A calibration method for magnetic dipole model based on polynomial expansion

Abstract

The present invention relates to the field of electromagnetic positioning technology, and in particular to a magnetic dipole model calibration method based on polynomial expansion. This calibration method establishes a magnetic dipole model between a three-axis induction coil and a single-axis transmitting coil to calculate its magnetic field strength; performs polynomial expansion on the induced electrical signal of the induction coil to minimize the error between it and the magnetic field strength calculated by the magnetic dipole model; and calculates the rotation matrix of the three-axis induction coil to make the magnetic fields of the three-axis induction coil orthogonal to each other. The present invention performs polynomial expansion on the electrical induction signal of the induction coil to make it fit the magnetic field calculated by the magnetic dipole, and at the same time iterates the optimal rotation matrix through an optimization algorithm to correct the non-orthogonal induction coil, ultimately improving the accuracy of magnetic positioning.

Description

Technical Field

[0001] The present invention relates to the technical field of electromagnetic positioning, and in particular to a magnetic dipole model calibration method based on polynomial expansion. Background Art

[0002] The magnetic dipole model is widely used in applications such as the positioning and status measurement of target objects. When the volume of the receiving coil is much smaller than the monitoring distance, the coil can be regarded as a magnetic dipole. However, in some actual position detection applications, since the detection distance is not much larger than the volume of the receiving coil, the size of the receiving coil cannot be ignored. The receiving coil has a certain physical size, and non-orthogonality factors must be considered due to manufacturing tolerances. This leads to differences between the actual received signal and the signal simulated by the model. This difference is particularly significant near the axis. Summary of the Invention

[0003] Other features and advantages of the present invention will be described in the following description, and in part will become apparent from the description, or will be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the structures particularly pointed out in the description and other drawings.

[0004] The purpose of the present invention is to overcome the above-mentioned shortcomings and provide a magnetic dipole model calibration method based on polynomial expansion. By performing a polynomial expansion on the electrical induction signal of the induction coil, it is made to fit the magnetic field calculated by the magnetic dipole. At the same time, the optimal rotation matrix is ​​iterated through the optimization algorithm to correct the non-orthogonal induction coil, and ultimately improve the accuracy of magnetic positioning. This correction method is fast and accurate and can solve the problem of large positioning error of the magnetic dipole at the axis.

[0005] The present invention provides a magnetic dipole model calibration method based on polynomial expansion, comprising:

[0006] S1. Establish a magnetic dipole model between the three-axis induction coil and the single-axis transmitting coil in advance and calculate the theoretical magnetic field strength;

[0007] S2. Perform polynomial expansion on the induced electrical signal of the triaxial induction coil and fit the induced magnetic field, so as to minimize the error between the induced magnetic field intensity and the theoretical magnetic field intensity calculated by the magnetic dipole model, and obtain the optimal solution with the minimum error. The method for solving the minimum error is an optimization iterative algorithm;

[0008] S3. Due to the non-orthogonality of the three-axis induction coil, there is a deflection between the induced magnetic field and the theoretical magnetic field. A rotation matrix is ​​set so that the theoretical magnetic field can be obtained by combining the induced magnetic field and the rotation matrix. The deflection between the induced magnetic field and the theoretical magnetic field can be obtained by calculating the rotation matrix of the three-axis induction coil. The rotation matrix is ​​obtained by an optimization iterative algorithm.

[0009] S4. After obtaining the rotation matrix between the induced magnetic field and the theoretical magnetic field, the rotation matrix is ​​set as a constant and applied to the actual positioning process. A magnetic dipole model is directly established between the three-axis induction coil and the single-axis transmitting coil. After solving the polynomial and correcting the rotation matrix, the actual position and posture of the three-axis induction coil are obtained to achieve precise positioning calibration.

[0010] In some embodiments, in step S2, the three-axis induction coil is placed at different positions in space, and the corresponding induced electrical signals d1, d2, and d3 of the three-axis induction coil are recorded. At the same time, based on polynomial expansion, the error between the fitted induced magnetic field B′ (B′1, B′2, B′3) and the theoretical magnetic field B (B1, B2, B3) calculated by the magnetic dipole model is minimized.

[0011] In some embodiments, taking the induced electrical signal d1 of one of the three-axis induction coils as an example, the polynomial expansion calculation formula of the induced electrical signal and the fitting magnetic field is:

[0012]

[0013] Among them, B′1 is the fitting magnetic field of the induction coil 1, d1 is the electrical signal obtained by the induction coil 1, n is the order of the polynomial expansion, which depends on the actual accuracy requirements, a0, a1...a n are the polynomial coefficients;

[0014] After fitting, the induced magnetic field B′(B′1, B′2, B′3) is obtained.

[0015] In some embodiments, a0, a1...a n The polynomial coefficients are the optimal solution obtained through iteration of the optimization algorithm, and the optimal solution a0, a1…a n , achieving the minimum error between the induced magnetic field B′(B′1, B′2, B′3) and the theoretical magnetic field B(B1, B2, B3) calculated by the magnetic dipole model.

[0016] In some embodiments, there are two ways to obtain the theoretical magnetic field B. One is to calculate it through a magnetic dipole model, and the other is to obtain the theoretical magnetic field distribution of the corresponding spatial point through simulation software.

[0017] In some embodiments, the transmitting coil and the induction coil are modeled using ANSYS Maxwell, Comsol, or Matlab simulation software to obtain the theoretical magnetic field strength B ( B1 , B2 , B3 ) at the induction coil.

[0018] In some embodiments, the coordinates of the three-axis induction coil are calculated, and the position of the three-axis induction coil in space is recorded as P l (x,y,z), then P l Magnetic field B at (x,y,z) l (B1,B2,B3):

[0019]

[0020] Among them, B T is a constant related to the magnet size and material, R l is the relative distance, H0 is specifically H0(m,n,p), where H0(m,n,p) is the magnetic field direction of the three-axis induction coil relative to the transmitting coil, that is, the posture of the three-axis induction coil.

[0021] In some embodiments, in step S3, the formula for solving the rotation matrix is:

[0022] RB′=B

[0023] R is the rotation matrix, B′ is the matrix composed of the fitted induced magnetic field, and B is the theoretical magnetic field obtained by the magnetic dipole model.

[0024] In some embodiments, the R rotation matrix is ​​iterated to obtain the optimal solution through an optimization algorithm.

[0025] By adopting the above technical solution, the beneficial effects of the present invention are:

[0026] The present invention performs a polynomial expansion on the electrically induced signal of the induction coil to fit it with the magnetic field calculated by the magnetic dipole. Simultaneously, an optimization algorithm is used to iteratively generate the optimal rotation matrix, which corrects the non-orthogonal induction coil and ultimately improves the accuracy of magnetic positioning. This calibration method is fast and accurate, and can solve the problem of large positioning errors of the magnetic dipole at the axis.

[0027] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure.

[0028] Undoubtedly, these and other objects of the present invention will become more apparent after the following detailed description of the preferred embodiment is described with reference to the various figures and drawings.

[0029] In order to make the above and other objects, features and advantages of the present invention more obvious and easy to understand, one or more preferred embodiments are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention but do not constitute a limitation of the present invention.

[0031] In the drawings, like components are given like reference numerals, and the drawings are schematic and not necessarily drawn to scale.

[0032] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only one or several embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on such drawings without paying any creative work.

[0033] Figure 1 Schematic diagram of the overall flow of the correction method in some embodiments of the present invention;

[0034] Figure 2 Schematic diagram of orthogonal coordinates in an electric dipole model in some embodiments of the present invention;

[0035] Figure 3 Schematic diagram of the induction coil structure in some embodiments of the present invention. DETAILED DESCRIPTION

[0036] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but are not intended to limit the present invention.

[0037] In addition, in the description of the present invention, it should be understood that the terms "center", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "axial", "radial", "circumferential", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0038] In the present invention, unless otherwise expressly specified or limited, terms such as "installed," "connected," "connect," and "fixed" should be interpreted broadly. For example, they may refer to fixed connections, removable connections, or integration; they may refer to direct connections or indirect connections through an intermediate medium; they may refer to internal communication between two components or interactions between two components. However, the term "direct connection" indicates that the two connected entities are not connected through a transitional structure, but are connected solely through a connecting structure to form a single entity. Those skilled in the art will understand the specific meanings of these terms in the present invention based on the specific circumstances.

[0039] In the present invention, unless otherwise clearly specified and limited, a first feature "above" or "below" a second feature may be that the first and second features are in direct contact, or the first and second features are in indirect contact through an intermediate medium. In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in an appropriate manner in any one or more embodiments or examples.

[0040] Reference Figure 1-3 , Figure 1 Schematic diagram of the overall flow of the correction method in some embodiments of the present invention; Figure 2 Schematic diagram of orthogonal coordinates in an electric dipole model in some embodiments of the present invention; Figure 3 Schematic diagram of the induction coil structure in some embodiments of the present invention.

[0041] According to some embodiments of the present invention, the present invention provides a magnetic dipole model calibration method based on polynomial expansion, comprising:

[0042] S1. Establish a magnetic dipole model between the three-axis induction coil and the single-axis transmitting coil in advance and calculate the theoretical magnetic field strength;

[0043] The specific structure of the three-axis induction coil is as follows Figure 3 As shown, there are two ways to obtain the theoretical magnetic field B. One is to calculate it through the magnetic dipole model, and the other is to obtain the theoretical magnetic field distribution of the corresponding space point through simulation software.

[0044] The method of calculating the theoretical magnetic field size through the magnetic dipole model is a common technique and will not be described in detail here. By modeling the transmitting coil and the induction coil using ANSYS Maxwell, Comsol or Matlab simulation software, the theoretical magnetic field strength B (B1, B2, B3) at the induction coil can also be obtained.

[0045] S2. Perform polynomial expansion on the induced electrical signals of the three-axis induction coil and fit the induced magnetic field. Minimize the error between the induced magnetic field intensity and the theoretical magnetic field intensity calculated by the magnetic dipole model, and obtain the optimal solution with the minimum error. The method for solving the minimum error is an optimization iterative algorithm similar to PSO or LM.

[0046] The three-axis induction coil is placed at different positions in space, and the corresponding induced electrical signals d1, d2, and d3 of the three-axis induction coil are recorded. At the same time, based on polynomial expansion, the error between the fitted induced magnetic field B′(B1′, B2′, B3′) and the theoretical magnetic field B(B1, B2, B3) calculated by the magnetic dipole model is minimized.

[0047] Taking the induced electrical signal d1 of one of the three-axis induction coils as an example, the polynomial expansion calculation formula of the induced electrical signal and the fitted magnetic field is:

[0048]

[0049] Among them, B1′ is the fitting magnetic field of the induction coil 1, d1 is the electrical signal obtained by the induction coil 1, n is the order of the polynomial expansion, which depends on the actual accuracy requirements, a0, a1...a n are the polynomial coefficients;

[0050] After fitting, the induced magnetic field B′(B′1, B′2, B′3) is obtained;

[0051] a0,a1...a n The polynomial coefficients are the optimal solution obtained through iteration of the optimization algorithm, and the optimal solution a0, a1…a n , achieving the minimum error between the induced magnetic field B′(B′1, B′2, B′3) and the theoretical magnetic field B(B1, B2, B3) calculated by the magnetic dipole model.

[0052] Find the coordinates of the three-axis induction coil, and record the position of the three-axis induction coil in space as P l (x,y,z), then P l Magnetic field B at (x,y,z) l (B1,B2,B3):

[0053]

[0054] Among them, BT is a constant related to the magnet size and material, R l is the relative distance, H0 is specifically H0(m,n,p), where H0(m,n,p) is the magnetic field direction of the three-axis induction coil relative to the transmitting coil, that is, the posture of the three-axis induction coil.

[0055] S3. Due to the non-orthogonality of the three-axis induction coil, there is a deflection between the induced magnetic field and the theoretical magnetic field. A rotation matrix is ​​set so that the theoretical magnetic field can be obtained by combining the induced magnetic field and the rotation matrix. The deflection between the induced magnetic field and the theoretical magnetic field can be obtained by calculating the rotation matrix of the three-axis induction coil. The rotation matrix is ​​obtained by an optimization iterative algorithm.

[0056] The formula for solving the rotation matrix is:

[0057] RB′=B

[0058] R is the rotation matrix, B′ is the matrix composed of the fitted induced magnetic field, and B is the theoretical magnetic field obtained by the magnetic dipole model;

[0059] The R rotation matrix is ​​the optimal solution obtained by iteration through an optimization algorithm similar to PSO or LM.

[0060] S4. After obtaining the rotation matrix between the induced magnetic field and the theoretical magnetic field, the rotation matrix is ​​set as a constant and applied to the actual positioning process. A magnetic dipole model is directly established between the three-axis induction coil and the single-axis transmitting coil. After solving the polynomial and correcting the rotation matrix, the actual position and posture of the three-axis induction coil are obtained to achieve precise positioning calibration.

[0061] Example

[0062] This embodiment provides a magnetic dipole model calibration method based on polynomial expansion, which specifically includes:

[0063] Place the three-axis induction coil at different positions in space and record the position coordinates P l (x, y, z), the magnetic field direction H0 of the triaxial induction coil relative to the uniaxial transmitting coil, and the electrical signals d1, d2, d3 of the induction coil.

[0064] By using ANSYS Maxwell simulation software, the dimensions and material characteristics of the transmitting coil are input to calculate the corresponding coordinates P l The theoretical magnetic field strength B(B x ,B y ,B z ).

[0065] The induced magnetic field B′ is expressed as follows using polynomial expansion:

[0066]

[0067]

[0068]

[0069] Through the PSO optimization iterative algorithm, the optimal solution a0, a1…a is obtained. n ,b0,b1…b n ,c0,c1…c n The parameters are such that the error between B′ and B is minimized. n is the order of the polynomial expansion, which depends on the actual accuracy requirements.

[0070] like Figure 3 As shown in the figure, since the three coils cannot be guaranteed to be in a completely orthogonal state during the manufacture of the three-axis induction coil, the non-orthogonality problem of the induction coil is corrected by setting the rotation matrix R. The corrected magnetic field is RB′. The optimal rotation matrix R is solved by the PSO optimization iterative algorithm, so that the error between RB′ and the theoretical magnetic field B is minimized.

[0071] Coordinate solution, through polynomial solution and rotation matrix correction, the three-axis induction coil can obtain the magnetic field strength at any position. There are 6 unknown variables P in solving the posture of the induction coil. l (x,y,z),H0(m,n,p), where A transmitting coil can be composed of three formulas:

[0072]

[0073]

[0074]

[0075] Therefore, the coordinates P of the corresponding induction coil in space can be solved by using two or more transmitting coils. l (x,y,z) and posture H0(m,n,p).

[0076] It should be understood that the embodiments disclosed herein are not limited to the specific processing steps or materials disclosed herein, but should extend to equivalent substitutions of such features understood by those skilled in the relevant art. It should also be understood that the terminology used herein is for the purpose of describing specific embodiments only and is not intended to be limiting.

[0077] The "embodiment" mentioned in the specification means that a particular feature or characteristic described in conjunction with the embodiment is included in at least one embodiment of the present invention. Therefore, the phrase or "embodiment" appearing in various places throughout the specification does not necessarily refer to the same embodiment.

[0078] Furthermore, the described features or characteristics may be combined in any other suitable manner into one or more embodiments. In the above description, some specific details, such as thickness, quantity, etc., are provided to provide a comprehensive understanding of the embodiments of the present invention. However, those skilled in the relevant art will appreciate that the present invention may be implemented without one or more of the above specific details or may be implemented using other methods, components, materials, etc.

Claims

1. A magnetic dipole model calibration method based on polynomial expansion, characterized in that: include S1. Establish a magnetic dipole model between the three-axis induction coil and the single-axis transmitting coil in advance and calculate the theoretical magnetic field strength; S2. Perform polynomial expansion on the induced electrical signal of the triaxial induction coil and fit the induced magnetic field, so as to minimize the error between the induced magnetic field intensity and the theoretical magnetic field intensity calculated by the magnetic dipole model, and obtain the optimal solution with the minimum error. The method for solving the minimum error is an optimization iterative algorithm; S3. Due to the non-orthogonality of the three-axis induction coil, there is a deflection between the induced magnetic field and the theoretical magnetic field. A rotation matrix is ​​set so that the theoretical magnetic field can be obtained by combining the induced magnetic field and the rotation matrix. The deflection between the induced magnetic field and the theoretical magnetic field can be obtained by calculating the rotation matrix of the three-axis induction coil. The rotation matrix is ​​obtained by an optimization iterative algorithm. S4. After obtaining the rotation matrix between the induced magnetic field and the theoretical magnetic field, the rotation matrix is ​​set as a constant and applied to the actual positioning process. A magnetic dipole model is directly established between the three-axis induction coil and the single-axis transmitting coil. After solving the polynomial and correcting the rotation matrix, the actual position and posture of the three-axis induction coil are obtained to achieve precise positioning calibration.

2. The magnetic dipole model calibration method based on polynomial expansion according to claim 1, characterized in that: In step S2, the three-axis induction coil is placed at different positions in space, and the corresponding induced electrical signals d1, d2, and d3 of the three-axis induction coil are recorded. At the same time, based on the polynomial expansion, the error between the fitted induced magnetic field B′(B1′, B2′, B3′) and the theoretical magnetic field B(B1, B2, B3) calculated by the magnetic dipole model is minimized.

3. The magnetic dipole model calibration method based on polynomial expansion according to claim 2, characterized in that: Taking the induced electrical signal d1 of one of the three-axis induction coils as an example, the polynomial expansion calculation formula of the induced electrical signal and the fitted magnetic field is: Among them, B1′ is the fitting magnetic field of the induction coil 1, d1 is the electrical signal obtained by the induction coil 1, n is the order of the polynomial expansion, which depends on the actual accuracy requirements, a0, a1...a n are the polynomial coefficients; After fitting, the induced magnetic field B′(B1′, B2′, B3′) is obtained.

4. The magnetic dipole model calibration method based on polynomial expansion according to claim 3, characterized in that: a0,a1...a n The polynomial coefficients are the optimal solutions obtained through iteration of the optimization algorithm. n , achieving the minimum error between the induced magnetic field B′(B1′, B2′, B3′) and the theoretical magnetic field B(B1, B2, B3) calculated by the magnetic dipole model.

5. The magnetic dipole model calibration method based on polynomial expansion according to claim 3, characterized in that: There are two ways to obtain the theoretical magnetic field B. One is to calculate it through the magnetic dipole model, and the other is to obtain the theoretical magnetic field distribution of the corresponding space point through simulation software.

6. The magnetic dipole model calibration method based on polynomial expansion according to claim 5, characterized in that: The transmitting coil and the induction coil are modeled by ANSYS Maxwell, Comsol or Matlab simulation software to obtain the theoretical magnetic field B (B1, B2, B3) at the induction coil.

7. The magnetic dipole model calibration method based on polynomial expansion according to claim 5, characterized in that: Find the coordinates of the three-axis induction coil, and record the position of the three-axis induction coil in space as P l (x,y,z), then P l Magnetic field B at (x,y,z) l (B1,B2,B3): Among them, B T is a constant related to the magnet size and material, R l is the relative distance, H0 is specifically H0(m,n,p), where H0(m,n,p) is the magnetic field direction of the three-axis induction coil relative to the transmitting coil, that is, the posture of the three-axis induction coil.

8. The magnetic dipole model calibration method based on polynomial expansion according to claim 1, characterized in that: In step S3, the formula for solving the rotation matrix is: RB′=B R is the rotation matrix, B′ is the fitted induced magnetic field, and B is the theoretical magnetic field obtained by the magnetic dipole model.

9. The magnetic dipole model calibration method based on polynomial expansion according to claim 8, characterized in that: The R rotation matrix is ​​the optimal solution obtained through iteration of the optimization algorithm.

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