CN112964248A - Real-time target body positioning method and system based on gravity gradient tensor data - Google Patents

Real-time target body positioning method and system based on gravity gradient tensor data Download PDF

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CN112964248A
CN112964248A CN202110175243.9A CN202110175243A CN112964248A CN 112964248 A CN112964248 A CN 112964248A CN 202110175243 A CN202110175243 A CN 202110175243A CN 112964248 A CN112964248 A CN 112964248A
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吴国超
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Second Institute of Oceanography MNR
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Abstract

The invention provides a method and a system for positioning a target body in real time based on gravity gradient tensor data. The method comprises the following steps: obtaining four groups of gravity gradient values in the x, y and z directions according to the spatial position relation of the four groups of gravity gradiometers, and calculating the gravity gradients in the x, y and z directions by using the four groups of gravity gradient values; evaluating the noise level and the data quality, testing the damping coefficient, and selecting the optimal value; and (3) completing real-time calculation of the space position of the target body by utilizing a gravity field space position linear calculation formula derived from the position field Poisson relation, performing scattered point statistical analysis and curve fitting on the calculation result, and determining the central position of the space of the target body. The method and the system for positioning the target body in real time based on the gravity gradient tensor data can realize real-time and rapid positioning of the gravity target body, do not need additional prior information constraint, have simple and convenient calculation process and stable and reliable calculation results.

Description

Real-time target body positioning method and system based on gravity gradient tensor data
Technical Field
The invention relates to the technical field of gravity detection, in particular to a method and a system for positioning a target body in real time based on gravity gradient tensor data.
Background
The accurate and rapid positioning of the spatial position of the target body is always a big hotspot and difficulty in the potential field exploration research. The gravity anomaly is caused by the uneven density distribution of the substances and reflects the spatial occurrence states of different substances. The gravity gradient tensor data has the advantages of high precision, multiple parameters and the like, and has higher resolution capability on a target body. With the continuous maturity of the gravity gradient tensor measurement technology, a plurality of gravity gradient tensor inversion methods are emerging, including spatial physical property distribution, physical property parameter inversion and the like. However, the existing algorithm has the disadvantages of complex calculation process, unstable inversion result, low calculation speed, and the need of matching with various prior information, and cannot realize real-time and rapid positioning.
Disclosure of Invention
The invention aims to provide a method and a system for positioning a gravity gradient tensor data-based target body in real time, which can realize real-time and rapid positioning of the gravity target body without additional prior information constraint, and have the advantages of simple and convenient calculation process and stable and reliable calculation result.
In order to solve the technical problem, the invention provides a real-time positioning method of a target body based on gravity gradient tensor data, which comprises the following steps: obtaining four groups of gravity gradient values in the x, y and z directions according to the spatial position relation of the four groups of gravity gradiometers, and calculating the gravity gradients in the x, y and z directions by using the four groups of gravity gradient values; evaluating the noise level and the data quality, testing the damping coefficient, and selecting the optimal value; and (3) completing real-time calculation of the space position of the target body by utilizing a gravity field space position linear calculation formula derived from the position field Poisson relation, performing scattered point statistical analysis and curve fitting on the calculation result, and determining the central position of the space of the target body.
In some embodiments, further comprising: and setting upper and lower limits of the spatial position according to spatial position prediction of the target body before evaluating the noise level and the data quality, testing the damping coefficient and selecting the optimal value.
In some embodiments, the real-time calculation of the spatial position of the target body is completed by using a gravity field spatial position linear calculation formula derived from the poisson relation of the potential field, and the calculation result is subjected to scattered point statistical analysis and curve fitting to define the spatial position of the target body, and the method comprises the following steps: and (5) solving the central position of the target body by utilizing curve normal distribution fitting.
In some embodiments, the normal distribution formula for fitting a curvilinear normal distribution is:
Figure BDA0002940490410000021
where σ is the standard deviation and μ is the mean.
In some embodiments, the criteria function for the curvilinear normal distribution fit is:
Figure BDA0002940490410000022
where A is the amplitude, σ is the standard deviation, and μ is the mean.
In some embodiments, the curvilinear normal distribution fit is a least squares fit.
In some embodiments, the four sets of gradiometers are erected in a measuring architecture of a right-angled tetrahedron.
In some embodiments, the formula for the linear calculation of the spatial position of the gravitational field according to the poisson relationship is as follows:
L＝-3(WTW+ε2U)-1WTK
wherein epsilon2For the damping coefficient, U is an identity matrix, and K is a magnetic field expression derived using the gravitational potential of a given magnetic body, i.e., a magnetic field expression in poisson's relationship.
In some embodiments, the real-time calculation of the spatial position of the target body is performed by using a gravity field spatial position linear calculation formula derived from the poisson relationship, and comprises the following steps: and performing inversion calculation of the spatial position by adopting a minimum variance solution.
In addition, the invention also provides a real-time positioning system of the target body based on the gravity gradient tensor data, which comprises the following components: one or more processors; a storage device for storing one or more programs, which when executed by the one or more processors, cause the one or more processors to implement the method for real-time localization of an object based on the gravitational gradient tensor data as described above.
After adopting such design, the invention has at least the following advantages:
the method is based on the gravity gradient tensor measurement technology, and based on a traditional magnetic dipole single-point positioning method, a calculation method is improved into the space position positioning of a gravity target body through a Poisson relationship. The method can realize real-time and rapid positioning of the gravity target body, does not need additional prior information constraint, and has simple and convenient calculation process and stable and reliable calculation result.
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The foregoing is only an overview of the technical solutions of the present invention, and in order to make the technical solutions of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and the detailed description.
FIG. 1 is a schematic diagram of a rectangular tetrahedron measurement architecture of four gravity full tensor gradiometers;
FIG. 2 is a schematic diagram of a sphere model;
FIG. 3 is a graph of the test results for model 1;
FIG. 4 is a schematic view of an underground air defense building;
FIG. 5 is a graph of test results for a simulated underground air defense cavity;
FIG. 6 is a graph of the effect of statistical analysis of scatter and distribution fitting on the test results.
Detailed Description
The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it will be understood that they are described herein for the purpose of illustration and explanation and not limitation.
The invention designs a calculation method capable of realizing rapid and real-time positioning of the spatial position of a target body based on the research foundation and marine gravity investigation experience of the author in the aspects of gravity field data processing and explanation for years and the existing gravity gradient tensor measurement technology and gravity magnetic field inversion method, and the method has high calculation speed and does not need excessive prior information. The invention can be used for gravity detection tasks carried by various rapid moving platforms (airborne, shipborne, vehicle-mounted and submersible), such as accurate positioning of military shelters, underwater target detection, special geological body circles and the like.
The method is based on the gravity gradient tensor measurement technology, and based on a traditional magnetic dipole single-point positioning method, a calculation method is improved into the space position positioning of a gravity target body through a Poisson relationship. The method can realize real-time and rapid positioning of the gravity target body, does not need additional prior information constraint, and has simple and convenient calculation process and stable and reliable calculation result.
First, a magnetic dipole single-point localization method and its relationship with the gravitational potential will be briefly described. Assuming that the magnetic target is far from the measuring point (the distance is more than 2.5 times of the self space length of the target), the magnetic target is regarded as a magnetic dipole. Under this condition, the magnetic field strength K from the magnetic target body L is:
K＝[3(m·L0)L0-m]/(4πL3)
where m is the magnetic moment of the magnetic target, L ═ L | is the distance from the magnetic target to the measurement point, and L is the distance from the magnetic target to the measurement point0L/L is a unit vector in the L direction.
Distance field source L + L0The magnetic field strength at dL is K
Figure BDA0002940490410000041
In a cartesian coordinate system:
Figure BDA0002940490410000051
the above expression is a magnetic gradient tensor expression, namely a magnetic field intensity three-component (K)x,Ky,Kz) The rate of change in 3 directions in space, denoted by P, is:
Figure BDA0002940490410000052
the above equation is integrated to obtain
Figure BDA0002940490410000053
Because L is L.L.L0Then, then
Figure BDA0002940490410000054
In the formula
Figure BDA0002940490410000055
Given the strengths of the magnetic field vectors in three directions at a point in the magnetic field and their magnetic gradient tensors, the magnetic target position can be calculated by the above equation.
Assuming that the heavy magnetic field boundaries of the target body are consistent and the magnetization intensity and the density are uniformly distributed, the magnetic potential U can be directly calculated from the gravity potential V according to the Poisson relationshipm：
Figure BDA0002940490410000056
Wherein M is magnetization intensity, V is gravity potential,
Figure BDA0002940490410000057
Mx,Myand MzMagnetization component in three directions, Vx,VyAnd VzThe gravity components in the three directions corresponding thereto. Thus, Kx,KyAnd KzCan be expressed as:
Figure BDA0002940490410000061
Figure BDA0002940490410000062
Figure BDA0002940490410000063
therefore, we can get a gravity field spatial position linear calculation mode:
L＝-3W-1K
wherein:
Figure BDA0002940490410000064
Figure BDA0002940490410000065
because the gravity field satisfies: v ═ 0, and × V ═ 0.
It is possible to obtain: vxy＝Vyx，Vxz＝Vzx，Vyz＝Vzy，Vxx+Vyy+Vzz0. Therefore, of the 9 gravity components acquired in each gravity gradient tensor system, 5 components are independent.
That is to say that the first and second electrodes,
Figure BDA0002940490410000066
the W type can also be expressed as the derivative of the K type in the three directions of x, y and z, and the right-angle tetrahedron measuring system consisting of four sets of gravity full tensor gradiometers designed by the invention can realize the real-time calculation of gradient values W in the three directions of x, y and z, namely
Figure BDA0002940490410000067
Figure BDA0002940490410000068
Figure BDA0002940490410000071
The invention adopts the least square error solution to carry out the inversion calculation of the space position,
L＝-3(WTW)-1WTK
because the bit field inversion calculation generally belongs to an ill-posed problem, a calculation result is sensitive to the noise level of data, and Gihonov regularization can be adopted in the actual calculation process to improve the inversion stability.
L＝-3(WTW+ε2U)-1WTK
Wherein epsilon2For damping coefficient, U is an identity matrix. By adding the damping coefficient, the stability of the solution can be improved to a certain extent. The divergence of the solution can be reduced by adding the damping coefficient, but the accuracy of the solution is reduced to a certain extent, so the magnitude of the damping coefficient needs to be balanced in practical calculation.
In addition, in order to further stabilize the inversion result, the upper and lower threshold values of the inversion result can be set to filter out a part of invalid solutions caused by false signals such as background fields, noise and the like. It can be assumed that L e (L)min,Lmax)，
Wherein L isminAnd LmaxRespectively as the upper and lower limits of the preset spatial range.
In order to further optimize the inversion result of the spatial position, particularly when the target body is not obvious in abnormality and the background noise level is high, the method carries out scatter statistics on the calculation results in the x direction, the y direction and the z direction respectively, and quantitatively analyzes the distribution state of the spatial position of the target body. On the basis, the central position of the target body is obtained by fitting the normal distribution of the curve. The normal distribution formula f (x) can be expressed as:
Figure BDA0002940490410000072
where σ is the standard deviation and μ is the mean. First, we assume that the scatter statistics of spatial positions computed in a certain direction conform to a normal distribution curve, and the criterion function Q can be expressed as:
Figure BDA0002940490410000073
wherein A is the amplitude. The method adopts least square solution to obtain a fitting curve, and finally obtains the maximum value and the confidence interval of the fitting curve.
The invention discloses a method for calculating the spatial position of a target body by using gravity gradient tensor data, which mainly comprises the following steps:
a) the reasonable layout of the gravity gradiometers, in order to realize the real-time performance and dynamic tracking of positioning, four sets of gravity full-tensor gradiometers need to be erected in the implementation process of the invention in a measuring framework mode of a right-angle tetrahedron (see figure 1). Four sets of values of gradients in x, y, and z directions can be obtained from their respective spatial positional relationships, and the gradients in the three directions are calculated using the four sets of values.
b) The spatial position of the target is predicted, and the upper and lower limits of r are set.
c) And evaluating the noise level and the data quality, testing the damping coefficient and selecting the optimal value.
And (4) completing real-time calculation of the spatial position of the target body by using the calculation formula, performing scattered point statistical analysis and curve fitting on the calculation result, and delineating the spatial position of the target body.
We detail the technical effect of the present invention by testing 2 different models:
(1) example 1
The invention designs a sphere model (see figure 2), and the spatial position is solved by using the calculation method. Wherein the central position of the sphere is (0, 0-10), the radius is 1m, and the density difference is 1g/cm3. FIG. 3 is a scatter distribution plot of the calculation results. Wherein, (a), (c) and (e) are respectively a sphere model test result overlook, side view and three-dimensional scatter distribution diagram; (b) and (d) and (f) are respectively a top view, a side view and a three-dimensional scatter distribution diagram of (a), (c) and (e) under a 5% noise environment. As can be seen from fig. 3, under the theoretical sphere model without noise, the center position of the target body can be very accurately located. Under 5% noise environmentThe spatial position of the target body can be very clearly defined. When the noise level is higher, the center position of the target body can be obtained by adopting methods such as scattered point statistical analysis, normal fitting and the like.
(2) Example 2
Example 2 an underground prevention and control construction model (see FIG. 4) was constructed in which the density of soil was set to 1.6g/cm3The density of the concrete wall is 2.4g/cm3The outer length and the outer width of the underground air defense building are both 80m, the height is 10m, the thickness of the concrete wall surface, the top and the bottom is 0.5m, the distance from the ground to the center of the air defense building is 300m, and therefore the center coordinate of the air defense building is (0, 300). Fig. 5 is a scatter distribution diagram of the calculation result. Wherein, (a), (c) and (e) are respectively a test result top view, a side view and a three-dimensional scatter distribution diagram; (b) and (d) and (f) are respectively a top view, a side view and a three-dimensional scatter distribution diagram of (a), (c) and (e) under a 5% noise environment. It can be seen from the scatter distribution diagram of the calculation result that the inversion result is concentrated under the noise-free environment, the target body position area can be very clearly distinguished from the corresponding histogram, and the target body central position obtained through normal fitting is (3.5, 1.4,289.4), which is very close to the set central position.
Fig. 6 verifies the applicability of the method in noisy environments by adding random noise. Wherein, (a), (b) and (c) are respectively a scattered point cylindrical statistical graph and a corresponding normal fitting curve of a test result in the X, Y and depth directions under a noise-free environment; (d) respectively showing a scattered point cylindrical statistical graph and a corresponding normal fitting curve of a test result in the X, Y and depth directions under the 5% noise environment; (g) and (h) and (i) respectively are a scattered point cylindrical statistical graph in the X direction, the Y direction and the depth direction of a test result in a 30% noise environment and a corresponding normal fitting curve. As can be seen from fig. 6, in a 5% noise environment, the scatter distribution plot of the inversion result can identify the abnormal region as a whole, but the number of the false abnormal points around the abnormal region is increased compared to that in a noise-free environment. The position area of the target body can be obtained clearly through the histogram, and the central position of the target body obtained by utilizing normal fitting is (17.7, -22.0,288.2), and is relatively close to the central position of the target body. In addition, in order to explore the using effect of the method in the strong noise environment, the method analyzes the calculation result under 30% of environmental noise. As can be seen from fig. 6(g), (h) and (i), the overall position can still be shown in the histogram, the peak is still obvious, and the central position of the target obtained after normal fitting is (26.1, -42.8,243.2). The calculation result shows that the method still has stronger applicability in stronger background noise environment, and the noise resistance in the horizontal direction is superior to that in the depth direction.
The invention also provides a real-time positioning system of the target body based on the gravity gradient tensor data. For example, the real-time object positioning system based on the gravity gradient tensor data can be used as a real-time positioning host in a gravity detection system. As described herein, a real-time target localization system based on gravity gradient tensor data can be used to implement real-time target localization functions in a gravity detection system. The real-time object localization system based on the gravity gradient tensor data may be implemented in a single node, or the functionality of the real-time object localization system based on the gravity gradient tensor data may be implemented in multiple nodes in the network. Those skilled in the art will appreciate that the term real-time object localization system based on gravity gradient tensor data includes devices in a broad sense, and that the present invention provides a real-time object localization system based on gravity gradient tensor data as just one example. The inclusion of the gravity gradient tensor data-based real-time object localization system is for clarity and is not intended to limit the application of the present invention to a particular gravity gradient tensor data-based real-time object localization system embodiment or to a class of gravity gradient tensor data-based real-time object localization system embodiments. At least some of the features/methods described herein may be implemented in a network device or component, such as a real-time object location system based on gravity gradient tensor data. For example, the features/methods of the present invention may be implemented in hardware, firmware, and/or software running installed on hardware. The real-time object positioning system based on the gravity gradient tensor data can be any equipment for processing, storing and/or forwarding data frames through a network, such as a server, a client, a data source and the like. The real-time object localization system based on gravity gradient tensor data may include a transceiver (Tx/Rx), which may be a transmitter, a receiver, or a combination thereof. Tx/Rx may be coupled to multiple ports (e.g., uplink and/or downlink interfaces) for transmitting and/or receiving frames from other nodes. The processor may be coupled to the Tx/Rx to process the frames and/or to determine to which nodes to send the frames. A processor may include one or more multi-core processors and/or memory devices, which may serve as data stores, buffers, and the like. The processor may be implemented as a general-purpose processor, or may be part of one or more Application Specific Integrated Circuits (ASICs) and/or Digital Signal Processors (DSPs).
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the present invention in any way, and it will be apparent to those skilled in the art that the above description of the present invention can be applied to various modifications, equivalent variations or modifications without departing from the spirit and scope of the present invention.

Claims (10)

1. A real-time target body positioning method based on gravity gradient tensor data is characterized by comprising the following steps:
obtaining four groups of gravity gradient values in the x, y and z directions according to the spatial position relation of the four groups of gravity gradiometers, and calculating the gravity gradients in the x, y and z directions by using the four groups of gravity gradient values;
evaluating the noise level and the data quality, testing the damping coefficient, and selecting the optimal value;
and (3) completing real-time calculation of the space position of the target body by utilizing a gravity field space position linear calculation formula derived from the position field Poisson relation, performing scattered point statistical analysis and curve fitting on the calculation result, and determining the central position of the space of the target body.
2. The method for real-time object positioning based on the gravity gradient tensor data according to claim 1, further comprising:
and setting upper and lower limits of the spatial position according to spatial position prediction of the target body before evaluating the noise level and the data quality, testing the damping coefficient and selecting the optimal value.
3. The method for real-time positioning of the target based on the gravity gradient tensor data according to claim 1, wherein the real-time calculation of the spatial position of the target is performed by using a gravity field spatial position linear calculation formula derived from a position field poisson relationship, and the calculation result is subjected to scattered point statistical analysis and curve fitting to define the spatial position of the target, and the method comprises the following steps:
and (5) solving the central position of the target body by utilizing curve normal distribution fitting.
4. The method for real-time positioning of an object based on gravity gradient tensor data as recited in claim 3, wherein a normal distribution formula for fitting a normal distribution of a curve is as follows:
Figure FDA0002940490400000011
where σ is the standard deviation and μ is the mean.
5. The method for real-time positioning of an object based on gravity gradient tensor data as recited in claim 4, wherein a criterion function of fitting a normal distribution of a curve is as follows:
Figure FDA0002940490400000021
where A is the amplitude, σ is the standard deviation, and μ is the mean.
6. The method of claim 5, wherein the normal distribution fit is a least squares fit.
7. The method for real-time object positioning based on gravitational gradient tensor data as recited in claim 1, wherein the four sets of gravity gradiometers are erected in a measuring architecture of a right-angled tetrahedron.
8. The method for real-time positioning of an object based on tensor data of gravity gradient as recited in claim 1, wherein the formula for linear calculation of spatial position of gravity field according to poisson's relationship is as follows:
L＝-3(WTW+ε2U)-1WTK
wherein epsilon2For the damping coefficient, U is an identity matrix, and K is a magnetic field expression derived using the gravitational potential of a given magnetic body, i.e., a magnetic field expression in poisson's relationship.
9. The method for real-time positioning of the target based on the gravity gradient tensor data as recited in claim 1, wherein the real-time calculation of the spatial position of the target is performed by using a gravity field spatial position linear calculation formula derived from poisson relations, and comprises the following steps:
and performing inversion calculation of the spatial position by adopting a minimum variance solution.
10. A system for real-time localization of an object based on gravitational gradient tensor data, comprising:
one or more processors;
a storage device for storing one or more programs,
when executed by the one or more processors, cause the one or more processors to implement the method for real-time localization of an object based on gravitational gradient tensor data according to any one of claims 1 to 9.
CN202110175243.9A 2021-02-09 2021-02-09 Real-time target body positioning method and system based on gravity gradient tensor data Pending CN112964248A (en)

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