A linear single-point positioning method based on a permanent magnet mechanical antenna

Abstract

The application discloses a linear single-point positioning method based on a permanent magnet mechanical antenna and belongs to the technical field of electromagnetic detection and positioning. The method comprises the following steps: establishing a Cartesian coordinate system with a three-axis magnetic field sensor as an origin, and the coordinate axis direction is the same as the sensor sensitive axis; measuring the radiated magnetic field data of the permanent magnet mechanical antenna with a known frequency and an equivalent magnetic moment; obtaining multiple uncertain positions in a half space based on the amplitude information of the measured data; excluding the wrong position according to the phase information of the measured magnetic field, selecting the only correct position, and completing the positioning. Compared with the traditional permanent magnet mechanical antenna positioning method based on numerical optimization, the application can utilize the amplitude and phase information of the radiated magnetic field, complete the calculation process faster, and expand the positioning range. By installing the application on a robot or a human body, accurate positioning can be realized in a global navigation satellite system denial environment, and the application has wide application potential.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic detection and positioning technology, specifically relating to a linear single-point positioning method based on a permanent magnet mechanical antenna, which is mainly used for the accurate positioning of human bodies / robots in GNSS denied environments. Background Technology

[0002] With the widespread application of Global Navigation Satellite Systems (GNSS) in positioning, navigation, and timing, many modern systems have become highly dependent on them. However, in certain special scenarios, such as urban canyons, underground facilities, underwater environments, and military scenarios, GNSS signals may be severely shielded, interfered with, or even completely disabled, making GNSS-based positioning infeasible. Therefore, achieving accurate and efficient positioning in environments with limited or no GNSS coverage has become an important research topic. To address this issue, researchers have begun exploring alternative positioning methods. Among these, positioning technology utilizing magnetic field properties has become an important research direction due to its strong anti-interference capability and independence from external wireless signal sources. Permanent magnet mechanical antennas are a novel positioning technology based on this concept. By generating a dynamic magnetic field through antenna rotation, a spatial magnetic field distribution can be formed around the target object, and the target's position can be estimated by utilizing changes in the magnetic field characteristics. This antenna positioning technology is particularly suitable for use in GNSS-denied environments. Current research and applications largely focus on improving positioning accuracy, adapting to more complex environments, and accelerating computational speed. While existing localization methods, such as those based on particle swarm optimization (PSO), can provide a certain level of accuracy, they often suffer from problems in practical applications, such as long computation times and an inability to handle localization needs over larger areas. As demands for real-time performance and computational efficiency increase, the limitations of existing technologies are becoming increasingly apparent. This makes further optimization of localization algorithms and expansion of their applicability a current research focus. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention provides a linear single-point positioning method based on a permanent magnet mechanical antenna. This method fully considers the amplitude and phase information of the radiated magnetic field, significantly improving positioning speed and expanding the positioning range. It can be used for rapid and accurate positioning of humans / robots in GNSS-denied environments.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A linear single-point positioning method based on a permanent magnet mechanical antenna is described below:

[0006] A Cartesian coordinate system is established with the triaxial magnetic field sensor as the origin, and the coordinate axes are in the same direction as the sensor's sensitive axes.

[0007] Measure the radiated magnetic field data generated by a permanent magnet mechanical antenna with a known frequency and equivalent magnetic moment;

[0008] Based on the amplitude information of the measured radiation magnetic field data, multiple mutually symmetrical uncertain positions in the half space are obtained. These multiple mutually symmetrical uncertain positions include eight possible positions of the mechanical antenna when the extreme value of the z-axis component of the radiation magnetic field is zero, or five possible positions of the mechanical antenna when the extreme value of the z-axis component of the radiation magnetic field is not zero.

[0009] Based on the phase information of the measured radiation magnetic field data, incorrect locations are eliminated, and the only correct location is selected to complete the positioning.

[0010] The beneficial effects of this invention are as follows:

[0011] (1) This invention fully considers the problem of slow calculation speed of traditional numerical optimization-based positioning methods and derives a faster linear positioning method.

[0012] (2) This invention expands the positioning range of the algorithm by simultaneously utilizing the amplitude and phase information of the radiation field of the mechanical antenna. Attached Figure Description

[0013] Figure 1 This is a flowchart of a linear single-point positioning method based on a permanent magnet mechanical antenna according to the present invention.

[0014] Figure 2 This is a schematic diagram showing the coordinate system, magnetic field sensor, and mechanical antenna positions established for this invention. Detailed Implementation

[0015] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0016] like Figure 1 As shown, the present invention provides a linear single-point positioning method based on a permanent magnet mechanical antenna, comprising the following steps: First, establishing a Cartesian coordinate system with a triaxial magnetic field sensor as the origin, the coordinate axes being aligned with the sensor's sensitive axes; second, measuring the radiated magnetic field generated by the cooperative mechanical antenna: measuring the radiated magnetic field data generated by the permanent magnet mechanical antenna with known frequency and equivalent magnetic moment; then, calculating feasible positions based on amplitude information: obtaining multiple uncertain positions in half-space based on the amplitude information of the measured data; finally, selecting the true position based on phase information: further eliminating erroneous positions based on the phase information of the measured magnetic field, selecting the unique correct position, and completing the positioning. The specific implementation steps are as follows:

[0017] First step, such as Figure 2 As shown, in spherical coordinates, the radiated magnetic field generated by a permanent magnet mechanical antenna at any measurement point in space is:

[0018] (1)

[0019] Among them, among them, and These represent the remanence and volume of a permanent magnet, respectively. This represents the position vector from the mechanical antenna to the sensor. This indicates the transpose operation. Represents position vector The mode, i.e., the distance between the mechanical antenna and the sensor, and These are the tilt angle and deflection angle of the mechanical antenna, respectively. Indicates wave number, and These are the magnetic permeability and dielectric constant of the propagation medium, respectively. Let j represent the rotational angular velocity of the mechanical antenna, j represent the imaginary unit, e represent the exponential function, and t represent time.

[0020] In addition, the magnetic field measured by the sensor is in Cartesian coordinates, so a coordinate transformation is required. The rotation matrix is:

[0021] (2)

[0022] Therefore, the radiated magnetic field in the Cartesian coordinate system is:

[0023] (3)

[0024] in, It consists of the three-axis components of the radiated magnetic field, which change with time in a sinusoidal manner.

[0025] The extreme values ​​in a period are determined by This indicates, and specifically includes:

[0026] (4)

[0027] (5)

[0028] (6)

[0029] First consideration From (6), we can obtain the following:

[0030] (7)

[0031] Substituting (7) into (4) and (5), we can deduce that:

[0032] (8)

[0033] (9)

[0034] make So there are Similarly, let ,have .Will Substituting (8) and (9) and squaring both sides of the equal sign, we get:

[0035] (10)

[0036] (11)

[0037] Summing the above equation, we get:

[0038] (12)

[0039] because Therefore, (12) can be rewritten as: ,in, Let be the coefficients. By solving the above quartic equation in one variable, two non-negative solutions can usually be calculated. Substituting into the above formula, we can obtain the distance between the mechanical antenna and the sensor.

[0040] Furthermore, the deflection angle of the mechanical antenna in the coordinate system can also be calculated accordingly, as follows:

[0041] (13)

[0042] The above analysis is for Non-singular points. However, for Regarding the singularity, its location requires further analysis, and it can be mainly divided into... and Two scenarios.

[0043] In the first case, Therefore, the angle of deflection can be any value. Under this condition, we have: Then (4) and (5) can be rewritten as:

[0044] (14)

[0045] (15)

[0046] Therefore, the distance between the mechanical antenna and the sensor is:

[0047] (16)

[0048] For the second case The mechanical antenna is located On the plane, at this time Then (4) and (5) can be rewritten as:

[0049] (17)

[0050] (18)

[0051] Squaring both sides of the above equation and summing them, we get:

[0052] (19)

[0053] Accordingly, the distance between the mechanical antenna and the sensor is:

[0054] (20)

[0055] Based on (17) and (18), the positional deflection angle can be expressed as:

[0056] (twenty one)

[0057] Right now:

[0058] (twenty two)

[0059] Thus, the half-space is obtained. Eight possible positions of the mechanical antenna under the condition or Five possible positions for the mechanical antenna under certain conditions.

[0060] Step 2: From (3), we know that the real part of the three-axis components of the magnetic field radiated by the mechanical antenna is:

[0061] (twenty three)

[0062] (twenty four)

[0063] (25)

[0064] The imaginary part of the three-axis components of the radiated magnetic field data from the mechanical antenna is:

[0065] (26)

[0066] (27)

[0067] (28)

[0068] in, Indicates the mechanical antenna at different times The azimuth angle below. The mechanical antenna is a low-frequency transmitter, which is effective for most detection ranges. ,at this time .

[0069] When the position parameters of the measurement point remain unchanged The phase also remains unchanged and only with respect to the variable. Relevant. Order They represent when Azimuth angle at extreme points For the corresponding time. According to formulas (23)-(25), when the z-axis component When located at an extreme point, we have ,Right now , .for The azimuth angle can be expressed as:

[0070] (29)

[0071] (30)

[0072] According to the auxiliary angle formula, we get:

[0073] (31)

[0074] (32)

[0075] in, and Is and Relevant variables.

[0076] In order to To reach an extreme point, the following must be satisfied:

[0077] (33)

[0078] (34)

[0079] Based on formulas (33) and (34), the final tilt angle of the mechanical antenna is calculated as follows:

[0080] (35)

[0081] Thus, incorrect antenna positions can be eliminated, and the only true mechanical antenna position can be selected based on (35).

[0082] Contents not described in detail in this specification are prior art known to those skilled in the art. Although exemplary embodiments of the invention have been described for illustrative purposes, those skilled in the art will understand that various modifications, additions, and substitutions in form and detail can be made without departing from the scope and spirit of the invention disclosed in the appended claims, and all such modifications and substitutions should fall within the protection scope of the appended claims. Furthermore, the various parts of the product and the various steps of the method claimed in this invention can be combined in any combination. Therefore, the description of the embodiments disclosed in this invention is not intended to limit the scope of the invention, but rather to describe the invention. Accordingly, the scope of the invention is not limited by the above embodiments, but is defined by the claims or their equivalents.

Claims

1. A linear single-point positioning method based on a permanent magnet mechanical antenna, characterized in that, Includes the following steps: A Cartesian coordinate system is established with the triaxial magnetic field sensor as the origin, and the coordinate axes are in the same direction as the sensor's sensitive axes. Measure the radiated magnetic field data generated by a permanent magnet mechanical antenna with a known frequency and equivalent magnetic moment; Based on the amplitude information of the measured radiation magnetic field data, multiple mutually symmetrical uncertain positions in the half space are obtained. These multiple mutually symmetrical uncertain positions include eight possible positions of the mechanical antenna when the extreme value of the z-axis component of the radiation magnetic field is zero, or five possible positions of the mechanical antenna when the extreme value of the z-axis component of the radiation magnetic field is not zero. Based on the phase information of the measured radiation magnetic field data, incorrect locations are eliminated, and the unique correct location is selected to complete the positioning. The amplitude information based on the measured radiation magnetic field data is used to obtain multiple mutually symmetrical uncertain positions in the half-space, including: Radiated magnetic field of permanent magnet mechanical antenna in Cartesian coordinate system for: （3） in, It is a radiating magnetic field. The three-axis components change with time in a sinusoidal manner. This refers to the radiated magnetic field generated by a permanent magnet mechanical antenna at any measurement point in space, in spherical coordinates. Represents the radiated magnetic field Rotation matrix for coordinate transformation. Indicates the transpose operation; set up The extreme values ​​in a period are determined by It means that when At that time, we obtained the following in sequence: （7） （8） （9） in, and These represent the remanence and volume of a permanent magnet, respectively. This represents the position vector from the mechanical antenna to the sensor; Let intermediate parameters , ,Will Substituting (8) and (9), we get: （12） when At that time, the deflection angle of the mechanical antenna position is: （13） consider When the tilt angle of the mechanical antenna position ,have ,at this time: （14） （15） At this point, the distance between the mechanical antenna and the sensor is: （16） consider When the tilt angle of the mechanical antenna position The mechanical antenna is located On a plane, ,at this time: （19） The distance between the mechanical antenna and the sensor is: （20） So The position deflection angle of the mechanical antenna is expressed as: （22） Thus, the half-space is obtained. Eight possible positions of the mechanical antenna under the condition or Five possible positions for the mechanical antenna under certain conditions.

2. The linear single-point positioning method based on a permanent magnet mechanical antenna according to claim 1, characterized in that, The step of eliminating erroneous positions and selecting the only correct position based on the phase information of the measured radiated magnetic field data includes calculating the real and imaginary parts of the three-axis components of the mechanical antenna radiated magnetic field data; make Representing the radiated magnetic field respectively triaxial components Azimuth angle at extreme points For the corresponding time, when the z-axis component When located at an extreme point, we have If you want To reach an extreme point, the following conditions must be met: （33） （34） Based on formulas (33) and (34), the final tilt angle of the mechanical antenna is calculated as follows: （35） Thus, incorrect antenna positions can be eliminated, and the only true mechanical antenna position can be selected according to equation (35).

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