y-axis) , roll angle (angle of rotation around the x-axis) , rotation matrix corresponding to the yaw angle , rotation matrix of the pitch angle , rotation matrix of the roll angle , are all 3x3 orthogonal matrices describing the orientation relationship between the carrier coordinate system and the measurement coordinate system, and the function is to establish the component mapping of the same physical quantity in the two coordinate systems, and to ensure that the physical quantity modulus is not changed after conversion. The transformation matrix of the measurement coordinate system and the carrier coordinate system is constructed The transformation matrix is obtained by multiplying the rotation matrix of the yaw angle, the rotation matrix of the roll angle and the rotation matrix of the pitch angle. The measurement coordinate system refers to the local horizontal coordinate system, and the carrier coordinate system refers to the coordinate system of the aircraft itself.

[0037] In an embodiment, the calculation formula of the rotation matrix and the transformation matrix is:

[0038] ,

[0039] ,

[0040] ,

[0041] .

[0042] S2 is the difference between the attitude angle measured by the navigation unit and the real attitude angle of the aircraft, and the transformation matrix is corrected to obtain the transformation matrix containing errors;

[0043] The navigation unit is a navigation unit provided by the aircraft for measuring the attitude angle, and there is an error between the real attitude angle of the aircraft and the real attitude angle of the aircraft. The real attitude angle of the aircraft is measured by a more accurate sensor.

[0044] In an embodiment, the difference between the attitude angle measured by the navigation unit and the real attitude angle of the aircraft is used to correct the transformation matrix to obtain the transformation matrix containing errors, including:

[0045] Convert the difference from the carrier coordinate system to the measurement coordinate system as the attitude error;

[0046] The attitude error is decomposed into x-direction error component, y-direction error component and z-direction error component;

[0047] The roll angle in the transformation matrix is added to the x-direction error component, the pitch angle is added to the y-direction error component, and the yaw angle is added to the z-direction error component.

[0048] The attitude error is represented as , is the x-direction error component, is the y-direction error component, is the z-direction error component.

[0049] S3 converts the gravity gradient tensor in the carrier coordinate system to the gravity gradient tensor in the measurement coordinate system using the transformation matrix with errors; expressed by the formula as:

[0050] ,

[0051] wherein, is the gravity gradient tensor in the measurement coordinate system, is the gravity gradient tensor in the carrier coordinate system.

[0052] S4 converts the vibration error from the carrier coordinate system to the measurement coordinate system using the transformation matrix with errors; expressed by the formula as: , is the vibration error in the measurement coordinate system, is the vibration error in the carrier coordinate system, the vibration error is the coupling between the vibration acceleration and the installation error angle of the gravity gradient sensor, the vibration error is constructed by gradient operation, that is, the coupled vibration acceleration is converted into the gravity gradient form by the three-dimensional spatial derivative operator ; wherein the installation error angle of the gravity gradient sensor is generated due to process deviation or flight vibration when the gravity gradient sensor is installed, expressed as:

[0053] .

[0054] S5 calculates the self-gradient error based on the mass distribution of each part of the aircraft;

[0055] The aircraft is decomposed into multiple cuboid components, and the initial coordinates of the center of gravity of each cuboid component are calculated;

[0056] The initial coordinates of the center of gravity are transformed by the transformation matrix to obtain the transformed coordinates of the center of gravity;

[0057] According to the transformed coordinates of the center of gravity, the boundaries of each cuboid component are calculated;

[0058] In the boundary range, the gravity gradient tensor components generated by each cuboid component at the observation point are calculated;

[0059] The gravity gradient tensor components of all cuboid components are superimposed to obtain the self-gradient error.

[0060] The mapping used in the calculation of the self-gradient error is derived from the cuboid gravity calculation formula, and the aircraft is approximately decomposed into multiple cuboid components, seeFigure 2 In an example, 5 cuboids are selected, which are the nose, the middle, the two wings and the tail, and the mass of each cuboid is , , , , and , and the size is , and the initial coordinates of the center of gravity are calculated as , , .

[0061] After the transformation matrix with error is obtained , the coordinates of the center of gravity of each part after transformation are , , , and the coordinate conversion formula is

[0062] ,

[0063] The boundary of the th cuboid part is calculated as

[0064] x direction: ;

[0065] y direction: ;

[0066] z direction: .

[0067] The gravity gradient tensor component generated by the th cuboid part at the observation point (origin) is , , which can be calculated according to the universal gravitation formula is the direction index: ,

[0068] is the gravity gradient tensor component of the th cuboid part, is the direction index, is the gravitational constant, is the density of each cuboid part, is the mass of the th cuboid part, , and are the length, width and height of the th cuboid part, , and are the length, width and height of the transformed barycentric coordinates of the cuboid component, is the volume of the cuboid component.

[0069] After superimposing the gravity gradient tensor components of all cuboid components, we can get:

[0070] ,

[0071] is the total number of cuboid components, the above process of solving the self-gradient error is called mapping.

[0072] S6 adopts a Gaussian white noise model to describe the measurement system random noise; a Gaussian white noise model is used to describe the measurement system random noise; the Gaussian white noise refers to the noise generated by random factors such as sensor thermal noise, electronic circuit noise, electromagnetic interference, etc., and its probability density conforms to the normal distribution.

[0073] S7 adds the gravity gradient tensor in the measurement coordinate system, the vibration error in the measurement coordinate system, the self-gradient error and the measurement system random noise to obtain a multi-source error model, which is expressed as:

[0074] .

[0075] Through the calculation of the error by the multi-source error model, the correct gravity gradient data reflecting the real earth gravity field is extracted. The direct extraction from the original collected data to the correct gravity gradient data is realized. The extracted correct gravity gradient data can be directly used in practical scenarios such as geological anomaly body identification and resource survey positioning, thereby reducing the complexity of subsequent data processing.

[0076] The above only describes the preferred embodiments of the present application and is not used to limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for modeling multi-source errors in airborne gravity gradiometry data, the method comprising: The method comprises the following steps: ​ constructing a transformation matrix of a measurement coordinate system and a carrier coordinate system; correcting the transformation matrix to obtain an error-containing transformation matrix by using a difference between an attitude angle measured by a navigation unit and a real attitude angle of the aircraft; converting a gravity gradient tensor in the carrier coordinate system into a gravity gradient tensor in the measurement coordinate system by using the error-containing transformation matrix; converting a vibration error from the carrier coordinate system to the measurement coordinate system by using the error-containing transformation matrix; calculating a self-gradient error by mapping based on a mass distribution of each part of the aircraft; adopting a Gaussian white noise model to describe random noise of a measurement system; adding the gravity gradient tensor in the measurement coordinate system, the vibration error in the measurement coordinate system, the self-gradient error and the random noise of the measurement system to obtain a multi-source error model.

2. The method according to claim 1, wherein, The transformation matrix is obtained by multiplying a rotation matrix of a yaw angle, a rotation matrix of a roll angle and a rotation matrix of a pitch angle.

3. The method according to claim 1, wherein the error-containing transformation matrix is obtained by correcting the transformation matrix by using a difference between an attitude angle measured by a navigation unit and a real attitude angle of the aircraft, and the method comprises the following steps: converting the difference from the carrier coordinate system to the measurement coordinate system as an attitude error quantity; decomposing the attitude error quantity into an x-direction error component, a y-direction error component and a z-direction error component; adding the roll angle in the transformation matrix by the x-direction error component, adding the pitch angle by the y-direction error component and adding the yaw angle by the z-direction error component.

4. The method according to claim 1, wherein the self-gradient error is calculated by mapping based on a mass distribution of each part of the aircraft, and the method comprises the following steps: decomposing the aircraft into a plurality of cuboid components to calculate initial coordinates of gravity centers of each cuboid component; transforming the initial coordinates of the gravity centers by the transformation matrix to obtain transformed gravity center coordinates; calculating boundaries of each cuboid component according to the transformed gravity center coordinates; calculating gravity gradient tensor components generated by each cuboid component at an observation point in the boundary range; superimposing the gravity gradient tensor components of all the cuboid components to obtain the self-gradient error. The formula used for calculating the gravity gradient tensor components generated by each cuboid component at the observation point in the boundary range is:

5. The method of claim 1, wherein, The vibration error is obtained by coupling vibration acceleration and a mounting error angle of the gravity gradient sensor and converting into a gravity gradient form by using a three-dimensional spatial derivative operator. ， Gxxi, Gyyi, Gzzi, Gxxi, Gyyi, Gzzi, mi, xi, yi, zi, li, wi, hi, xi, yi, zi, 6. The method of claim 1, wherein, ​

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