CN111220947B - Magnetic induction through-the-earth positioning method based on path loss - Google Patents
Magnetic induction through-the-earth positioning method based on path loss Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/06—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements
Abstract
The invention provides a magnetic induction through-the-earth positioning method based on path loss, and belongs to the technical field of magnetic induction through-the-earth positioning. The method utilizes the geometrical relationship between the intersection points of the central axes of the two receivers and the transmitter coils on the ground and the ground to calculate the horizontal distance between the transmitter and the receiver. Deducing the corresponding relation between the intensity of the magnetic induction through-the-earth positioning signal at a certain point on the ground under the rectangular coordinate system and the depth of the underground transmitter from the ground, determining the distance between the transmitter and the ground according to the intensity of the magnetic induction through-the-earth positioning signal at a certain point on the ground, and realizing the vertical depth positioning based on the path loss. The invention analyzes the change rule of the horizontal component, the vertical component and the sum vector of the through-the-earth positioning signal along with the depth distance between the underground transmitter and the ground, establishes the one-to-one corresponding relation between the positioning signal and the vector and the depth between the transmitter and the ground, and realizes more accurate through-the-earth positioning based on the attenuation of the earth medium to the signal.
Description
Technical Field
The invention relates to the technical field of magnetic induction through-the-earth positioning, in particular to a magnetic induction through-the-earth positioning method based on path loss.
Background
The through-the-earth positioning technology plays an important role in the fields of mine disaster rescue, tunnel construction, underground navigation and the like. However, in the earth medium, electromagnetic waves are easily affected by medium changes or obstacles, and significant attenuation and multipath phenomenon occur when passing through a medium such as rock or water, which seriously affects the transmission distance and positioning accuracy of a through-the-earth positioning signal. The extremely-low frequency magnetic induction signal can greatly reduce the loss of the conductive ground medium to the electromagnetic field. The quasi-static magnetic field is a non-stray field, and multipath phenomena such as reflection and scattering do not occur when the quasi-static magnetic field propagates in the earth. This technique is therefore used in through-the-earth positioning. There are a number of problems with existing through-the-earth positioning systems.
A through-the-earth localization system that employs square wave electromagnetic through-the-earth localization signals of several hundred to several kilohertz. A single-axis coil transmitter of the system is horizontally placed in a mine roadway or horizontally wound on a mine support, and a single-axis coil receiver is horizontally placed on the ground. During positioning, a transmitter under a mine continuously transmits a through-the-earth positioning signal, and a worker on the ground continuously moves a receiver for detecting the through-the-earth positioning signal until the through-the-earth positioning signal is detected. The through-the-earth positioning system can only determine the approximate location of the downhole transmitter and cannot achieve accurate through-the-earth positioning including direction and distance between transceivers.
The horizontal component of a magnetic field signal generated by a single-axis annular electrified coil horizontally placed underground on the ground right above the coil is 0, and the vertical component of the magnetic field signal is larger than that of other positions on the ground. In positioning, a worker on the ground holding a horizontally oriented single axis coil receiver moves around the ground area above the transmitter until the detected magnetic field signal is maximized. And then, vertically placing the receiving coil, and if the detected signal intensity of the magnetic field is 0, indicating that the current position is positioned right above the underground transmitting coil. The method can determine the position of the intersection point of the central axis of the underground transmitting coil and the ground (horizontal positioning), but cannot determine the depth of the underground transmitting coil from the ground (vertical positioning).
The annular energizing coil horizontally placed underground can generate an induction magnetic field on the ground, and the horizontal component of the induction magnetic field is minimum in the direction perpendicular to the central axis of the energizing coil. In positioning, the rescue personnel on the ground continuously rotate the vertically placed single-axis toroidal receiving coil in the horizontal direction until the detected magnetic field signal is minimal. And the central axis of the annular receiving coil is perpendicular to the central axis of the annular electrifying and transmitting coil. Therefore, the intersection line of the plane of the annular receiving coil and the horizontal ground passes through the intersection point of the central axis of the transmitting coil and the ground. However, one such intersection line cannot determine the position of the intersection point of the central axis of the transmitting coil and the ground, so that the receiver on the ground is moved, the above steps are repeated, and the intersection line of the plane of the second receiving coil and the ground is obtained, wherein the intersection point of the two intersection lines is the intersection point of the central axis of the transmitting coil and the ground. This method also only enables horizontal positioning.
And establishing a coupling matrix between the triaxial orthogonal transmitting coil and the triaxial orthogonal receiving coil. During positioning, each axis of the three-axis orthogonal transmitting coil sequentially transmits magnetic induction through-the-earth positioning signals with different frequencies, and after the three-axis orthogonal receiving coil receives the positioning signals, the amplitude and the direction of the signals are substituted into the coupling matrix to solve the relative position between the receiving coil and the transmitting coil. The method can realize horizontal positioning and vertical positioning, but when the magnetically induced through-the-earth positioning signal propagates in the earth medium, dielectric loss occurs, which can cause positioning error of the method.
Disclosure of Invention
The present invention is directed to a magnetic induction through-the-earth positioning method based on path loss, so as to solve at least one technical problem in the background art.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a magnetic induction through-the-earth positioning method based on path loss.A magnetic induction signal transmitter is a single-shaft annular electrified coil which is horizontally placed underground;
the magnetic induction signal receiver is two three-axis orthogonal induction type magnetic core coils which are placed on the ground; one axis of the three-axis orthogonal induction type magnetic core coil is vertical to the horizontal ground, and the other two axes are parallel to the horizontal ground;
a sine current is conducted in the single-axis annular electrified coil, and a quasi-static magnetic field excited by the sine current respectively generates induced voltage signals at two ends of the three-axis orthogonal induction type magnetic core coil; determining the direction and the intensity of the magnetic induction through-the-earth positioning signal according to the intensity of the triaxial orthogonal induction voltage signal;
vector superposition is carried out on the induced voltage signals of the two axes parallel to the ground, and the straight line of the superposed signals passes through the intersection point of the central axis of the single-axis annular electrified coil and the ground;
calculating the distance between the intersection point and the axis orthogonal induction type magnetic core coil in a triangle formed by the two three-axis orthogonal induction type magnetic core coils and the intersection point to finish horizontal positioning;
and converting the corresponding relation of the signal intensity between the magnetic induction signal transmitter and the magnetic induction signal receiver from a spherical coordinate system to a rectangular coordinate system, and establishing the corresponding relation of the magnetic induction through-the-earth positioning signal and the vector with the depth of the transmitter to complete depth positioning.
Preferably, a spherical coordinate system is established by taking the central point of the single-axis annular energized coil as the origin of coordinates, and the signal intensity of the magnetic induction through-the-earth positioning signal is as follows:
wherein n represents the number of turns of the single-axis annular energizing coil, r' represents the distance between the central point of the receiver three-axis orthogonal induction type magnetic core coil and the central point of the single-axis annular energizing coil, theta represents the included angle between the connecting line of the central point of the three-axis orthogonal induction type magnetic core coil and the central point of the single-axis annular energizing coil and the central axis of the single-axis annular energizing coil, sigma represents the electrical conductivity of the ground medium, and mu represents the electrical conductivity of the ground medium0The magnetic permeability of the earth medium is represented, and R represents the radius of the single-axis annular electrified coil;
the current of the transmitter coil is I ═ I0Sin ω t, where ω represents the angular frequency of the current and t represents time, then
Wherein n is0(t) represents the spectrally randomly distributed geomagnetic noise in the magnetically induced through-the-earth localization signal.
Preferably, the horizontal component of the through-the-earth positioning signal passes through the intersection point of the central axis of the single-axis annular electrified coil and the ground, the distance between the two receivers on the ground and the angle of the vertex angle of the two receivers are measured in a triangle formed by the two receivers and the intersection point, the distance between the intersection point and the receivers is calculated according to the sine theorem, and horizontal positioning is completed.
Preferably, in the formula (2)
Expressing the electrical conductivity σ and magnetic permeability μ of the medium through the earth0The resulting attenuation of the strength of the magnetically induced through-the-earth locating signal; in the formula (2)
The intensity attenuation of the magnetic induction through-the-earth positioning signal caused by the distribution rule of the magnetic dipole magnetic field is represented;
then, the signal intensity of the magnetic induction through-ground positioning signal is monotonically decreased along with the increase of r', and the corresponding relation between the signal intensity of the magnetic induction through-ground positioning signal and the depth of the transmitter under the rectangular coordinate system is determined, so that the vertical positioning is realized.
Preferably, the magnetic induction through-the-earth positioning signal received by the receiver is subjected to vector decomposition to obtain a horizontal component and a vertical component, a spherical coordinate system adopted by the formula (2) is converted into a rectangular coordinate system, and the spherical coordinates (r', theta, phi) of the receiver are simplified into (r, z), phi represents an included angle between a connecting line of the receiver and the intersection point and an x axis, and z represents a distance between the transmitter and the ground.
Preferably, when the influence of geomagnetic noise is neglected, the through-the-earth localization signal intensity peak in the formula (2) is
Performing vector decomposition on B in the formula (5); firstly, B is decomposed into a component along an r axis and a component along a theta axis in a spherical coordinate system, and then the two components are subjected to vector decomposition along a z axis and an H1 axis respectively to obtain a horizontal component B of BH1And a vertical component BZ1：
Preferably, the correspondence relationship between r', θ and the rectangular coordinates r, z in the spherical coordinate system is:
By substituting formula (7) for formula (6), the horizontal component and the vertical component of the magnetically induced through-the-earth positioning signal B in the rectangular coordinate system can be obtained as follows:
the corresponding relationship of the magnetically induced through-the-earth positioning signal B to z is
Preferably, r and B are substituted into equation (9), and iterative calculation is performed, so that the Z value where equation (9) holds is the depth of the underground transmitter from the ground.
The invention has the beneficial effects that: the change rule of the horizontal component, the vertical component and the sum vector of the through-the-earth positioning signal along with the depth distance from the underground transmitter to the ground is analyzed, the one-to-one correspondence relationship between the positioning signal and the vector and the depth from the ground of the transmitter to the ground is established, and more accurate through-the-earth positioning based on the attenuation of the earth medium to the signal is realized.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a schematic diagram of a positioning principle model of a magnetic induction through-the-earth positioning system according to an embodiment of the present invention.
Fig. 2 is a relative position diagram of a single-axis toroidal coil transmitter and a three-axis orthogonal induction type magnetic core coil receiver of the magnetic induction through-the-earth positioning system according to the embodiment of the present invention in a three-dimensional coordinate system.
Fig. 3 is a schematic diagram of horizontal positioning according to an embodiment of the present invention.
Fig. 4 is a schematic vector decomposition diagram of the magnetic induction through-the-earth signal B according to the embodiment of the present invention.
Fig. 5 is a schematic vertical plane structure diagram of a magnetic induction through-the-earth positioning system according to an embodiment of the present invention.
Fig. 6 is a schematic diagram illustrating a corresponding relationship between signal strength and positioning depth according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below by way of the drawings are illustrative only and are not to be construed as limiting the invention.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
For the purpose of facilitating an understanding of the present invention, the present invention will be further explained by way of specific embodiments with reference to the accompanying drawings, which are not intended to limit the present invention.
It should be understood by those skilled in the art that the drawings are merely schematic representations of embodiments and that the elements shown in the drawings are not necessarily required to practice the invention.
Example 1
The embodiment 1 of the invention provides a magnetic induction through-the-earth positioning method based on path loss. The receiver is a three-axis orthogonal induction type magnetic core coil placed on the ground, one axis of the coil is perpendicular to the horizontal ground, and the other two axes are parallel to the horizontal ground. Between the transceivers is a ground medium having electrical conductivity. Sinusoidal current with a certain frequency (such as 10Hz) is conducted in a multi-turn coil of the transmitter, a quasi-static magnetic field excited by the current penetrates through a ground medium to reach a receiver on the ground, induced voltage signals are respectively generated at two ends of three magnetic core coils of the receiver, and the direction and the intensity of the magnetic induction through-the-earth positioning signals can be determined according to the intensity of the three-axis orthogonal induced voltage signals.
Horizontal positioning is achieved by determining the orientation and distance between the central axis of the transmitter coil and the receiver. After the three-axis receiver on the ground detects the magnetic induction through-the-ground positioning signal, the signal detected by the two axes parallel to the ground is subjected to vector superposition, and at the moment, the straight line of the superposed signal passes through the intersection point of the central axis of the underground transmitting coil and the ground. Two receivers distributed at different positions on the ground can generate two straight lines, and the intersection point of the straight lines is the intersection point of the central axis of the transmitting coil and the ground. In a triangle formed by the intersection points of the central axes of the two receivers and the transmitting coil and the ground, measuring the distance between the two receivers on the ground and the angle of the vertex angle of the two receivers, and calculating the distance between the intersection point of the central axis of the transmitting coil and the ground and any one receiver according to the sine theorem so as to finish horizontal positioning.
The corresponding relation of the signal intensity between the transmitter and the receiver is converted from a cylindrical coordinate system to a rectangular coordinate system, the change rule of the horizontal component, the vertical component and the sum vector of the through-the-earth positioning signal along with the depth distance of the underground transmitter from the ground is analyzed, the one-to-one corresponding relation of the positioning signal and the vector and the depth of the transmitter from the ground is established, and the depth positioning is completed.
As shown in fig. 1, the transmitter is a single-axis multi-turn annular energizing coil horizontally placed underground, two receivers at different positions above the ground are both three-axis orthogonal induction type magnetic core coil sensors, one axis of the coil is perpendicular to the horizontal ground, and the other two axes are parallel to the horizontal ground. Between the transmitter and the receiver is a ground medium with electrical conductivity. Sinusoidal current with a certain frequency (such as 10Hz) is conducted in a multi-turn coil of the transmitter, a quasi-static magnetic field excited by the current penetrates through a ground medium to reach a receiver on the ground, induced voltage signals are generated at two ends of three magnetic core coils of the receiver respectively, and the receiver can restore the induced voltage signals into magnetic induction through-the-earth positioning signals. The magnetic induction lines in fig. 1 are curved lines, and the magnetic induction lines at the two receivers do not point to the transmitter coil, so that the position of the transmitter coil cannot be directly judged by the direction of the magnetic field at the receivers. But positioning the transmitter coil can be achieved indirectly by both horizontal and vertical positioning.
As shown in fig. 2, in a three-dimensional rectangular coordinate system with a point O as an origin, the transmitter is located at the origin of the coordinates, and the center of the antenna coil coincides with the origin O. The dashed box in fig. 2 represents the ground, receiver Q1And Q2And the point C is the intersection point of the axis of the transmitter coil and the ground. Q1And Q2At a distance r from the point C1And r2The distance of point C from the origin O is z. Q1And Q2Are each r 'away from the point O'1And r'2，Q1O and Q2The included angles of O and the z axis are respectively theta1And theta2，Q1C and Q2The included angles between the C and the x axis are respectively phi1And phi2. The radius of the transmitter antenna coil is R, the number of coil turns is n, and the current in the coil is I. A spherical coordinate system is established by taking the point O as an origin to obtain Q1Dot sum Q2The through-the-earth localization of the spots localizes the signal strength.
In example 1 of the present invention, Q1For example, the through-the-earth localization signal strength is:
in example 1 of the present inventionIn (1), let the electrical conductivity of the earth medium be sigma and the magnetic permeability be mu0The geomagnetic noise approximately randomly distributed in the frequency spectrum is n0(t) transmitter coil current I ═ I0Sin ω t, where ω is the angular frequency of the current and t is the time. Then:
from the formula (22), Q1Through-the-earth location signal strength of a point
Phi and phi1This is irrelevant, indicating that the signal at this point lies in plane OCQ1Inner, horizontal component B thereofH1Point of direction C, likewise Q2Through-the-earth localization signal horizontal component B of a pointH2Also points to points C, BH1And BH2On the straight line Q1C and Q2C may collectively determine the location of point C. To Q1Dot sum Q2Distance between points, < Q >2Q1C and < Q1Q2C, measuring, and calculating Q according to sine theorem1Length r of C1Or Q2Length r of C2. To this end, point C is relative to Q1Dot or Q2The orientation and the distance of the point are acquired, and horizontal positioning is realized.
In inventive example 1, in formula (22)
Representing the electrical conductivity σ and magnetic permeability μ of the medium through the earth0The resulting magnetic induction through the earth locates the signal strength attenuation.
In the formula (22)
Representing the attenuation of the strength of the magnetically induced through-the-earth positioning signal caused by the distribution rule of the magnetic dipole magnetic field.
The two attenuation representatives
From r'1Is monotonically decreased, and a rectangular coordinate system is deduced according to the monotonous decrease of the increase
And the one-to-one correspondence with the transmitter depth realizes the vertical positioning based on the path loss.
In particular, as can be seen from fig. 2, the receiver Q1And Q2Component B of magnetically induced through-the-earth positioning signal in horizontal directionH1And BH2Points to point C and thus the location of point C can be determined from these two points. As shown in fig. 3, point C, Q in fig. 31Dot sum Q2The points correspond to fig. 2. Q1The horizontal quadrature component of the point through-the-earth localization signal is Bx1And By1And the sum vector is BH1，Q2Point and Q1Points are similar and correspond to B respectivelyx2、By2、BH2. Since the through-the-earth locating signal is a standard sine wave, the direction of the signal alternates periodically with time, although B in FIGS. 2 and 3H1、BH2Look in the opposite direction but the expression is the same. Q1Dot sum Q2The measured distance between the points is d,
as can be seen from FIG. 3, point C is located at BH1And BH2At the intersection of the straight lines, this determines the transmitter and Q in the ground1Dot or Q2Horizontal orientation between points. According to the sine theorem, Q1The horizontal distance between the point and the underground transmitter is:
it can be determined to this end that underground transmitters are located along BH1In the opposite direction of (1) and Q1Distance between points of
Just below the ground.
Example 2
In embodiment 2 of the present invention, in order to determine the depth of the transmitter, the terrestrial receiver Q in equation (22) is used1Point magnetic induction through-the-earth positioning signal
Carry out vector decomposition to obtain
Horizontal component B ofH1And a vertical component BZ1Converting the spherical coordinate system adopted by the formula (22) into a rectangular coordinate system, and converting Q into a rectangular coordinate system1Sphere coordinate of points (r'1,θ,φ1) Simplified as (r)1,z)，φ1Indicating the receiver Q1An included angle between a connecting line of the intersection point C and the x axis, z represents the distance between the transmitter and the ground, and a rectangular coordinate system is deduced
And r1And z. Bound Q1C distance between two points r1According to Q1Point magnetic induction through-the-earth positioning signal intensity
The distance z between the transmitter and the ground is determined.
As shown in FIG. 4, is Q1Point magnetic induction through-the-earth positioning signal
Vector exploded view of (1), axis H1 in FIG. 4 and axis B in FIG. 2H1Coincidence, OCQ1The plane corresponds to OCQ in fig. 21Plane, the origin O and z axes in the two figures coincide with each other. As can be seen from FIG. 4, at right triangle OCQ1The distance z between the transmitter and the ground is:
r in formula (24)1Has passed through formula (23)) As a result, in example 2 of the present invention, θ was determined again1The depth z of the transmitter from the ground can be solved. The method comprises the following specific steps:
q in equation (22) regardless of the influence of geomagnetic noise1The peak value of the through-point positioning signal intensity is
Performing vector decomposition on B in the formula (25); firstly, B is decomposed into a component along an r axis and a component along a theta axis in a spherical coordinate system, and then the two components are subjected to vector decomposition along a z axis and an H1 axis respectively to obtain a horizontal component B of BH1And a vertical component BZ1。
Q in FIG. 41I corresponds to
Q1B and Q1F corresponds to
In spherical coordinates erAnd eθThe component of the direction. Q1B and Q1The component vector of F along the H1 axis and the Z axis is
Therefore, the temperature of the molten metal is controlled,
the components in the directions of the H1 axis and the Z axis are respectively
From the formula (25)
And is less than AQ1B＝∠COQ1Thus, therefore, it is
By substituting formula (29) for formula (27)
The components in the horizontal and vertical directions are respectively
As shown in FIG. 5, Q is added1The spherical coordinates of the points are converted into rectangular coordinates. OCQ in FIG. 51The plane corresponds to OCQ in fig. 21Plane, horizontal axis H1 corresponds to vector B in FIG. 2H1In the opposite direction, the origin O and z axes in the two figures coincide with each other. As can be seen from FIG. 2, | CQ in FIG. 61|＝r1，|CO|＝z，|OQ1|＝r′1，∠COQ1＝θ1. Thus Q1Point-and-ball coordinate r'1、θ1And the rectangular coordinate r1And z is in correspondence with
Obtaining the solution
Q can be obtained by substituting formula (32) for formula (30)1Point magnetic induction through-the-earth positioning signal
The horizontal component and the vertical component in the rectangular coordinate system are
Q1Point magnetic induction through-the-earth positioning signal
Has a modulus value of
In embodiment 2 of the present invention, the limitation of the working environment of the magnetic induction through-the-earth positioning system to the factors such as volume and power consumption is comprehensively considered, and a set of feasible standard parameters is set. Because underground space is limited, the volume of a transmitter antenna is not suitable to be overlarge, the radius R of a transmitter coil is not more than 2m at most, the number n of turns of the transmitter coil is set to be 3300 turns, the effective value of current I of the transmitter coil is 4A, and because most strata do not contain ferromagnetic substances such as iron, cobalt, nickel and the like, the ground magnetic permeability is taken as the vacuum magnetic permeability mu0＝4π×10-7H/m, conductivity σ set to 5X 10-3And (5) S/m. The signal frequency f is set to 10 Hz. B can be obtained by substituting the above parameters into the formulae (33) and (34)H1、BZ1And
law as a function of z.
As shown in fig. 6, is the ground Q1Simulation result of variation of point magnetic induction through-the-earth positioning signal intensity along with depth z of transmitter from ground, Q1Distance r from point C1Is 200 m. As shown in fig. 6, magnetically induced through-the-earth location signals
Horizontal component B ofH1And a vertical component BZ1The intensity of the magnetic induction through-the-earth positioning signal is increased and then reduced along with the increase of z
Monotonically decreasing as z increases. Experiments prove that when r is1The law shown in fig. 6 holds when other values are taken.
Will r is1And
substituting equation 34), the transcendental equation of equation (34) has only one variable z, and the iterative calculation is carried out on equation (34), so that the z value of equation (34) is the depth of the underground transmitter from the ground, and the vertical positioning based on the path loss is realized.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (1)
1. A magnetic induction through-the-earth positioning method based on path loss is characterized in that:
the magnetic induction signal transmitter is a single-shaft annular electrified coil which is horizontally placed underground;
the magnetic induction signal receiver is two three-axis orthogonal induction type magnetic core coils which are placed on the ground; one axis of the three-axis orthogonal induction type magnetic core coil is vertical to the horizontal ground, and the other two axes are parallel to the horizontal ground;
a sine current is conducted in the single-axis annular electrified coil, and a quasi-static magnetic field excited by the sine current respectively generates induced voltage signals at two ends of the three-axis orthogonal induction type magnetic core coil; determining the direction and the intensity of the magnetic induction through-the-earth positioning signal according to the intensity of the triaxial orthogonal induction voltage signal;
vector superposition is carried out on the induced voltage signals of the two axes parallel to the ground, and the straight line of the superposed signals passes through the intersection point of the central axis of the single-axis annular electrified coil and the ground;
calculating the distance between the intersection point and the axis orthogonal induction type magnetic core coil in a triangle formed by the two three-axis orthogonal induction type magnetic core coils and the intersection point to finish horizontal positioning;
converting the corresponding relation of the signal intensity between the magnetic induction signal transmitter and the magnetic induction signal receiver from a spherical coordinate system to a rectangular coordinate system, establishing the corresponding relation of the magnetic induction through-the-earth positioning signal and the vector with the depth of the transmitter, and completing depth positioning;
the central point of using unipolar annular circular current coil establishes the spherical coordinate system as the origin of coordinates, and then magnetic induction through the earth positioning signal's signal strength is:
wherein n represents the number of turns of the single-axis annular energizing coil, r' represents the distance between the central point of the receiver three-axis orthogonal induction type magnetic core coil and the central point of the single-axis annular energizing coil, theta represents the included angle between the connecting line of the central point of the three-axis orthogonal induction type magnetic core coil and the central point of the single-axis annular energizing coil and the central axis of the single-axis annular energizing coil, sigma represents the electrical conductivity of the ground medium, and mu represents the electrical conductivity of the ground medium0The magnetic permeability of the earth medium is represented, and R represents the radius of the single-axis annular electrified coil;
the current of the transmitter coil is I ═ I0Sin ω t, where ω represents the angular frequency of the current and t represents time, then
Wherein n is0(t) represents geomagnetic noise randomly distributed on a frequency spectrum in the magnetically induced through-the-earth positioning signal;
the horizontal component of the through-the-earth positioning signal passes through the intersection point of the central axis of the single-axis annular electrified coil and the ground, the distance between two receivers on the ground and the angle of the vertex angle of the two receivers are measured in a triangle formed by the two receivers and the intersection point, the distance between the intersection point and the receivers is calculated according to the sine theorem, and horizontal positioning is completed;
in the formula (2)
Expressing the electrical conductivity σ and magnetic permeability μ of the medium through the earth0The resulting attenuation of the strength of the magnetically induced through-the-earth locating signal; in the formula (2)
The intensity attenuation of the magnetic induction through-the-earth positioning signal caused by the distribution rule of the magnetic dipole magnetic field is represented;
then, the signal intensity of the magnetic induction through-ground positioning signal is monotonically decreased along with the increase of r', and the corresponding relation between the signal intensity of the magnetic induction through-ground positioning signal and the depth of the transmitter under a rectangular coordinate system is determined, so that vertical positioning is realized;
carrying out vector decomposition on the magnetic induction through-the-earth positioning signal received by the receiver to obtain a horizontal component and a vertical component, converting a spherical coordinate system adopted by the formula (2) into a rectangular coordinate system, and simplifying the spherical coordinates (r', theta and phi) of the receiver into (r and z), wherein phi represents an included angle between a connecting line of the receiver and the intersection point and an x axis, and z represents a distance between the transmitter and the ground;
if the influence of geomagnetic noise is neglected, the through-the-earth positioning signal intensity peak in the formula (2) is
Performing vector decomposition on B in the formula (5); firstly, B is decomposed into a component along an r axis and a component along a theta axis in a spherical coordinate system, and then the two components are subjected to vector decomposition along a z axis and an H1 axis respectively to obtain a horizontal component B of BH1And a vertical component BZ1：
In the spherical coordinate system, the corresponding relation between r', theta and the rectangular coordinates r and z is as follows:
by substituting formula (7) for formula (6), the horizontal component and the vertical component of the magnetically induced through-the-earth positioning signal B in the rectangular coordinate system can be obtained as follows:
the corresponding relationship of the magnetically induced through-the-earth positioning signal B to z is
And substituting r and B into the formula (9) to carry out iterative calculation, wherein the Z value formed by the formula (9) is the depth of the underground transmitter from the ground.
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