A magnetic dipole positioning method based on ellipse fitting

Abstract

The present application belongs to the technical field of high-precision positioning of micro systems. The present application provides a magnetic dipole positioning method based on ellipse fitting. The disclosed embodiment establishes a sensor and a magnetic source model, and uses a conversion matrix based on the spatial relationship between the rotating magnetic dipole and the three-axis fluxgate sensor so that the sensor output magnetic field can correctly reflect the three-axis magnetic field information of the rotating magnetic dipole. Then the rotating magnetic dipole spatial magnetic field is modeled, and it is proposed to use logical proof to obtain the relationship between the sensor output ellipse parameters and the actual rotating magnetic dipole spatial parameters. This relationship is used to optimize parameters, improve the accuracy of parameter estimation based on a large number of test values, list the relationship between position parameters and the two based on the relationship between ellipse parameters and spatial parameters, and finally use a particle swarm algorithm to further estimate the position parameters to improve accuracy, and finally obtain a specific target estimated position based on the three-dimensional spatial position parameters.

Description

Technical Field

[0001] The disclosed embodiments relate to the technical field of high-precision positioning of micro-systems, and in particular to a magnetic dipole positioning method based on ellipse fitting. Background Art

[0002] With the gradual development of science and technology, precise positioning technology provides important reference conditions for the development of many key fields. Positioning using magnetic fields has attracted much attention because of its non-contact, high cost-effectiveness and good positioning accuracy. The use of magnetic field measurement systems in modern medical, geological survey, and military applications, and the use of sensors to locate the target based on the magnetic field characteristics are becoming more and more common. Commonly used sensors such as three-axis fluxgates have the characteristics of good three-dimensional space effects, small size, and low cost, but they are also subject to the interference of modern complex magnetic field environments and must continuously improve data processing methods in order to achieve better positioning accuracy. Using single or multiple magnetic sensors for spatial positioning and improving positioning accuracy has always been a hot topic in academia and industry.

[0003] Defects and deficiencies of existing technologies: Traditional positioning methods, such as triangulation and centroid methods, usually rely on the geometric relationship between the sensor and the target and the signal strength to determine the target position. For traditional methods, when the target and the sensor are in the same horizontal plane, a scenario of approximately 0 / 0 will appear in the parameter estimation. When there is a small noise in the measurement value, it will cause a large deviation in the position estimation, resulting in a singular result. This phenomenon mainly stems from the fact that the sensor and the target may be in a special geometric configuration such as collinearity or equidistant, resulting in a lack of sufficient geometric constraints in the positioning equations, which in turn challenges the uniqueness and stability of the solution. In addition, the signal strength measurement is affected by environmental noise, multipath effects and signal attenuation, making it difficult to accurately calculate the target position on the same plane. Therefore, these traditional positioning methods are prone to introduce uncertainty and reduce positioning accuracy when dealing with positioning problems on the horizontal plane, especially in environments where the signal and geometric information are insufficient or limited. In summary, the performance of the existing technology in this scenario lacks stability and certainty, which limits its effectiveness and credibility in real-world applications. Summary of the invention

[0004] In order to avoid the shortcomings of the prior art, the present application provides a magnetic dipole positioning method based on ellipse fitting to solve the problem in the prior art that when the target and the sensor are in the same horizontal plane, a scenario of approximate 0 / 0 will appear in the parameter estimation, and when a small noise appears in the measured value, it will cause a large deviation in the position estimation, resulting in singular results.

[0005] According to an embodiment of the present disclosure, a magnetic dipole positioning method based on ellipse fitting is provided, the method comprising:

[0006] Step S1, using a conversion matrix to perform coordinate conversion on the receiving magnetic field of the three-axis fluxgate sensor and the three-component magnetic moment of the target single rotating magnetic dipole to obtain the relationship between the receiving magnetic field and the target magnetic moment;

[0007] Step S2, selecting a plane projection, and using a matrix least square solution method to process the relationship between the position parameter and the magnetic field parameter of the three-axis fluxgate sensor, and the relationship between the received magnetic field and the target magnetic moment, so as to obtain an estimated value of the position parameter; wherein the plane projection includes an xoy plane projection, an xoz plane projection, and a yoz plane projection;

[0008] Step S3, using the coplanar relationship of all measurement points and combining the SVD method, respectively obtain the estimated values ​​of the spatial parameters of the components of the received magnetic field in the three-axis directions;

[0009] Step S4, constructing a cost function according to the estimated value of the position parameter, the estimated value of the space parameter and the actual target position parameter to be estimated;

[0010] Step S5, based on the cost function, using the particle swarm algorithm to estimate the actual target position parameters to be estimated, and removing the erroneous solutions in combination with the prior information, so as to obtain the coordinates corresponding to the target magnetic source on the plane projection;

[0011] Step S6, select the remaining plane projections in turn, repeat steps S2 to S5, obtain the coordinates corresponding to the target magnetic source on the remaining plane projections, and obtain the estimated position of the target in the three-dimensional space.

[0012] Furthermore, the relationship between the received magnetic field and the target magnetic moment is:

[0013]

[0014] in, is the target magnetic moment, is the rotation matrix from the magnetic dipole coordinate system to the sensor coordinate system, is the receiving magnetic field of the three-axis fluxgate sensor.

[0015] Further, step S2 includes:

[0016] Choose any one of the xoy, xoz and yoz projections;

[0017] When the plane projection is an ellipse, the relationship between the position parameters and the magnetic field parameters of the three-axis fluxgate sensor is obtained according to the ellipse equation of the receiving magnetic field of the three-axis fluxgate;

[0018] A number of magnetic field data are obtained at a number of measuring points, and the relationship between the position parameters and magnetic field parameters of the three-axis fluxgate sensor, and the relationship between the received magnetic field and the target magnetic moment are processed using a matrix least square solution method to obtain an estimated value of the position parameter.

[0019] Further, a plurality of magnetic field data are acquired at a plurality of measuring points, and a relationship between a position parameter and a magnetic field parameter of a three-axis fluxgate sensor, and a relationship between a received magnetic field and a target magnetic moment are processed using a matrix least squares solution method to obtain an estimated value of the position parameter, including:

[0020] For a set of magnetic field data, combined with the ellipse equation, a set of measurement equations is obtained;

[0021] Traversing n sets of magnetic field data to obtain n sets of measurement equations, and obtaining a measurement equation group according to the n sets of measurement equations;

[0022] The matrix least square solution method is used to fit the measurement equations to an ellipse to obtain the estimated values ​​of the position parameters.

[0023] Furthermore, the magnetic field data is projected as an ellipse on the xoy plane, and the expression of the measurement equation on this plane is:

[0024]

[0025] in, is the first coefficient, is the second coefficient, is the third coefficient, and , and are constants, The magnetic sensor receives the component of the magnetic field on the X-axis. The magnetic sensor receives the component of the magnetic field on the Y axis. is the target magnetic moment;

[0026] The expression of the measurement equations is:

[0027]

[0028] in, A first aggregation matrix for receiving magnetic fields of n groups of sensors, , is the component of the magnetic field received by the magnetic sensor on the X-axis in the first set of measurement equations, is the component of the magnetic field received by the magnetic sensor on the Y axis in the first set of measurement equations, is the component of the magnetic field received by the magnetic sensor on the Z axis in the first set of measurement equations, is the component of the magnetic field received by the magnetic sensor on the X-axis in the nth set of measurement equations, is the component of the magnetic field received by the magnetic sensor on the Y axis in the nth set of measurement equations, is the component of the magnetic field received by the magnetic sensor on the Z axis in the nth set of measurement equations, is the aggregation matrix of n groups of target magnetic moments, , is the estimated value of the location parameter, , is the first constant matrix, is the second constant matrix, is the third constant matrix, , , ;

[0029] The expressions for the estimated values ​​of the ellipse fitting parameters are:

[0030] .

[0031] Further, step S3 includes:

[0032] Based on the estimated value of the location parameter, the formula for fitting the ellipse in two-dimensional space becomes:

[0033]

[0034] in, for Middle j elements;

[0035] All measurement points are distributed on the same zero-crossing plane, then:

[0036]

[0037] in, is the first constant, is the second constant, is the third constant, The magnetic sensor receives the component of the magnetic field on the Z axis;

[0038] Based on n sets of magnetic field data, matrix operations are used to process and obtain:

[0039]

[0040] in, A second aggregation matrix for receiving magnetic fields of n groups of sensors, , is the spatial parameter, ;

[0041] right Perform SVD decomposition to obtain:

[0042]

[0043] in, is the left singular vector matrix, is a diagonal matrix, is the right singular vector matrix;

[0044] The spatial parameters are obtained according to the singular value decomposition characteristics. Estimated value of , the estimated value of the spatial parameter for The eigenvector corresponding to the smallest eigenvalue of The third column vector of represents:

[0045]

[0046] in, is the right singular vector matrix The third column vector of .

[0047] Furthermore, the cost function of the particle swarm algorithm is:

[0048]

[0049] in, is the weight coefficient, , is the position of the target relative to the measurement point, is the matrix discussed for the xoy plane, is the unit normal vector of the plane;

[0050] The iterative formula of the particle swarm algorithm is:

[0051]

[0052] in, is the current velocity of the particle, is the updated particle velocity, is the first position parameter, is the second position parameter, is the optimal position for an individual, is the global best position, is the current position of the particle, is the updated particle position.

[0053] Furthermore, the particle swarm algorithm includes:

[0054] Step 1: Randomly initialize the particle swarm size N and the position of each particle and speed , and set the individual optimal position of each particle and the global optimal position ;

[0055] Step 2: Calculate the current position of each particle The fitness value of ; Among them, the fitness formula is:

[0056]

[0057] Step 3: If the current fitness value is better than the individual best fitness value, update the individual best position ; If the current fitness value is better than the global best fitness value, update the global best position ;

[0058] Step 4: Update the particle's current velocity based on the inertia weight, learning factor, and random number , and then use the updated particle velocity to adjust the particle position ;

[0059] Step 5: If the maximum number of iterations is reached or the global optimal fitness value meets the preset accuracy requirement, the algorithm is terminated; otherwise, return to step 2.

[0060] The technical solution provided by the embodiments of the present disclosure may have the following beneficial effects:

[0061] In the embodiment of the present disclosure, through the above-mentioned magnetic dipole positioning method based on ellipse fitting, on the one hand, the characteristics of a single rotating magnetic dipole are utilized, and the target magnetic moment of the magnetic dipole is used to convert the coordinates with the magnetic field received by the three-axis fluxgate sensor, and the output of the three-axis fluxgate sensor is used to represent the magnetic field generated by the magnetic dipole. Then, it is proved that the three-plane projection of the magnetic field output of the three-axis fluxgate sensor in the three-dimensional space coordinate system is an ellipse or a straight line, and the conditions for the two results to be established when the projection is a straight line or an ellipse are given. According to the analysis of the above conditions, the relationship between the position parameter and the spatial parameter and the normal vector of the projection plane of the position parameter is established, so that the magnetic dipole position information can be estimated according to the position parameter and the spatial parameter. According to the known target magnetic dipole magnetic moment information, the three components of the magnetic field intensity output by the three-axis fluxgate measured by a large number of experiments can be used to estimate the relationship parameters between the three components of the magnetic field and the magnetic moment through the ellipse equation. And the plane position relationship is combined with the matrix singular value decomposition method to obtain the projection plane parameters. Then, the cost function is formed according to the relationship between the position parameter, the spatial parameter and the actual target position parameter. The particle swarm algorithm is used to estimate the actual target position parameters, so as to obtain the final estimated position according to the measured value, and then obtain On the other hand, this method has significant advantages in small size and high-precision positioning. Especially when the magnetic dipole and the three-axis magnetic sensor are When the two axes are in the same plane, the existence of singular solutions is avoided and the positioning effect is excellent. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] The accompanying drawings herein are incorporated into the specification and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification are used to explain the principles of the present disclosure. Obviously, the accompanying drawings described below are only some embodiments of the present disclosure, and for ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without creative work.

[0063] Figure 1 A magnetic dipole positioning method based on ellipse fitting in an exemplary embodiment of the present disclosure is shown;

[0064] Figure 2 A schematic diagram showing an ellipse fitting of a single rotating magnetic dipole in an exemplary embodiment of the present disclosure;

[0065] Figure 3 A schematic diagram showing parameter estimation using a particle swarm algorithm in an exemplary embodiment of the present disclosure;

[0066] Figure 4 A schematic diagram showing positioning of a single rotating magnetic dipole using a three-axis fluxgate sensor in an exemplary embodiment of the present disclosure;

[0067] Figure 5 A comparison diagram of simulation results between the rotating magnetic dipole positioning method proposed in the present application and the traditional method in an exemplary embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0068] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that the disclosure will be more comprehensive and complete and to fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0069] In addition, the accompanying drawings are only schematic illustrations of the embodiments of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the figures represent the same or similar parts, and their repeated descriptions will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0070] This example embodiment provides a magnetic dipole positioning method based on ellipse fitting. Figure 1 As shown in , the magnetic dipole positioning method based on ellipse fitting may include: steps S1 to S6.

[0071] Step S1, using a conversion matrix to perform coordinate conversion on the receiving magnetic field of the three-axis fluxgate sensor and the three-component magnetic moment of the target single rotating magnetic dipole to obtain the relationship between the receiving magnetic field and the target magnetic moment;

[0072] Step S2, selecting a plane projection, and using a matrix least square solution method to process the relationship between the position parameter and the magnetic field parameter of the three-axis fluxgate sensor, and the relationship between the received magnetic field and the target magnetic moment, so as to obtain an estimated value of the position parameter; wherein the plane projection includes an xoy plane projection, an xoz plane projection, and a yoz plane projection;

[0073] Step S3, using the coplanar relationship of all measurement points and combining the SVD method, respectively obtain the estimated values ​​of the spatial parameters of the components of the received magnetic field in the three-axis directions;

[0074] Step S4, constructing a cost function according to the estimated value of the position parameter, the estimated value of the space parameter and the actual target position parameter to be estimated;

[0075] Step S5, based on the cost function, using the particle swarm algorithm to estimate the actual target position parameters to be estimated, and removing the erroneous solutions in combination with the prior information, so as to obtain the coordinates corresponding to the target magnetic source on the plane projection;

[0076] Step S6, select the remaining plane projections in turn, repeat steps S2 to S5, obtain the coordinates corresponding to the target magnetic source on the remaining plane projections, and obtain the estimated position of the target in the three-dimensional space.

[0077] Through the above-mentioned magnetic dipole positioning method based on ellipse fitting, on the one hand, the characteristics of a single rotating magnetic dipole are utilized, and the target magnetic moment of the magnetic dipole is used to convert the coordinates with the magnetic field received by the three-axis fluxgate sensor, and the output of the three-axis fluxgate sensor is used to represent the magnetic field generated by the magnetic dipole. Then it is proved that the three-plane projection of the magnetic field output of the three-axis fluxgate sensor in the three-dimensional space coordinate system is an ellipse or a straight line, and the conditions for the two results to be established when the projection is a straight line or an ellipse are given. According to the analysis of the above conditions, the relationship between the position parameter and the spatial parameter and the normal vector of the projection plane of the position parameter is established, so that the magnetic dipole position information can be estimated according to the position parameter and the spatial parameter. According to the known target magnetic dipole magnetic moment information, the three components of the magnetic field intensity output by the three-axis fluxgate measured by a large number of experiments can be used to estimate the relationship parameters between the three components of the magnetic field and the magnetic moment through the ellipse equation. And the projection plane parameters are obtained by using the plane position relationship combined with the matrix singular value decomposition method. Then the cost function is formed according to the relationship between the position parameter, the spatial parameter and the actual target position parameter. The actual target position parameters are estimated using the particle swarm algorithm, so that the final estimated position is obtained according to the measured value, and then the On the other hand, this method has significant advantages in small size and high-precision positioning. Especially when the magnetic dipole and the three-axis magnetic sensor are When the two axes are in the same plane, the existence of singular solutions is avoided and the positioning effect is excellent.

[0078] Next, we will refer to Figures 1 to 5 Each step of the above-mentioned magnetic dipole positioning method based on ellipse fitting in this example implementation is described in more detail.

[0079] In one embodiment, Figure 2 As shown, it is a schematic diagram of the ellipse fitting of a single rotating magnetic dipole. In the scenario of positioning a single rotating magnetic dipole, the rotating magnetic dipole is placed horizontally on a horizontal plane, and the magnetic sensor (i.e., a three-axis fluxgate sensor) is also placed horizontally to receive the rotating magnetic field. Taking the coordinate system of the rotating magnetic dipole as the reference coordinate system, the rotation plane of the rotating magnetic dipole is set as the xoy reference plane, and the direction of the rotation axis is defined as the z-axis direction. In this case, when the distance between the target and the measuring sensor exceeds 2.5 times the length of the target itself, the target can be equivalent to a rotating magnetic dipole. Its expression is:

[0080]

[0081] in, is the target magnetic moment, is the position of the target relative to the measurement point, , for The component on the x-axis, for The component on the y-axis, for The component on the z-axis, represents the rotation matrix from the rotating magnetic dipole coordinate system to the sensor coordinate system, represents the three-axis fluxgate sensor coordinate system, m is the rotating magnetic dipole coordinate system, It can be expressed as:

[0082]

[0083] in, is the vacuum permeability, is the identity matrix, is the distance between the measuring point and the target, which can be expressed according to the three-dimensional distance formula as .

[0084] When the rotating magnetic dipole is in a rotating state, the magnetic moment of the rotating magnetic dipole can be divided into three axes: x, y, and z:

[0085]

[0086] in, for The component on the x-axis, for The component on the y-axis, for The component on the z-axis, since the rotating magnetic dipole always rotates in the horizontal plane, does not involve height changes, , and They can be expressed as:

[0087]

[0088] Considering that the rotating magnetic dipole coordinate system and the magnetic sensor coordinate system are both in the horizontal plane, according to the matrix operation method and spatial geometric relationship, the rotation matrix from the rotating magnetic dipole coordinate system to the sensor coordinate system is It can be expressed as:

[0089]

[0090] in, is the proportionality factor between the two vectors.

[0091] Introducing the magnetic moment in the rotating magnetic dipole coordinate system (i.e. the three-axis fluxgate sensor receives the magnetic field), which can be expressed as:

[0092]

[0093] At this time, the magnetic field generated by the rotating magnetic dipole can be expressed as:

[0094]

[0095] According to the decomposition of the three-axis magnetic moment in the fluxgate coordinate system, the three-axis magnetic moment components of the rotating magnetic dipole can be expressed as:

[0096]

[0097] in, for The component on the x-axis, for The component on the y-axis.

[0098] At this time, the magnetic field received by the magnetic sensor can be expressed as:

[0099]

[0100] in, is the magnetic field generated by the rotation of the rotating magnetic dipole, To measure the noise of the sensor, the acceleration sensor can be used to project the magnetic sensor onto the When the measurement noise is small, the noise can be ignored, and the magnetic field generated by the rotating magnetic dipole is used to approximate the receiving magnetic field of the three-axis fluxgate sensor, which is expressed by the formula: , in subsequent reasoning, we can use To replace .

[0101] Will Written in the form of a 3*3 matrix:

[0102]

[0103] in, is the element in the first row and first column of the matrix, is the element in the first row and second column of the matrix, is the element in the first row and third column of the matrix, is the element in the second row and first column of the matrix, is the element in the second row and second column of the matrix, is the element in the second row and third column of the matrix, is the element in the third row and first column of the matrix, is the element in the third row and second column of the matrix, is the element in the third row and third column of the matrix.

[0104] Sensor Output Rewritten according to the x, y, and z axes:

[0105]

[0106] Take the xoy plane as the observation object, the sensor output The projection output on the xoy plane is:

[0107]

[0108] in, for The component on the x-axis, for The component on the y-axis, .

[0109] when hour,

[0110] in, is the proportionality coefficient between the two vectors, The projection on the xoy plane is a straight line. According to the matrix operation rules, the following exists:

[0111]

[0112] according to The expression of the sensor actual position and the angle between the xoy plane α You can get:

[0113]

[0114] when hour, is reversible, then there exists:

[0115]

[0116] Multiplying the left and right sides of the equation by their own transpose gives us the expression for the ellipse.

[0117]

[0118] Since it is assumed that the projection of the sensor output on the xoy plane is a straight line, according to , which is expressed as the sum of the magnetic moments in the x-axis and y-axis directions, we get:

[0119]

[0120] For the magnetic field value at any time t, , and Distributed in the same plane, is the unit normal vector of the xoy plane, is the first element of the unit normal vector of the xoy plane, is the second element of the unit normal vector of the xoy plane, is the third element of the unit normal vector of the xoy plane. It satisfies:

[0121]

[0122] because and are two independent vectors. The sum of the above formula is 0, so the value in the brackets is 0, that is:

[0123]

[0124] The plane normal vector can be calculated :

[0125]

[0126] Similarly, the projection of the sensor output on the xoz and yoz planes can be proved to be a straight line or an ellipse. Based on the above analysis, the relationship between position parameters, space parameters and position parameters is established. According to the position parameters and space parameters, the position information of the rotating magnetic dipole can be estimated.

[0127] In one embodiment, according to the above inference, the output of the magnetic sensor is a three-dimensional ellipse in space, and at least one of its projections on the xoy, xoz and yoz planes is an ellipse. Assume that its projection on the xoy plane is an ellipse. Combined with the ellipse expression, it can be seen that the left side of the ellipse expression equation at this time is an ellipse containing , , The expressions of the three magnetic field variables. We use three constant values , , To represent the coefficient of the magnetic field variable, the following relationship can be obtained.

[0128]

[0129] When there are n measurement points, n sets of measurement equations can be obtained, which can be written as:

[0130]

[0131] in , , They can be expressed as:

[0132]

[0133] in, is the first constant matrix, is the second constant matrix, is the third constant matrix, , , .

[0134] When the measurement data is sufficient, the only way to obtain Estimated value of , combined with the matrix least squares solution method:

[0135]

[0136] At this time, the ellipse formula fitted in two-dimensional space becomes:

[0137]

[0138] in for The jth element in .

[0139] At the same time, considering that all measurement points are distributed on the same zero-crossing plane, there exists:

[0140]

[0141] When there are n sets of measurement points, the relationship is expressed using matrix operations.

[0142]

[0143] in , Respectively expressed as:

[0144]

[0145] right Perform SVD decomposition:

[0146]

[0147] According to the singular value decomposition characteristics, we can get Estimated value of Can be expressed as The third column vector of , which corresponds to the eigenvector corresponding to the minimum eigenvalue, is expressed as:

[0148]

[0149] Estimate the target position based on the position parameters and spatial parameters:

[0150] According to the output data of the magnetic sensor, the ellipse fitting parameters can be obtained and According to this relationship, the estimated value is estimated using the optimization algorithm, and the parameter estimation cost function is:

[0151]

[0152] in is the weight coefficient, It can be expressed by the following formula:

[0153]

[0154] Since the gradient value of the above cost function is not easy to obtain by direct derivation, the particle swarm algorithm is used to derive the variables To estimate the parameters, the iterative formula is:

[0155]

[0156] in, is the current velocity of the particle, is the updated particle velocity, is the first position parameter, is the second position parameter, is the optimal position for an individual, is the global best position, is the current position of the particle, is the updated particle position. The first formula is based on the particle's current velocity and the speed parameter corrected by the historical best position and the speed parameter corrected by the global optimal position Get the updated particle speed The second formula is the particle speed updated according to the first formula Add current location Get the updated location .

[0157] The general steps of the particle swarm algorithm are:

[0158] Step 1: Randomly initialize the particle swarm size N and the position of each particle and speed , and set the individual best position of each particle and the global optimal position ;

[0159] Step 2: Calculate the current position of each particle The fitness value of ; Among them, the fitness formula is:

[0160]

[0161] Step 3: If the current fitness value is better than the individual best fitness value, update the individual best position ; If the current fitness value is better than the global best fitness value, update the global best position ;

[0162] Step 4: Update the particle's current velocity based on the inertia weight, learning factor, and random number , and then use the updated particle velocity to adjust the particle position ;

[0163] Step 5: If the maximum number of iterations is reached or the global optimal fitness value meets the preset accuracy requirement, the algorithm is terminated; otherwise, return to step 2.

[0164] like Figure 3 As shown in Figure 1, it is a schematic diagram of using particle swarm algorithm for parameter estimation.

[0165] Considering It has the characteristic of being symmetrical at the origin. ,exist .

[0166] Therefore, the estimated results All of them conform to the cost function, and there is a problem of virtual solution. In actual use, the target position can usually be restricted according to prior information to remove the virtual solution and obtain the correct result.

[0167] The present application estimates parameters based on the relationship between position parameters, spatial parameters and a single rotating magnetic dipole according to the position parameters. The three-axis fluxgate sensor is used to locate the rotating magnetic dipole. When the magnetic sensor and the rotating magnetic dipole are in the same horizontal plane, the positioning effect is good.

[0168] In addition, when the height is high, the error is similar to that of the conventional method. When the target is less different from the three-axis fluxgate sensor in the height direction, the positioning error of the method proposed in this application is smaller than that of the conventional method.

[0169] In a specific embodiment, Figure 4 FIG. 1 is a schematic diagram of using a three-axis fluxgate sensor to locate a single rotating magnetic dipole.

[0170] In a specific embodiment, On a square scale, height Z = 0.1m, starting from the coordinate (0.5, 0.5), a real position is placed every 1m up, down, left and right. Each position is simulated 15 times according to the traditional method and the rotating magnetic dipole positioning method. The real position is represented by a square, the positioning result of the traditional method is represented by a circle, and the positioning result of the rotating magnetic dipole positioning method proposed in this application is represented by an asterisk. The simulation results are shown in FIG. Figure 5 It can be seen that the positioning result of the rotating magnetic dipole positioning method proposed in the present application is better than that of the traditional method.

[0171] This method has significant advantages in small size and high-precision positioning. When the magnetic dipole and the three-axis magnetic sensor are in the same plane, the situation of singular solutions is avoided and the positioning effect is excellent. When the height difference between the magnetic dipole and the three-axis magnetic sensor is small, the effect of this method is still better than the traditional method. When the height difference is high, the errors of the two methods are roughly the same.

[0172] Through the above-mentioned magnetic dipole positioning method based on ellipse fitting, on the one hand, the characteristics of a single rotating magnetic dipole are utilized, and the target magnetic moment of the magnetic dipole is used to convert the coordinates with the magnetic field received by the three-axis fluxgate sensor, and the output of the three-axis fluxgate sensor is used to represent the magnetic field generated by the magnetic dipole. Then it is proved that the three-plane projection of the magnetic field output of the three-axis fluxgate sensor in the three-dimensional space coordinate system is an ellipse or a straight line, and the conditions for the two results to be established when the projection is a straight line or an ellipse are given. According to the analysis of the above conditions, the relationship between the position parameters and the spatial parameters and the normal vector of the projection plane of the position parameters is established, so that the magnetic dipole position information can be estimated according to the position parameters and the spatial parameters. According to the known target magnetic dipole magnetic moment information, the three components of the magnetic field intensity output by the three-axis fluxgate measured by a large number of experiments can be used to estimate the relationship parameters between the three components of the magnetic field and the magnetic moment through the ellipse equation. The projection plane parameters are obtained by combining the plane position relationship with the matrix singular value decomposition method. The particle swarm algorithm is used to estimate the actual target position parameters, so that the final estimated position is obtained according to the measured value, and then the position is obtained. Coordinate location information.

[0173] The application is simple to verify in practice and can locate the magnetic dipole target without complex structure.

[0174] The present application is aimed at positioning a rotating magnetic dipole. The magnetic field generated by a rotating magnetic dipole does not exist in nature, which reduces the dependence on environmental information. Therefore, the experiment has low requirements for the magnetic field environment and can improve the target signal-to-noise ratio through simple bandpass filtering. It can also work effectively in unknown or changing environments.

[0175] This application does not rely on the spatial relative relationship between the magnetic source target and the three-axis fluxgate sensor, and can be completed without additional measurement of spatial angle information, etc. This simplifies the positioning steps and prevents further loss of positioning accuracy due to measurement errors.

[0176] This method handles complex geometric relationships by fitting projections in three-dimensional space, which can better simulate the magnetic field distribution in actual physical environments.

[0177] This application performs positioning by using the expression between the spatial parameters and the target geometric parameters to solve, and then further calculates the cost function of the estimated value of the position parameter, the estimated value of the spatial parameter and the actual position parameter of the target. Parameter estimation is performed to avoid the 0 / 0 situation in the parameter estimation formula of the traditional method. When there is a small noise in the measurement value, it will not have a significant impact on the result. The positioning effect is good when the sensor and the magnetic dipole target are on the same horizontal plane, achieving accurate positioning in this scenario.

[0178] This application uses a particle swarm algorithm, which has global optimization capabilities and fast convergence characteristics that make it suitable for real-time positioning needs. It can search for the global optimal solution in a complex magnetic field environment and improve the algorithm's robustness to outliers and noise.

[0179] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the embodiments of the present disclosure, the meaning of "multiple" is two or more, unless otherwise clearly and specifically defined.

[0180] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example" or "some examples" etc. 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 disclosure. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification.

[0181] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. This application is intended to cover any modification, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary techniques in the art that are not disclosed in the present disclosure. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present disclosure are indicated by the appended claims.

Claims

1. A magnetic dipole positioning method based on ellipse fitting, characterized in that: The method includes: Step S1, using a conversion matrix to perform coordinate conversion on the receiving magnetic field of the three-axis fluxgate sensor and the three-component magnetic moment of the target single rotating magnetic dipole to obtain the relationship between the receiving magnetic field and the target magnetic moment; Step S2, selecting a plane projection, and using a matrix least square solution method to process the relationship between the position parameter and the magnetic field parameter of the three-axis fluxgate sensor, and the relationship between the received magnetic field and the target magnetic moment, so as to obtain an estimated value of the position parameter; wherein the plane projection includes an xoy plane projection, an xoz plane projection, and a yoz plane projection; Step S3, using the coplanar relationship of all measurement points and combining the SVD method, respectively obtain the estimated values ​​of the spatial parameters of the components of the received magnetic field in the three-axis directions; Step S4, constructing a cost function according to the estimated value of the position parameter, the estimated value of the space parameter and the actual target position parameter to be estimated; Step S5, based on the cost function, using the particle swarm algorithm to estimate the actual target position parameters to be estimated, and removing the erroneous solutions in combination with the prior information, so as to obtain the coordinates corresponding to the target magnetic source on the plane projection; Step S6, select the remaining plane projections in turn, repeat steps S2 to S5, obtain the coordinates corresponding to the target magnetic source on the remaining plane projections, and obtain the estimated position of the target in three-dimensional space; wherein, The magnetic field data is projected as an ellipse on the xoy plane, and the expression of the measurement equation on this plane is: in, is the first coefficient, is the second coefficient, is the third coefficient, and , and are constants, The magnetic sensor receives the component of the magnetic field on the X-axis. The magnetic sensor receives the component of the magnetic field on the Y axis. is the target magnetic moment; The expression of the measurement equations is: in, A first aggregation matrix for receiving magnetic fields of n groups of sensors, , is the component of the magnetic field received by the magnetic sensor on the X-axis in the first set of measurement equations, is the component of the magnetic field received by the magnetic sensor on the Y axis in the first set of measurement equations, is the component of the magnetic field received by the magnetic sensor on the Z axis in the first set of measurement equations, is the component of the magnetic field received by the magnetic sensor on the X-axis in the nth set of measurement equations, is the component of the magnetic field received by the magnetic sensor on the Y axis in the nth set of measurement equations, is the component of the magnetic field received by the magnetic sensor on the Z axis in the nth set of measurement equations, is the aggregation matrix of n groups of target magnetic moments, , is the estimated value of the location parameter, , is the first constant matrix, is the second constant matrix, is the third constant matrix, , , ; The expressions for the estimated values ​​of the ellipse fitting parameters are: Based on the estimated value of the location parameter, the formula for fitting the ellipse in two-dimensional space becomes: in, for Middle j elements, ; All measurement points are distributed on the same zero-crossing plane, then: in, is the first constant, is the second constant, is the third constant, The magnetic sensor receives the component of the magnetic field on the X-axis. The magnetic sensor receives the component of the magnetic field on the Y axis. The magnetic sensor receives the component of the magnetic field on the Z axis; Based on n sets of magnetic field data, matrix operations are used to process and obtain: in, A second aggregation matrix for receiving magnetic fields of n groups of sensors, , is the spatial parameter, ; right Perform SVD decomposition to obtain: in, is the left singular vector matrix, is a diagonal matrix, is the right singular vector matrix; The estimated value of the spatial parameter is obtained according to the singular value decomposition characteristics , the estimated value of the spatial parameter for The eigenvector corresponding to the smallest eigenvalue of The third column vector of represents: in, is the right singular vector matrix The third column vector of ; The cost function of the particle swarm algorithm is: in, is the weight coefficient, , is the position of the target relative to the measurement point, is the matrix discussed for the xoy plane, is the unit normal vector of the plane; The iterative formula of the particle swarm algorithm is: in, is the individual learning weight, Learn weights for the group, is the current velocity of the particle, is the updated particle velocity, is the first position parameter, is the second position parameter, is the optimal position for an individual, is the global best position, is the current position of the particle, is the updated particle position.

2. The magnetic dipole positioning method based on ellipse fitting according to claim 1, characterized in that: The relationship between the receiving magnetic field and the target magnetic moment is: in, is the target magnetic moment, is the rotation matrix from the magnetic dipole coordinate system to the sensor coordinate system, is the receiving magnetic field of the three-axis fluxgate sensor.

3. The magnetic dipole positioning method based on ellipse fitting according to claim 2, characterized in that: Step S2 includes: Choose any one of the xoy, xoz and yoz projections; When the plane projection is an ellipse, the relationship between the position parameters and the magnetic field parameters of the three-axis fluxgate sensor is obtained according to the ellipse equation of the receiving magnetic field of the three-axis fluxgate; A number of magnetic field data are obtained at a number of measuring points, and the relationship between the position parameters and magnetic field parameters of the three-axis fluxgate sensor, and the relationship between the received magnetic field and the target magnetic moment are processed using a matrix least square solution method to obtain an estimated value of the position parameter.

4. The magnetic dipole positioning method based on ellipse fitting according to claim 3, characterized in that: The step of acquiring a plurality of magnetic field data at a plurality of measurement points, and processing the relationship between the position parameter and the magnetic field parameter of the three-axis fluxgate sensor, and the relationship between the received magnetic field and the target magnetic moment by using a matrix least square solution method to obtain an estimated value of the position parameter includes: For a set of magnetic field data, combined with the ellipse equation, a set of measurement equations is obtained; Traversing n sets of magnetic field data to obtain n sets of measurement equations, and obtaining a measurement equation group according to the n sets of measurement equations; The matrix least square solution method is used to fit the measurement equations to an ellipse to obtain the estimated values ​​of the position parameters.

5. The magnetic dipole positioning method based on ellipse fitting according to claim 4, characterized in that: Particle swarm optimization includes: Step 1: Randomly initialize the particle swarm size N and the position of each particle and speed , and set the individual best position of each particle and the global optimal position ; Step 2: Calculate the current position of each particle The fitness value of ; Among them, the fitness formula is: Step 3: If the current fitness value is better than the individual best fitness value, update the individual best position ; If the current fitness value is better than the global best fitness value, update the global best position ; Step 4: Update the particle's current velocity based on the inertia weight, learning factor, and random number , and then use the updated particle velocity to adjust the particle position ; Step 5: If the maximum number of iterations is reached or the global optimal fitness value meets the preset accuracy requirement, the algorithm is terminated; otherwise, return to step 2.

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