Aerial gravity gradient measurement data multi-source error modeling method

Abstract

The invention belongs to the technical field of airborne gravity measurement, and particularly relates to an airborne gravity gradient measurement data multi-source error modeling method, 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 the gravity gradient tensor under the carrier coordinate system into a gravity gradient tensor under a measurement coordinate system by using the error-containing transformation matrix; converting the vibration error from a carrier coordinate system to a measurement coordinate system by using an error-containing transformation matrix; calculating a self-gradient error through mapping based on the mass distribution of each part of the airplane; describing random noise of a measurement system by adopting a Gaussian white noise model; and adding the gravity gradient tensor under the measurement coordinate system, the vibration error under the measurement coordinate system, the self-gradient error and the random noise of the measurement system to obtain a multi-source error model. Weak noise interference can be effectively detected, the approximation degree of an output result and actual measurement data is high, and the aviation gravity gradient measurement precision is greatly improved.

Description

Technical Field

[0001] This application belongs to the field of airborne gravity measurement technology, specifically relating to a multi-source error modeling method for airborne gravity gradient measurement data. Background Technology

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

[0003] In existing technologies, gravity gradient measurement signals are susceptible to various noise interferences, including self-gradients caused by the carrier's own mass, flight vibrations, attitude deviations, and measurement system noise. These error sources are coupled into the measurement data through different mechanisms, making them difficult to effectively separate and correct.

[0004] Existing error processing methods are mostly designed for single error sources and lack systematic analysis of the coupling mechanism of multi-source errors. This results in insufficient robustness of error models, making them unable to accurately adapt to different flight attitudes and mass distribution changes. Furthermore, their ability to detect weak noise is limited, which seriously affects the accuracy of measurement data. Summary of the Invention

[0005] This application provides a multi-source error modeling method for airborne gravity gradient measurement data, which solves the problem that existing models are 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 mass distribution changes.

[0006] A multi-source error modeling method for airborne gravity gradient measurement data, provided according to an embodiment of this application, includes: Construct the transformation matrix between the measurement coordinate system and the carrier coordinate system; The difference between the attitude angles measured by the navigation unit and the actual attitude angles of the aircraft is used to correct the transformation matrix and obtain the transformation matrix containing the error. The gravity gradient tensor in the carrier coordinate system is converted into the gravity gradient tensor in the measurement coordinate system using a transformation matrix containing errors. The vibration error is transformed from the carrier coordinate system to the measurement coordinate system using a transformation matrix containing the error. Based on the mass distribution of various parts of the aircraft, the self-gradient error is calculated through mapping. The random noise of the measurement system is described using a Gaussian white noise model; The multi-source error model is obtained by 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.

[0007] Furthermore, 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.

[0008] Furthermore, using the difference between the attitude angles measured by the navigation unit and the aircraft's actual attitude angles, the transformation matrix is ​​corrected to obtain an error-containing transformation matrix, including: The difference is transformed from the carrier coordinate system to the measurement coordinate system and used as the attitude error. The attitude error is decomposed into x-direction error components, y-direction error components, and z-direction error components. Add the x-direction error component to the roll angle, the y-direction error component to the pitch angle, and the z-direction error component to the yaw angle in the transformation matrix.

[0009] Furthermore, based on the mass distribution of various parts of the aircraft, the self-gradient error is calculated by mapping, including: decomposing the aircraft into multiple cuboid parts and calculating the initial coordinates of the center of gravity of each cuboid part; The initial coordinates of the barycenter are transformed using a transformation matrix to obtain the transformed barycenter coordinates. Calculate the boundary of each cuboid component based on the transformed centroid coordinates; Within the boundary range, calculate the gravity gradient tensor components generated by each cuboid component at the observation point; The self-gradient error is obtained by superimposing the gravity gradient tensor components of all cuboid parts.

[0010] Furthermore, within the boundary region, the gravity gradient tensor components generated by each cuboid component at the observation point are calculated using the following formula: , For the first Gravity gradient tensor components of a cuboid component For direction index, The gravitational constant, The density of each cuboid component, For the first The mass of the 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.

[0011] 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.

[0012] Compared with the prior art, this application has at least the following beneficial effects: 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

[0013] Figure 1 A flowchart illustrating the multi-source error modeling method for airborne gravity gradient measurement data provided in this application embodiment; 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

[0014] 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.

[0015] 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.

[0016] See Figure 1 As shown in the embodiment of this application, a multi-source error modeling method for airborne gravity gradient measurement data includes: S1 constructs the transformation matrix between the measurement coordinate system and the carrier coordinate system; Based on yaw angle (the angle of rotation about the z-axis) Pitch angle (angle of rotation about the y-axis) Roll angle (the angle of rotation about the x-axis) The rotation matrix corresponding to the yaw angle Rotation matrix of pitch angle Rotation matrix of roll angle Both are 3×3 orthogonal matrices describing the orientational relationship between the carrier coordinate system and the measurement coordinate system. Their function is to establish the component mapping of the same physical quantity in the two coordinate systems, ensuring that the magnitude of the physical quantity remains unchanged after transformation. The transformation matrix between the measurement coordinate system and the carrier coordinate system is constructed. The transformation matrix is ​​obtained by multiplying the rotation matrices for the yaw angle, roll angle, and pitch angle. The measurement coordinate system refers to the local horizontal coordinate system, while the carrier coordinate system refers to the aircraft's own coordinate system.

[0017] In one embodiment, the formulas for calculating the rotation matrix and the transformation matrix are as follows: , , , .

[0018] S2 uses the difference between the attitude angles measured by the navigation unit and the actual attitude angles of the aircraft to correct the transformation matrix and obtain a transformation matrix containing errors. The navigation unit is an integral part of the aircraft used to measure attitude angles, but there is an error between it and the aircraft's actual attitude angles. The aircraft's actual attitude angles are measured by more precise sensors.

[0019] In one embodiment, the transformation matrix is ​​corrected using the difference between the attitude angles measured by the navigation unit and the actual attitude angles of the aircraft to obtain an error-containing transformation matrix, including: The difference is transformed from the carrier coordinate system to the measurement coordinate system and used as the attitude error. The attitude error is decomposed into x-direction error components, y-direction error components, and z-direction error components. Add the x-direction error component to the roll angle, the y-direction error component to the pitch angle, and the z-direction error component to the yaw angle in the transformation matrix.

[0020] The attitude error is expressed as , It is the error component in the x-direction. It is the error component in the y-direction. It is the error component in the z-direction.

[0021] S3 uses a transformation matrix containing errors to convert the gravity gradient tensor in the carrier coordinate system into the gravity gradient tensor in the measurement coordinate system; this is expressed by the following formula: , in, To measure the gravity gradient tensor in the coordinate system, Let g be the gravity gradient tensor in the carrier coordinate system.

[0022] S4 uses a transformation matrix containing the error to transform the vibration error from the carrier coordinate system to the measurement coordinate system; expressed by the formula: , To measure the vibration error in the coordinate system, The vibration error is the vibration acceleration in the carrier coordinate system. and the installation error angle of the gravity gradient sensor The coupling between them is used to construct vibration error through gradient calculation. That is, through the three-dimensional spatial derivative operator The coupled vibration acceleration is converted into a gravity gradient; where the installation error angle of the gravity gradient sensor is... This occurs during the installation of the gravity gradient sensor due to manufacturing defects or flight vibrations. It is represented as: .

[0023] S5 calculates the self-gradient error based on the mass distribution of various parts of the aircraft through mapping. The aircraft is decomposed into multiple cuboid parts, and the initial coordinates of the center of gravity of each cuboid part are calculated. The initial coordinates of the barycenter are transformed using a transformation matrix to obtain the transformed barycenter coordinates. Calculate the boundary of each cuboid component based on the transformed centroid coordinates; Within the boundary range, calculate the gravity gradient tensor components generated by each cuboid component at the observation point; The self-gradient error is obtained by superimposing the gravity gradient tensor components of all cuboid parts.

[0024] The mapping used in calculating the self-gradient error is derived from the formula for calculating the weight of a cuboid, approximating the aircraft as multiple cuboid components. See [link to relevant documentation]. Figure 2 As shown, in one example, five cuboids are selected: the nose, the middle section, the two wings, and the tail. The mass of each cuboid is... The five cuboids are respectively , , , and The size is The initial coordinates of the centroid are calculated as ( , , ).

[0025] Transformation matrix containing error After the transformation, the coordinates of the center of gravity of each component are ( , , The coordinate transformation formula is: , Calculate the first The boundaries of each cuboid component are: x-direction: ; y direction: ; z-direction: .

[0026] No. The gravity gradient tensor components generated by the cuboid component at the observation point (origin) ( According to the law of universal gravitation, it can be calculated that... Directional index: , For the first Gravity gradient tensor components of a cuboid component For direction index, The gravitational constant, The density of each cuboid component, For the first The mass of the 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] After superimposing the gravity gradient tensor components of all the cuboid parts, we can obtain: , Given the total number of cuboid components, the above solution calculates the self-gradient error. The process is called mapping.

[0028] S6 uses a Gaussian white noise model to describe the random noise of the measurement system; Gaussian white noise model is used. Describes random noise in a measurement system; Gaussian white noise refers to noise generated by random factors such as sensor thermal noise, electronic circuit noise, and electromagnetic interference, and its probability density follows a normal distribution.

[0029] 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 random noise of the measurement system to obtain a multi-source error model, expressed as: .

[0030] By calculating errors using a multi-source error model, accurate gravity gradient data reflecting the true Earth's gravity field is extracted. This enables direct extraction of accurate gravity gradient data from raw collected data. The extracted accurate gravity gradient data can be directly used in practical scenarios such as geological anomaly identification and resource survey location, reducing the complexity of subsequent data processing.

[0031] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for multi-source error modeling of airborne gravity gradient measurement data, characterized in that, include: Construct the transformation matrix between the measurement coordinate system and the carrier coordinate system; The difference between the attitude angles measured by the navigation unit and the actual attitude angles of the aircraft is used to correct the transformation matrix and obtain the transformation matrix containing the error. The gravity gradient tensor in the carrier coordinate system is converted into the gravity gradient tensor in the measurement coordinate system using a transformation matrix containing errors. The vibration error is transformed from the carrier coordinate system to the measurement coordinate system using a transformation matrix containing the error. Based on the mass distribution of various parts of the aircraft, the self-gradient error is calculated through mapping. The random noise of the measurement system is described using a Gaussian white noise model; The multi-source error model is obtained by 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.

2. The method for multi-source error modeling of airborne gravity gradient measurement data according to claim 1, characterized in that, 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.

3. The method for multi-source error modeling of airborne gravity gradient measurement data according to claim 1, characterized in that, Using the difference between the attitude angles measured by the navigation unit and the actual aircraft attitude angles, the transformation matrix is ​​corrected to obtain an error-inclusive transformation matrix, including: The difference is transformed from the carrier coordinate system to the measurement coordinate system and used as the attitude error. The attitude error is decomposed into x-direction error components, y-direction error components, and z-direction error components. Add the x-direction error component to the roll angle, the y-direction error component to the pitch angle, and the z-direction error component to the yaw angle in the transformation matrix.

4. The method for multi-source error modeling of airborne gravity gradient measurement data according to claim 1, characterized in that, Based on the mass distribution of various parts of the aircraft, the self-gradient error is calculated by mapping, including: decomposing the aircraft into multiple cuboid parts and calculating the initial coordinates of the center of gravity of each cuboid part. The initial coordinates of the barycenter are transformed using a transformation matrix to obtain the transformed barycenter coordinates. Calculate the boundary of each cuboid component based on the transformed centroid coordinates; Within the boundary range, calculate the gravity gradient tensor components generated by each cuboid component at the observation point; The self-gradient error is obtained by superimposing the gravity gradient tensor components of all cuboid parts.

5. The method for multi-source error modeling of airborne gravity gradient measurement data according to claim 1, characterized in that, Within the boundary region, the gravity gradient tensor components generated by each cuboid component at the observation point are calculated using the following formula: ， For the first Gravity gradient tensor components of a cuboid component For direction index, The gravitational constant, The density of each cuboid component, For the first The mass of the 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.

6. The method for multi-source error modeling of airborne gravity gradient measurement data according to claim 1, characterized in that, 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.

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