A method of calibrating a magnetic field generator of a medical electromagnetic positioning system

Abstract

The application discloses a kind of magnetic field generator calibration methods of medical electromagnetic positioning system, comprising: sensitivity detection of single-axis receiving coil;Acquisition is used for calibration Actual induction electromotive force dataset, by building standard coordinate system framework, the induction electromotive force of single-axis receiving coil under known pose is collected;By constructing magnetic field model, obtain the theoretical induction electromotive force dataset for calibration;By two dataset construction iterative optimization objective function, the placement pose and equivalent radius of transmitting coil are optimized using Levenberg-Marquardt optimization algorithm, calibrate inherent error caused by process in magnetic field generator.The application realizes the individual calibration of the placement pose and equivalent radius of each transmitting coil in magnetic field generator by obtaining the induction capacity of single-axis receiving coil in advance.

Description

Technical Field

[0001] The present invention relates to the technical field of medical electromagnetic positioning systems, and in particular to a magnetic field generator calibration method for medical electromagnetic positioning systems. Background Art

[0002] A medical electromagnetic positioning system typically consists of a magnetic field generator, a system control unit, a sensor interface unit, several sensors, and a computer. A five-degree-of-freedom sensor is a single-axis receiving coil. The position of the single-axis receiving coil is determined by the difference between the actual induced electromotive force (EMF) and the theoretical induced electromotive force derived from the magnetic field model. This difference serves as the objective function to be optimized. Actual positioning error is affected by multiple factors, including the accuracy of the magnetic dipole model, environmental metal interference, and manufacturing process precision. Current calibration methods for medical electromagnetic positioning systems are mostly based on the position and pose of the receiving sensor. Common methods include global interpolation, such as high-order polynomial fitting, and local interpolation, such as trilinear interpolation and spline interpolation. However, attitude-based calibration methods provide a comprehensive calibration of the entire system, accounting for all error factors, and can be susceptible to miscalibration. The magnetic field model is based on the position and pose of the magnetic field generator coil and the inner and outer diameters of the coil itself. During manufacturing, it is difficult to ensure consistent dimensions for each excitation coil. Furthermore, the fixtures used to secure the coils are also subject to manufacturing errors. Therefore, it is necessary to perform a separate calibration of the magnetic field generator before the final pose calibration, and to calibrate the coil's equivalent radius and spatial placement. Although there are related methods for calibrating magnetic field generators, existing methods do not separate the inductive capability of the single-axis receiving coil from other calibration parameters. This results in the calibration results being incompatible when replacing single-axis receiving coils with different inductive capabilities. In addition, existing magnetic field generator calibration methods do not account for the processing errors of the coil itself. Therefore, improvements to these methods are expected to improve the overall tracking accuracy of the system, and the calibration results of the transmitting coil can also be used to position the six-degree-of-freedom receiving coil. Summary of the Invention

[0003] The purpose of the present invention is to overcome the shortcomings of the existing technology and provide a magnetic field generator calibration method for a medical electromagnetic positioning system. By obtaining the induction capability of a single-axis receiving coil in advance, the placement position and equivalent radius of each transmitting coil in the magnetic field generator can be individually calibrated.

[0004] To achieve the above objectives, the present invention provides a technical solution: a method for calibrating a magnetic field generator of a medical electromagnetic positioning system, wherein the electromagnetic positioning system includes a magnetic field generator, a system control unit, a sensor interface unit, multiple sensors, and a computer, wherein one of the five-degree-of-freedom sensors is a single-axis receiving coil. The calibration method only needs to be applied to one single-axis receiving coil and includes the following steps:

[0005] S1. Collect the induced electromotive force of multiple sets of single-axis receiving coils under uniform magnetic fields of different intensities, and fit the relationship between the induced electromotive force and the uniform magnetic field strength, which is called the sensitivity of the single-axis receiving coil. By constructing a magnetic field model, analyze the size of the theoretical magnetic field strength of the single-axis receiving coil under the position of n transmitting coils in different positions in the magnetic field generator, and convert it into theoretical induced electromotive force by combining the sensitivity. Analyze the theoretical induced electromotive force of the single-axis receiving coil under different specified positions to form a theoretical induced electromotive force data set for calibration.

[0006] S2. Time-sharingly excite n transmitting coils in different positions in the magnetic field generator, and collect n induced electromotive forces of the corresponding transmitting coils in different specified positions of the single-axis receiving coil as actual induced electromotive forces, to form an actual induced electromotive force data set for calibration;

[0007] S3. The error vector and objective function for iterative optimization are constructed based on the difference between the corresponding theoretical induced electromotive force and the actual induced electromotive force in the theoretical induced electromotive force data set and the actual induced electromotive force data set. The Levenberg-Marquardt optimization algorithm is used to perform iterative optimization with the posture and equivalent radius of the transmitting coil as the target optimization parameters to obtain the optimal posture and equivalent radius of all transmitting coils, and the offset of the placement posture and equivalent radius is compensated to achieve calibration of the magnetic field generator.

[0008] Furthermore, in step S1, a tightly wound multi-layer multi-turn coil is processed and the magnetic field strength B at the center of the multi-layer multi-turn coil is analyzed. c With the excitation current I c Relationship: B c =cI c , c is a parameter describing the linear relationship between the excitation current and the magnetic field strength, wherein the deviation between the simulation and the actual measurement results at the center of the multi-layer multi-turn coil is compared to verify the precision of the processing;

[0009] Taking advantage of the characteristic that tightly wound multi-layer multi-turn coils generate uniform magnetic fields on the central axis and its vicinity, a single-axis receiving coil is fixed at the center of the multi-layer multi-turn coils to collect the induced electromotive force of the single-axis receiving coil under different field strengths, forming a magnetic field composed of the actual field strength B. i and the induced electromotive force E i A dataset composed of i∈[1,Nc ] represents the i-th group of data, N c represents the total number of groups of data;

[0010] When the single-axis receiving coil is fixed at the center of a tightly wound multi-layer multi-turn coil and the magnetic moment directions of the two are consistent, the magnetic field strength B c The relationship between the corresponding induced electromotive force E is: E=μωSN r B c , where μ is the magnetic induction coefficient, ω is the angular frequency of the excitation current, S and N r are the cross-sectional area and number of turns of the single-axis receiving coil respectively. Except for ω, the other three variables are difficult to measure accurately. Therefore, K = μωSN is used. r It represents the inductive capability of the single-axis receiving coil, also known as sensitivity. K is fitted using the above-obtained data set.

[0011] Furthermore, in step S1, a magnetic field model is constructed based on the magnetic dipole model. In the Cartesian coordinate system of the electromagnetic positioning system, the placement coordinates of the jth transmitting coil are w O j =(a j ,b j ,c j ), where a j 、b j 、c j They are w O j Coordinate values ​​on the x, y, and z axes, magnetic moment direction vector w H j =(m j ,n j ,p j ), where m j 、n j 、p j They are w H j The components in the x, y, and z axes, and Construct the spherical coordinate system of the jth transmitting coil, with the origin set to w O j , using the coordinates in the spherical coordinate system The Cartesian coordinate system representing the electromagnetic positioning system w H j , where ρ j =1 means w H j The radial distance, θ j and denote the polar angle and azimuth angle respectively, then and Therefore, the basic parameters of the calibration of a single transmitting coil in a magnetic field generator include

[0012] In the Cartesian coordinate system of the electromagnetic positioning system, based on the magnetic dipole model, the position in space is w P=( w x, w y, w z), the magnetic field simulation is performed on a single-axis receiving coil with an attitude Euler angle of (α, β, γ), where w x、 w y、 w z are w The coordinate values ​​of P on the x, y, and z axes, α, β, and γ are the pitch angle, yaw angle, and roll angle in the Euler angle respectively; the position of the electromagnetic positioning system in the Cartesian coordinate system w P's magnetic field vector w The calculation formula for B is as follows:

[0013]

[0014] Where μ0 = 4π × 10 -7 is the magnetic permeability in vacuum, N is the number of turns of the transmitting coil, I g is the amplitude of the transmitting coil excitation current, r is the equivalent radius of the magnetic dipole model, and w r= w P- w O j Represents the vector from the center of the transmitting coil to the single-axis receiving coil; Substituting the corresponding parameters, the position of the electromagnetic positioning system in the Cartesian coordinate system can be obtained w The magnetic field magnitude wB of P in the x, y, and z axes x 、wB y 、wB z The calculation method is:

[0015]

[0016] In the formula, the intermediate variable The rotation matrix that converts the Euler angle of the single-axis receiving coil into the Cartesian coordinate system of the electromagnetic positioning system and the Cartesian coordinate system of the single-axis receiving coil The calculation of is as follows:

[0017]

[0018] Thus, the magnetic fields of the three axes x, y, and z in the Cartesian coordinate system of the single-axis receiving coil can be obtained. s B x 、 s B y 、 s Bz The calculation formula is as follows:

[0019]

[0020] Taking the magnetic moment direction of the uniaxial receiving coil as the z-axis direction of the coordinate system, only s B z Can be converted into the theoretical induced electromotive force ε of the single-axis receiving coil j , of size ε j =K s B z .

[0021] Furthermore, in step S2, a standard coordinate system is constructed and a single-axis receiving coil holder is designed to collect the electromotive force amplitude of the single-axis receiving coil when n different transmitting coils are working, which is called the actual induced electromotive force. In the case of time-sharing excitation of the transmitting coil, the n electromotive force amplitude of the single-axis receiving coil in the mth posture is (ε 1m ',ε 2m ',ε 3m ',...,ε jm ',...,ε nm '), where ε nm ' represents the nth electromotive force amplitude at the mth posture, and a total of M groups are collected.

[0022] Furthermore, in step S3, when the jth transmitting coil is working, the parameters to be optimized are where r j is the equivalent radius of the transmitting coil as a magnetic dipole model. The theoretical induced electromotive force of the single-axis receiving coil in the mth position is expressed as ε jm (p j ), and the corresponding actual induced electromotive force is ε jm ', select M positions in the tracking domain, then the error vector e between the theoretical induced electromotive force and the actual induced electromotive force j (p j )for:

[0023] e j (p j )=ε j (p j )-ε j '

[0024] Where, ε j (p j ) and ε j ' are respectively composed of M ε jm (p j ) and ε jm 'The column vector composed of the objective function to be optimized F cj (pj ) is calculated as follows:

[0025]

[0026] The Levenberg-Marquardt optimization algorithm is used to optimize the parameter p. j For optimization, the fixed theoretical position of the transmitting coil and the theoretical inner diameter of the machining are selected as the initial values ​​of the iteration, and p k Represents the parameter p under the kth iteration j , the calculation steps of each iteration are as follows:

[0027] a. Let the error vector e under the kth iteration j (p k )=(e j1 ,e j2 ,...,e jM ),e jM It is e j (p k ) in the Mth vector element, calculate the Jacobian matrix J of the error vector k and the Heiser matrix H k as follows:

[0028]

[0029] Where, J k T is the matrix J k The transpose of

[0030] b. The Levenberg-Marquardt optimization algorithm combines the Gauss-Newton method and the steepest descent method, and uses the damping coefficient to dynamically adjust the impact of the steepest descent method on the iterative step size during the iteration process. The step size of each iteration is d k for:

[0031] d k =(J k T J k +λ k I)- 1 (-J k T )e j (p k )

[0032] Where I is the sixth-order unit matrix, λ k is the damping coefficient;

[0033] c. The determination of the damping coefficient includes the determination of the initial value and the dynamic change during the iteration process. According to the initial Heiser matrix, the initial damping coefficient can be calculated as:

[0034] λk =τ*max(diag(Η k ))*||e j (p k )|| 1.5

[0035] Where, τ is a pre-set parameter, diag(Η k ) indicates H k All elements of the diagonal; during the iteration, for each step of the prediction step, by calculating the scaling factor The damping coefficient is modified dynamically according to the size of cj (p k ) and F cj (d k +p k ) are the optimization parameters p k and d k +p k The objective function value when is the matrix d k The transpose of r k Reflects the accuracy of the prediction step size. When r k When r<0, the direction of the predicted step length is opposite to the direction of fitness value reduction, the damping coefficient should be increased quickly and the current prediction should be abandoned. k ≥0, the current forecast should be accepted, and the damping coefficient should be adjusted with r k Dynamically adjust the changes in , and improve the consistency between the iterative step direction and the actual fitness value reduction direction;

[0036] d. When the parameters in the iteration process meet any of the following conditions, the iteration ends and the final result is obtained:

[0037] ① Where e1 is the first-order derivative termination condition;

[0038] ②||d k ||<e2(||p k ||+e2), where e2 is the termination condition of the change step distance;

[0039] ③The number of iterations iter>=e3, where e3 is the maximum number of iterations.

[0040] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0041] 1. The present invention designs a method for measuring the sensitivity of a single-axis receiving coil, which separates the inductive capability of the single-axis receiving coil from other parameters to be calibrated. This helps to achieve separate calibration of the magnetic field generator and is applicable to the tracking of multiple single-axis receiving coils with different inductive capabilities.

[0042] 2. The present invention designs a method that can simultaneously calibrate the placement position of the transmitting coil and the equivalent radius of the transmitting coil when it is approximated as a magnetic dipole model, which is used to calibrate the inherent errors caused by process processing.

[0043] 3. The present invention uses the Levenberg-Marquardt optimization algorithm to calibrate the magnetic field generator, which can achieve fast and accurate calibration given appropriate initial values. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a flow chart of the method of the present invention.

[0045] Figure 2 This is a simulation diagram of the coil magnetic field used for sensitivity testing.

[0046] Figure 3 This is a schematic diagram of the magnetic field model based on the magnetic dipole model.

[0047] Figure 4 This is a diagram of the fixture and standard coordinate system framework for obtaining the theoretical position of the single-axis receiving coil during calibration.

[0048] Figure 5 This is a detailed schematic diagram of a single-axis receiving coil and its holder.

[0049] Figure 6 This is a working diagram of the transmitting coil and the single-axis receiving coil. DETAILED DESCRIPTION

[0050] The present invention will be described in further detail below with reference to the embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0051] like Figures 1 to 6 As shown, this embodiment provides a method for calibrating a magnetic field generator for a medical electromagnetic positioning system. The electromagnetic positioning system includes a magnetic field generator, a system control unit, a sensor interface unit, multiple sensors, and a computer. One of the five-degree-of-freedom sensors is a single-axis receiving coil. The calibration method only needs to be applied to a single-axis receiving coil. Based on the sensitivity of the single-axis receiving coil, the method uses a magnetic dipole model and the Levenberg-Marquardt optimization algorithm to calibrate a single transmitting coil in the magnetic field generator. The specific details are as follows:

[0052] S1. Collect the induced electromotive force of multiple sets of single-axis receiving coils under uniform magnetic fields of different intensities, and fit the relationship between the induced electromotive force and the uniform magnetic field strength, which is called the sensitivity of the single-axis receiving coil. By constructing a magnetic field model, analyze the theoretical magnetic field strength of the single-axis receiving coil under the position of n transmitting coils in different positions in the magnetic field generator. Combined with the sensitivity, it is converted into a theoretical induced electromotive force. The theoretical induced electromotive force of the single-axis receiving coil under different specified positions is analyzed to form a theoretical induced electromotive force data set for calibration. The specific situation is as follows:

[0053] Processing a tightly wound multi-layer multi-turn coil, such as Figure 2 As shown, the magnetic induction lines at the center of the coil and its vicinity have similar colors and the same direction, which can be approximated as a uniform magnetic field. The field strength at the center can be accurately obtained, and the magnetic field strength B at the center of the multi-layer multi-turn coil can be calculated. c With the excitation current I c Relationship: B c =cI c , c is a parameter describing the linear relationship between the excitation current and the magnetic field strength, wherein the deviation between the simulation and the actual measurement results at the center of the multi-layer multi-turn coil is compared to verify the precision of the processing;

[0054] When the single-axis receiving coil is fixed at the center of a tightly wound multi-layer multi-turn coil and the magnetic moment directions of the two are consistent, the magnetic field strength B c The relationship between the corresponding induced electromotive force E is: E=μωSN r B c , where μ is the magnetic induction coefficient, ω is the angular frequency of the excitation current, S and N r are the cross-sectional area and number of turns of the single-axis receiving coil respectively. Except for ω, the other three variables are difficult to measure accurately. Therefore, K = μωSN is used. r It represents the inductive capability of the single-axis receiving coil, also known as sensitivity. K is fitted using the above-obtained data set.

[0055] Fix the single-axis receiving coil at the center of the processed coil for sensitivity detection, excite it with currents of different sizes, and collect the actual magnetic field B generated by different excitation currents. i The induced electromotive force E of the single-axis receiving coil under i Size, where i∈[1,N c ] represents the i-th group of data, and N represents the total number of data groups. Perform sensitivity linear fitting on the collected data set: E i =KB i +b, the corresponding sensitivity K and b are calculated as follows:

[0056]

[0057] Where b is the intercept of the fitted line.

[0058] After obtaining the sensitivity of the single-axis receiving coil, the magnetic field model needs to be constructed. The magnetic field model is constructed based on the magnetic dipole model. Figure 3 As shown, in the Cartesian coordinate system of the electromagnetic positioning system, the placement coordinates of the jth transmitting coil are w O j =(a j ,b j ,c j ), where a j 、b j 、c j They are w O j Coordinate values ​​on the x, y, and z axes, magnetic moment direction vector w H j =(m j ,n j ,p j ), where m j 、n j 、p j They are w H j The components in the x, y, and z axes, and Construct the spherical coordinate system of the jth transmitting coil, with the origin set to w O j , using the coordinates in the spherical coordinate system Represents the Cartesian coordinate system of the electromagnetic positioning system w H j , where ρ j =1 means w H j The radial distance, θ j and denote the polar angle and azimuth angle respectively, then and Therefore, the basic parameters of the calibration of a single transmitting coil in a magnetic field generator include

[0059] In the Cartesian coordinate system of the electromagnetic positioning system, based on the magnetic dipole model, the position in space is w P=( w x, w y, w z), the magnetic field simulation is performed on a single-axis receiving coil with an attitude Euler angle of (α, β, γ), where w x、 w y、 w z are wThe coordinate values ​​of P on the x, y, and z axes, α, β, and γ are the pitch angle, yaw angle, and roll angle in the Euler angle respectively. w Magnetic field vector at position P w The calculation formula for B is as follows:

[0060]

[0061] Where μ0 = 4π × 10 -7 is the magnetic permeability in vacuum, N is the number of turns of the transmitting coil, I g is the amplitude of the coil excitation current, r is the equivalent radius of the magnetic dipole model, and w r= w P- w O j Represents the vector from the center of the transmitting coil to the single-axis receiving coil; Substituting the corresponding parameters, the position of the electromagnetic positioning system in the Cartesian coordinate system can be obtained w The magnitude of the magnetic field in the x, y, and z axes of P w B x 、 w B y 、 w B z The calculation method is:

[0062]

[0063] In the formula, the intermediate variable The rotation matrix that converts the Euler angle of the single-axis receiving coil into the Cartesian coordinate system of the electromagnetic positioning system and the Cartesian coordinate system of the single-axis receiving coil The calculation of is as follows:

[0064]

[0065] Thus, the magnetic fields of the three axes x, y, and z in the Cartesian coordinate system of the single-axis receiving coil can be obtained. s B x 、 s B y 、 s B z The calculation formula is as follows:

[0066]

[0067] Taking the magnetic moment direction of the uniaxial receiving coil as the z-axis direction of the coordinate system, only s B z Can be converted into the theoretical induced electromotive force ε of the single-axis receiving coil j , of size ε j =K s B z .

[0068] S2. By time-sharingly exciting n transmitting coils in different positions in the magnetic field generator, the n induced electromotive forces of the corresponding transmitting coils at different specified positions of the single-axis receiving coil are collected as actual induced electromotive forces, forming an actual induced electromotive force data set for calibration. The specific situation is as follows:

[0069] like Figure 4 As shown in the figure, a standard coordinate system frame is built and a single-axis receiving coil fixture is designed to collect the electromotive force amplitude of the single-axis receiving coil when different transmitting coils are working, which is called the actual induced electromotive force. The fixture is fixed in different holes of the standard coordinate system frame to collect the induced electromotive force data of multiple groups of single-axis receiving coils at different positions. When the single-axis receiving coil is excited in time-sharing mode, the n electromotive force amplitude of the single-axis receiving coil at the mth position is (ε 1m ',ε 2m ',ε 3m ',...,ε jm ',...,ε nm '), where ε nm ' represents the nth electromotive force amplitude at the mth posture, that is, the actual induced electromotive force, and a total of M groups are collected. Figure 5 The direction of the hole machined in the fixture determines the position of the coil in the standard coordinate system. Figure 6 The figure shows the working diagram of 8 transmitting coils and one single-axis receiving coil.

[0070] S3. The error vector and objective function for iterative optimization are constructed based on the difference between the theoretical induced electromotive force and the actual induced electromotive force in the theoretical induced electromotive force dataset and the actual induced electromotive force dataset. The Levenberg-Marquardt optimization algorithm is used to iteratively optimize the position and equivalent radius of the transmitting coil as the target optimization parameters to obtain the optimal position and equivalent radius of all transmitting coils. The offset of the position and equivalent radius is compensated to achieve the calibration of the magnetic field generator. The specific situation is as follows:

[0071] When the jth transmitting coil is working, let the parameters to be optimized where r j is the equivalent radius of the transmitting coil as a magnetic dipole model. The theoretical induced electromotive force of the single-axis receiving coil in the mth position is expressed as ε jm (p j ), and the corresponding actual induced electromotive force is ε jm ', select M poses in the tracking domain, then the error vector ej(pj) between the theoretical induced electromotive force and the actual induced electromotive force is:

[0072] e j (p j )=εj (p j )-ε j '

[0073] Where, ε j (p j ) and ε j ' are respectively composed of M ε jm (p j ) and ε jm 'The column vector composed of the objective function to be optimized F cj (p j ) is calculated as follows:

[0074]

[0075] The Levenberg-Marquardt optimization algorithm is used to optimize the parameter p. j For optimization, the fixed theoretical position of the transmitting coil and the theoretical inner diameter of the machining are selected as the initial values ​​of the iteration, and p k Represents the parameter p under the kth iteration j , the calculation steps of each iteration are as follows:

[0076] a. Let the error vector e under the kth iteration j (p k )=(e j1 ,e j2 ,...,e jM ),e jM It is e j (p k ) in the Mth vector element, calculate the Jacobian matrix J of the error vector k and the Heiser matrix H k as follows:

[0077]

[0078] H k =J k T J k

[0079] Where, J k T is the matrix J k The transpose of

[0080] b. The Levenberg-Marquardt optimization algorithm combines the Gauss-Newton method and the steepest descent method, and uses the damping coefficient to dynamically adjust the impact of the steepest descent method on the iterative step size during the iteration process. The step size of each iteration is d k for:

[0081] d k =(J kT J k +λ k I) -1 (-J k T )e j (p k )

[0082] Where I is the sixth-order unit matrix, λ k is the damping coefficient;

[0083] c. The determination of the damping coefficient includes the determination of the initial value and the dynamic change during the iteration process. According to the initial Heiser matrix, the initial damping coefficient can be calculated as:

[0084] λ k =τ*max(diag(Η k ))*||e j (p k )|| 1.5

[0085] Where, τ is a pre-set parameter, diag(Η k ) indicates H k All elements of the diagonal; during the iteration, for each step of the prediction step, by calculating the scaling factor The damping coefficient is modified dynamically according to the size of cj (p k ) and F cj (d k +p k ) are the optimization parameters p k and d k +p k The objective function value when is the matrix d k The transpose of r k Reflects the accuracy of the prediction step size. When r k When r<0, the direction of the predicted step length is opposite to the direction of fitness value reduction, the damping coefficient should be increased quickly and the current prediction should be abandoned. k ≥0, the current forecast should be accepted, and the damping coefficient should be adjusted with r k Dynamically adjust the changes in , and improve the consistency between the iterative step direction and the actual fitness value reduction direction;

[0086] d. When the parameters in the iteration process meet any of the following conditions, the iteration ends and the final result is obtained:

[0087] ① Where e1 is the first-order derivative termination condition;

[0088] ②||dk || <e2(||p k ||+e2), where e2 is the termination condition of the change step distance;

[0089] ③The number of iterations iter>=e3, where e3 is the maximum number of iterations.

[0090] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be considered as equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A method for calibrating a magnetic field generator of a medical electromagnetic positioning system, wherein the electromagnetic positioning system comprises a magnetic field generator, a system control unit, a sensor interface unit, a plurality of sensors, and a computer, wherein one of the five-degree-of-freedom sensors is a single-axis receiving coil; the calibration method need only be applied to one single-axis receiving coil, and is characterized in that: The following steps are involved: S1. Collect the induced electromotive force of multiple sets of single-axis receiving coils under uniform magnetic fields of different intensities, and fit the relationship between the induced electromotive force and the uniform magnetic field strength, which is called the sensitivity of the single-axis receiving coil. By constructing a magnetic field model, analyze the size of the theoretical magnetic field strength of the single-axis receiving coil under the position of n transmitting coils in different positions in the magnetic field generator, and convert it into theoretical induced electromotive force by combining the sensitivity. Analyze the theoretical induced electromotive force of the single-axis receiving coil under different specified positions to form a theoretical induced electromotive force data set for calibration. The magnetic field model is constructed based on the magnetic dipole model. In the Cartesian coordinate system of the electromagnetic positioning system, the placement coordinates of the jth transmitting coil are w O j =(a j ,b j ,c j ), where a j 、b j 、c j They are w O j Coordinate values ​​on the x, y, and z axes, magnetic moment direction vector w H j =(m j ,n j ,p j ), where m j 、n j 、p j They are w H j The components in the x, y, and z axes, and Construct the spherical coordinate system of the jth transmitting coil, with the origin set to w O j , using the coordinates in the spherical coordinate system The Cartesian coordinate system representing the electromagnetic positioning system w H j , where ρ j =1 means w H j The radial distance, θ j and denote the polar angle and azimuth angle respectively, then and Therefore, the basic parameters of the calibration of a single transmitting coil in a magnetic field generator include In the Cartesian coordinate system of the electromagnetic positioning system, based on the magnetic dipole model, the position in space is w P=( w x, w y, w z), the magnetic field simulation is performed on a single-axis receiving coil with an attitude Euler angle of (α, β, γ), where w x、 w y、 w z are w The coordinate values ​​of P on the x, y, and z axes, α, β, and γ are the pitch angle, yaw angle, and roll angle in the Euler angle respectively; the position of the electromagnetic positioning system in the Cartesian coordinate system w P's magnetic field vector w The calculation formula for B is as follows: Where μ0 = 4π × 10 -7 is the magnetic permeability in vacuum, N is the number of turns of the transmitting coil, I g is the amplitude of the transmitting coil excitation current, r is the equivalent radius of the magnetic dipole model, and w r= w P- w O j Represents the vector from the center of the transmitting coil to the single-axis receiving coil; Substituting the corresponding parameters, the position of the electromagnetic positioning system in the Cartesian coordinate system can be obtained w The magnitude of the magnetic field in the x, y, and z axes of P w B x 、 w B y 、 w B z The calculation method is: In the formula, the intermediate variable The rotation matrix that converts the Euler angle of the single-axis receiving coil into the Cartesian coordinate system of the electromagnetic positioning system and the Cartesian coordinate system of the single-axis receiving coil The calculation of is as follows: Thus, the magnetic fields of the three axes x, y, and z in the Cartesian coordinate system of the single-axis receiving coil can be obtained. s B x 、 s B y 、 s B z The calculation formula is as follows: Taking the magnetic moment direction of the uniaxial receiving coil as the z-axis direction of the coordinate system, only s B z Can be converted into the theoretical induced electromotive force ε of the single-axis receiving coil j , of size ε j =K s B z ; S2. Time-sharingly excite n transmitting coils in different positions in the magnetic field generator, and collect n induced electromotive forces of the corresponding transmitting coils in different specified positions of the single-axis receiving coil as actual induced electromotive forces, to form an actual induced electromotive force data set for calibration; S3. The error vector and objective function for iterative optimization are constructed based on the difference between the corresponding theoretical induced electromotive force and the actual induced electromotive force in the theoretical induced electromotive force data set and the actual induced electromotive force data set. The Levenberg-Marquardt optimization algorithm is used to perform iterative optimization with the posture and equivalent radius of the transmitting coil as the target optimization parameters to obtain the optimal posture and equivalent radius of all transmitting coils, and the offset of the placement posture and equivalent radius is compensated to achieve calibration of the magnetic field generator.

2. The method for calibrating a magnetic field generator of a medical electromagnetic positioning system according to claim 1, characterized in that: In step S1, a tightly wound multi-layer multi-turn coil is processed and the magnetic field strength B at the center of the multi-layer multi-turn coil is analyzed. c With the excitation current I c Relationship: B c =cI c , c is a parameter describing the linear relationship between the excitation current and the magnetic field strength, wherein the deviation between the simulation and the actual measurement results at the center of the multi-layer multi-turn coil is compared to verify the precision of the processing; Taking advantage of the characteristic that tightly wound multi-layer multi-turn coils generate uniform magnetic fields on the central axis and its vicinity, a single-axis receiving coil is fixed at the center of the multi-layer multi-turn coils to collect the induced electromotive force of the single-axis receiving coil under different field strengths, forming a magnetic field composed of the actual field strength B. i and the induced electromotive force E i A dataset composed of i∈[1,N c ] represents the i-th group of data, N c represents the total number of groups of data; When the single-axis receiving coil is fixed at the center of a tightly wound multi-layer multi-turn coil and the magnetic moment directions of the two are consistent, the magnetic field strength B c The relationship between the corresponding induced electromotive force E is: E=μωSN r B c , where μ is the magnetic induction coefficient, ω is the angular frequency of the excitation current, S and N r are the cross-sectional area and number of turns of the single-axis receiving coil respectively. Except for ω, the other three variables are difficult to measure accurately. Therefore, K = μωSN is used. r It represents the inductive capability of the single-axis receiving coil, also known as sensitivity. The above data set is used to fit K.

3. The method for calibrating a magnetic field generator of a medical electromagnetic positioning system according to claim 2, characterized in that: In step S2, a standard coordinate system is constructed and a single-axis receiving coil holder is designed to collect the electromotive force amplitude of the single-axis receiving coil when n different transmitting coils are working, which is called the actual induced electromotive force. In the case of time-sharing excitation of the transmitting coil, the n electromotive force amplitude of the single-axis receiving coil in the mth position is (ε 1m ′,ε 2m ′,ε 3m ′,...,ε jm ′,...,ε nm ′), where ε nm ′ represents the nth electromotive force amplitude at the mth posture, and a total of M groups are collected.

4. The method for calibrating a magnetic field generator of a medical electromagnetic positioning system according to claim 3, characterized in that: In step S3, when the jth transmitting coil is working, let the parameters to be optimized where r j is the equivalent radius of the transmitting coil as a magnetic dipole model. The theoretical induced electromotive force of the single-axis receiving coil in the mth position is expressed as ε jm (p j ), and the corresponding actual induced electromotive force is ε jm ′, select M poses in the tracking domain, then the error vector e between the theoretical induced electromotive force and the actual induced electromotive force j (p j )for: e j (p j )=e j (p j )-e j ′ Where, ε j (p j ) and ε j ′ are respectively composed of M ε jm (p j ) and ε jm ′, the objective function to be optimized F cj (p j ) is calculated as follows: The Levenberg-Marquardt optimization algorithm is used to optimize the parameter p. j For optimization, the fixed theoretical position of the transmitting coil and the theoretical inner diameter of the machining are selected as the initial values ​​of the iteration, and p k Represents the parameter p under the kth iteration j , the calculation steps of each iteration are as follows: a. Let the error vector e under the kth iteration j (p k )=(e j1 ,e j2 ,...,e jM ),e jM It is e j (p k ) in the Mth vector element, calculate the Jacobian matrix J of the error vector k and the Heiser matrix H k as follows: H k =J k T J k Where, J k T is the matrix J k The transpose of b. The Levenberg-Marquardt optimization algorithm combines the Gauss-Newton method and the steepest descent method, and uses the damping coefficient to dynamically adjust the impact of the steepest descent method on the iterative step size during the iteration process. The step size of each iteration is d k for: d k \(J k T J k +λ k I) -1 (-J k T )and j ( p k ) Where I is the sixth-order unit matrix, λ k is the damping coefficient; c. The determination of the damping coefficient includes the determination of the initial value and the dynamic change during the iteration process. According to the initial Heiser matrix, the initial damping coefficient can be calculated as: l k =τ*max(diag(Η k ))*||e j (p k )|| 1.5 Where, τ is a pre-set parameter, diag(Η k ) indicates H k All elements of the diagonal; during the iteration, for each step of the prediction step, by calculating the scaling factor The damping coefficient is modified dynamically according to the size of cj (p k ) and F cj (d k +p k ) are the optimization parameters p k and d k +p k The objective function value when is the matrix d k The transpose of r k Reflects the accuracy of the prediction step size. When r k When r<0, the direction of the predicted step length is opposite to the direction of fitness value reduction, the damping coefficient should be increased quickly and the current prediction should be abandoned. k ≥0, the current forecast should be accepted, and the damping coefficient should be adjusted with r k Dynamically adjust the changes in , and improve the consistency between the iterative step direction and the actual fitness value reduction direction; d. When the parameters in the iteration process meet any of the following conditions, the iteration ends and the final result is obtained: ① Where e1 is the first-order derivative termination condition; ②||d k ||<e2(||p k ||+e2), where e2 is the termination condition of the change step distance; ③The number of iterations iter>=e3, where e3 is the maximum number of iterations.

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