An ellipse fitting positioning method and system based on rotating permanent magnet magnetic beacon

Abstract

A method and system for positioning by ellipse fitting based on a rotating permanent magnet magnetic beacon belongs to the field of navigation, guidance and control. The present invention solves the problems of low positioning accuracy and low data processing efficiency of existing methods. The present invention derives the quasi-static magnetic field distribution law of the rotating permanent magnet magnetic beacon based on the magnetic dipole model, and then projects the three-dimensional space vector onto the xoz plane and the yoz plane, uses the least squares method to perform ellipse fitting on the two-dimensional vector, and finally constructs a positioning model based on the fitted ellipse coefficient to achieve high-precision positioning of the target. In addition, the separation of the magnetic field vector is avoided, the data processing time is shortened, and the efficiency of data processing is improved. The method of the present invention can be applied to the field of navigation, guidance and control.

Description

Technical Field

[0001] The invention belongs to the field of navigation, guidance and control, and in particular relates to an ellipse fitting positioning method and system based on a rotating permanent magnet magnetic beacon. Background Art

[0002] With the increasing complexity of human activity and the deepening exploration of unknown space, high-precision navigation and positioning in complex scenarios has become one of the most pressing scientific challenges. The navigation and positioning system based on rotating permanent magnet magnetic beacons is a semi-autonomous relative navigation and positioning system with high penetration and strong interference resistance. It can provide long-term and stable positioning services in denied environments, complementing the shortcomings of other navigation and positioning systems. It has broad application prospects in fields such as underground pipeline laying, oil drilling, and fire rescue.

[0003] Currently, low-frequency magnetic field positioning systems typically use the eigenvector method to locate target points. However, this method struggles to separate the magnetic fields generated by the equivalent magnetic moments of the permanent magnets along each axis during data processing. This results in long processing times and low data processing efficiency. Furthermore, the azimuth angle solution results in large errors, resulting in low target positioning accuracy. To address these shortcomings, it is crucial to propose a new positioning algorithm that reduces data processing time and improves positioning accuracy. Summary of the Invention

[0004] The purpose of the present invention is to solve the problems of low positioning accuracy and low data processing efficiency of existing methods, and to propose an ellipse fitting positioning method and system based on a rotating permanent magnet magnetic beacon.

[0005] The technical solution adopted by the present invention to solve the above technical problems is:

[0006] According to one aspect of the present invention, an ellipse fitting positioning method based on a rotating permanent magnet magnetic beacon comprises the following steps:

[0007] Step 1: Establish a three-dimensional rectangular coordinate system with the center of the rotating permanent magnet magnetic beacon as the coordinate origin. The rotating permanent magnet magnetic beacon rotates around the z-axis of the three-dimensional rectangular coordinate system at an angular frequency ω. The rotating permanent magnet magnetic beacon is deduced at the measurement point Quasi-static magnetic field distribution at

[0008] According to the quasi-static magnetic field distribution The projection coordinates in the x-axis direction and the projection coordinates in the z-axis direction are fitted with the ellipse equation of the xoz plane, according to the quasi-static magnetic field distribution The projection coordinates in the y-axis direction and the projection coordinates in the z-axis direction are fitted to the ellipse equation of the yoz plane;

[0009] Step 2: Construct column vector Para based on the coefficients of the ellipse equation of the xoz plane xz , according to the coefficients of the ellipse equation of the yoz plane, the column vector Para is formed yz , and based on the column vector Para xz and column vector Para yz Construct positioning model;

[0010] Step 3: Use the target point The magnetic sensor at the target point collects the quasi-static magnetic field distribution of the rotating permanent magnet magnetic beacon and The quasi-static magnetic field distribution at is projected onto the xoz and yoz planes, and then the elliptic equations of the xoz and yoz planes are fitted respectively. The coefficients of the elliptic equations are then substituted into the positioning model constructed in step 2 to calculate the position of the target point.

[0011] According to another aspect of the present invention, an ellipse fitting positioning system based on a rotating permanent magnet magnetic beacon includes a positioning model construction module and a target position solution module, wherein:

[0012] The positioning model construction module is used to construct a positioning model; the specific process of positioning model construction is:

[0013] The rotating permanent magnet magnetic beacon rotates around the z-axis of the three-dimensional rectangular coordinate system at an angular frequency ω. It is deduced that the rotating permanent magnet magnetic beacon at the measurement point Quasi-static magnetic field distribution at

[0014]

[0015] in, Indicates that the rotating permanent magnet magnetic beacon is at the measuring point The quasi-static magnetic field distribution at B x express The projection coordinate in the x-axis direction of the three-dimensional rectangular coordinate system, B y express The projection coordinate in the y-axis direction of the three-dimensional rectangular coordinate system, B z express The projection coordinates in the z-axis direction of the three-dimensional rectangular coordinate system, M represents the magnetic moment of the rotating permanent magnet magnetic beacon, μ0 is the magnetic permeability of the air, r0 is the relative distance between the rotating permanent magnet magnetic beacon and the measuring point, represents the relative pitch angle between the rotating permanent magnet beacon and the measurement point, θ0 represents the relative azimuth angle between the rotating permanent magnet beacon and the measurement point, φ represents the initial phase of the rotating permanent magnet beacon, and t represents time;

[0016] According to the quasi-static magnetic field distribution The projection coordinates in the x-axis direction and the projection coordinates in the z-axis direction fit the ellipse parametric equation of the xoz plane to obtain the ellipse parametric equation coefficients Para of the xoz plane xz1 、Para xz2 and Para xz3 ;

[0017] According to the quasi-static magnetic field distribution The projection coordinates in the y-axis direction and the projection coordinates in the z-axis direction fit the ellipse equation of the yoz plane to obtain the ellipse parameter equation coefficients Para of the yoz plane yz1 、Para yz2 and Para yz3 ;

[0018] The coefficients of the ellipse equation according to the xoz plane are Para xz1 、Para xz2 and Para xz3 Construct column vector Para xz , according to the coefficient of the ellipse equation of the yoz plane Para yz1 、Para yz2 and Para yz3 Construct column vector Para yz , then based on the column vector Para xz and column vector Para yz Construct positioning model:

[0019]

[0020] in, Para θ and Para r All are intermediate variables;

[0021] The target position calculation module is used to calculate the target point position according to the positioning model; the working process of the target position calculation module is as follows:

[0022] Use target points The magnetic sensor at the location collects the quasi-static magnetic field distribution of the rotating permanent magnet magnetic beacon

[0023] Where θ represents the relative azimuth angle between the rotating permanent magnet beacon and the target point, r is the relative distance between the rotating permanent magnet beacon and the target point, is the relative pitch angle between the rotating permanent magnet magnetic beacon and the target point;

[0024] According to the quasi-static magnetic field distribution The projection coordinates in the x-axis direction and the projection coordinates in the z-axis direction are fitted to the ellipse equation of the xoz plane, and the coefficients of the ellipse equation are obtained as follows:

[0025]

[0026] Among them, Para x ' z1 、Para x ' z2 and Para x ' z3 According to the target point The xoz plane elliptic equation coefficients fitted from the quasi-static magnetic field distribution at

[0027] According to the quasi-static magnetic field distribution The ellipse equation of the yoz plane is fitted with the projection coordinates in the y-axis direction and the projection coordinates in the z-axis direction. The coefficients of the ellipse equation are:

[0028]

[0029] Among them, Para′ yz1 、Para′ yz2 and Para′ yz3 According to the target point The coefficients of the YOZ plane ellipse equation fitted from the quasi-static magnetic field distribution at ;

[0030] Calculating intermediate variables Para′ θ and Para′ θ :

[0031]

[0032] Para′ θ and Para′ θ Substitute the constructed positioning model to calculate the relative azimuth and distance between the rotating permanent magnet beacon and the target point:

[0033]

[0034] The two calculated relative pitch angles are respectively recorded as and Then and Substitute into the following formula and solve The corresponding relative azimuth angle θ 01 , The corresponding relative azimuth angle θ 02 :

[0035]

[0036] If θ 01is equal to the calculated relative azimuth θ, then determine is the relative pitch angle between the rotating permanent magnet magnetic beacon and the target point;

[0037] If θ 02 is equal to the calculated relative azimuth θ, then determine is the relative pitch angle between the rotating permanent magnet magnetic beacon and the target point.

[0038] The beneficial effects of the present invention are:

[0039] The present invention derives the quasi-static magnetic field distribution of a rotating permanent magnet beacon based on a magnetic dipole model. Then, by projecting a three-dimensional space vector onto the xoz and yoz planes, the two-dimensional vector is fitted with an ellipse using the least squares method. Finally, a positioning model is constructed based on the fitted ellipse coefficients, achieving high-precision positioning of the target. This method also avoids separating the magnetic field vectors, shortening data processing time and improving data processing efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a schematic diagram of the rotating permanent magnet model in the spatial rectangular coordinate system;

[0041] Figure 2 It is a block diagram of an ellipse fitting positioning system based on a rotating permanent magnet magnetic beacon of the present invention;

[0042] Figure 3 This is a flow chart of an ellipse fitting positioning method based on a rotating permanent magnet magnetic beacon of the present invention;

[0043] Figure 4a This is a comparison diagram of the pitch angle error between the method of the present invention and the traditional eigenvector method;

[0044] Figure 4b This is a comparison diagram of the azimuth error between the method of the present invention and the traditional characteristic vector method;

[0045] Figure 5 This is a comparison diagram of the distance error between the method of the present invention and the traditional feature vector method;

[0046] Figure 6 This is a comparison chart of the solution time between the method of the present invention and the traditional eigenvector method. DETAILED DESCRIPTION

[0047] Specific implementation method 1: Combination Figure 1 and Figure 3 This embodiment describes an ellipse fitting positioning method based on a rotating permanent magnet magnetic beacon, and the method specifically includes the following steps:

[0048] Step 1: Establish a three-dimensional rectangular coordinate system with the center of the rotating permanent magnet magnetic beacon as the coordinate origin. The rotating permanent magnet magnetic beacon rotates around the z-axis of the three-dimensional rectangular coordinate system at an angular frequency ω. The rotating permanent magnet magnetic beacon at the measurement point is derived from the magnetic dipole model. Quasi-static magnetic field distribution at

[0049] According to the quasi-static magnetic field distribution The projection coordinates in the x-axis direction and the projection coordinates in the z-axis direction are fitted with the ellipse equation of the xoz plane, according to the quasi-static magnetic field distribution The projection coordinates in the y-axis direction and the projection coordinates in the z-axis direction are fitted to the ellipse equation of the yoz plane;

[0050] Step 2: Construct column vector Para based on the coefficients of the ellipse equation of the xoz plane xz , according to the coefficients of the ellipse equation of the yoz plane, the column vector Para is formed yz , and based on the column vector Para xz and column vector Para yz Construct positioning model;

[0051] Step 3: Use the target point The magnetic sensor at the target point collects the quasi-static magnetic field distribution of the rotating permanent magnet magnetic beacon and The quasi-static magnetic field distribution at is projected onto the xoz and yoz planes, and then the elliptic equations of the xoz and yoz planes are fitted respectively. The coefficients of the elliptic equations are then substituted into the positioning model constructed in step 2 to calculate the position of the target point.

[0052] The specific implementation process is as follows Figure 2 As shown in the figure, the rotating permanent magnet magnetic beacon generates a quasi-static magnetic field when it rotates at a preset speed. After the magnetic sensor collects the magnetic field signal of the target point, the collected magnetic field signal is converted by A / D. The converted magnetic field data is filtered to extract the magnetic field vector of the rotating permanent magnet; and the extracted magnetic field vector is fitted with an ellipse to obtain the ellipse equation coefficient. The obtained ellipse equation coefficient is substituted into the positioning model to calculate the spatial position of the target point.

[0053] Specific embodiment 2: This embodiment is different from the specific embodiment 1 in that the rotating permanent magnet magnetic beacon is at the measuring point Quasi-static magnetic field distribution at for:

[0054]

[0055] in, Indicates that the rotating permanent magnet magnetic beacon is at the measuring point The quasi-static magnetic field distribution at Bx express The projection coordinate in the x-axis direction of the three-dimensional rectangular coordinate system, B y express The projection coordinate in the y-axis direction of the three-dimensional rectangular coordinate system, B z express The projection coordinates in the z-axis direction of the three-dimensional rectangular coordinate system, M represents the magnetic moment of the rotating permanent magnet magnetic beacon, μ0 is the magnetic permeability of the air, r0 is the relative distance between the rotating permanent magnet magnetic beacon and the measuring point, represents the relative pitch angle between the rotating permanent magnet beacon and the measurement point, θ0 represents the relative azimuth angle between the rotating permanent magnet beacon and the measurement point, φ represents the initial phase of the rotating permanent magnet beacon, and t represents time.

[0056] Other steps and parameters are the same as those in the first embodiment.

[0057] Specific embodiment three: This embodiment is different from specific embodiment one or two in that the quasi-static magnetic field distribution The projection coordinates in the x-axis direction and the projection coordinates in the z-axis direction fit the ellipse equation of the xoz plane; specifically:

[0058]

[0059] For B in formula (2) x and B z Perform ellipse fitting and obtain the fitting equation:

[0060] B x 2 +Para xz1 B z 2 +Para xz2 B x B z =Para xz3 (3)

[0061] Among them, the fitting equation coefficient Para xz1 、Para xz2 and Para xz3 They are:

[0062]

[0063] Other steps and parameters are the same as those in the first or second embodiment.

[0064] If the parametric equations for x and y in the xoy two-dimensional plane are as shown in Equation (5), then the corresponding rectangular coordinate equations are shown in Equation (6). Substituting Equation (5) into Equation (6) yields the coefficients of the equation in Equation (6).

[0065]

[0066] x 2 +Ky 2 +Nxy=P (6)

[0067]

[0068] because Therefore, the curve represented by equation (6) is an ellipse, and equation (5) is the parametric equation of a plane ellipse.

[0069] Due to the quasi-static magnetic field distribution of the present invention The projection coordinates in the x-axis, y-axis, and z-axis directions also satisfy formula (5), and the fitting equation coefficients also meet the conditions. Therefore, the fitting equations of the projection coordinates in the x-axis direction and the projection coordinates in the z-axis direction are also ellipses, and the fitting equations of the projection coordinates in the y-axis direction and the projection coordinates in the z-axis direction are also ellipses.

[0070] Specific embodiment 4: This embodiment differs from any one of the specific embodiments 1 to 3 in that the quasi-static magnetic field distribution The projection coordinates in the y-axis direction and the projection coordinates in the z-axis direction fit the ellipse equation of the yoz plane; specifically:

[0071]

[0072] For B in formula (8) y and B z Perform ellipse fitting and obtain the fitting equation:

[0073] B y 2 +Para yz1 B z 2 +Para yz2 B y B z =Para yz3 (9)

[0074] Among them, the coefficient of the fitting equation Para yz1 、Para yz2 and Para yz3 They are:

[0075]

[0076] The other steps and parameters are the same as those in the first to third embodiments.

[0077] Specific embodiment 5: This embodiment differs from any one of the specific embodiments 1 to 4 in that the column vector Para is formed based on the coefficients of the ellipse equation of the xoz plane. xz , specifically:

[0078]

[0079] Among them, Para xz1 、Para xz2 and Para xz3 Both are column vectors Para xz Elements in .

[0080] The other steps and parameters are the same as those in the first to fourth embodiments.

[0081] Specific embodiment 6: This embodiment is different from the specific embodiments 1 to 5 in that the column vector Para is formed according to the ellipse equation coefficients of the yoz plane. yz , specifically:

[0082]

[0083] Among them, Para yz1 、Para yz2 and Para yz3 Both are column vectors Para yz Elements in .

[0084] The other steps and parameters are the same as those in the first to fifth embodiments.

[0085] Specific embodiment seven: This embodiment differs from any one of the specific embodiments one to six in that the column vector Para xz and column vector Para yz Construct a positioning model; specifically:

[0086]

[0087] in, Para θ and Para r All are intermediate variables.

[0088] The other steps and parameters are the same as those in the first to sixth embodiments.

[0089] Specific embodiment eight: This embodiment differs from any one of specific embodiments one to seven in that the ellipse equation fitting adopts the least square method.

[0090] The other steps and parameters are the same as those in the first to seventh embodiments.

[0091] According to the quasi-static magnetic field distribution Taking the projection coordinates in the x-axis direction and the projection coordinates in the z-axis direction as an example to fit the ellipse parametric equation of the xoz plane, the specific process of least squares fitting is:

[0092] For magnetic field data B x and B z Sampling is performed, and the following expression is obtained based on the sampling results:

[0093] B x (i) 2 +Para xz1 B z (i) 2 +Para xz2 B x (i)B z (i) = Para xz3 i=1,2,.....,n (14)

[0094] Where n represents the total number of discrete sampling points, so the following equation can be constructed from the above formula:

[0095]

[0096] The ellipse fitting parameter Para can be calculated by the least squares method xz1 、Para xz2 and Para xz3 :

[0097]

[0098] Specific embodiment 9: This embodiment differs from any one of specific embodiments 1 to 8 in that the specific process of step 3 is as follows:

[0099] Step 3: Utilize the target point The magnetic sensor at the location collects the quasi-static magnetic field distribution of the rotating permanent magnet magnetic beacon

[0100]

[0101] Where θ represents the relative azimuth angle between the rotating permanent magnet beacon and the target point, r is the relative distance between the rotating permanent magnet beacon and the target point, is the relative pitch angle between the rotating permanent magnet magnetic beacon and the target point;

[0102] Step 32: Based on the quasi-static magnetic field distribution The projection coordinates in the x-axis direction and the projection coordinates in the z-axis direction fit the ellipse equation of the xoz plane, and the obtained ellipse equation coefficients are related to θ, r and The relationship is:

[0103]

[0104] Among them, Para x ' z1 、Para x ' z2 and Para x ' z3 According to the target point The xoz plane elliptic equation coefficients fitted from the quasi-static magnetic field distribution at;

[0105] Step 3: According to the quasi-static magnetic field distribution The ellipse equation of the yoz plane is fitted with the projection coordinates in the y-axis direction and the projection coordinates in the z-axis direction. The coefficients of the ellipse equation are:

[0106]

[0107] Among them, Para′ yz1 、Para′ yz2 and Para′ yz3 According to the target point The coefficients of the YOZ plane ellipse equation fitted from the quasi-static magnetic field distribution at ;

[0108] Step 3 and 4: Calculate the intermediate variables according to formula (18) and formula (19) Para′ θ and Para′ θ :

[0109]

[0110] Step 35: Para′ θ and Para′ θ Substitute the positioning model constructed in step 2 to calculate the relative azimuth and distance between the rotating permanent magnet beacon and the target point:

[0111]

[0112] The two relative pitch angles calculated in equation (21) are respectively expressed as and Then and Substituting into equation (22), we can get The corresponding relative azimuth angle θ 01 , The corresponding relative azimuth angle θ 02 :

[0113]

[0114] If θ 01 If the relative azimuth angle θ is equal to the one calculated in equation (21), then we can determine is the relative pitch angle between the rotating permanent magnet magnetic beacon and the target point;

[0115] If θ 02 If the relative azimuth angle θ is equal to the one calculated in equation (21), then we can determine is the relative pitch angle between the rotating permanent magnet magnetic beacon and the target point.

[0116] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0117] From the positioning model constructed in step 2, we can know The analytical solution of is a double value, so let’s make the following assumptions:

[0118]

[0119] Will and Substitution In the equation, we can solve the corresponding θ 01 and θ 02 If we assume that θ 01 =θ 02 =θ, then It is as follows about The solution of the system of equations is:

[0120]

[0121] Each equation in formula (24) can be equivalent to a quadratic equation. Since the constant terms and solutions of the three equations are equal, we can get formula (25). At the same time, from formulas (26)-(27), we can know that Para x ' z1 、Para′ yz1 Both are greater than or equal to 0.

[0122] 9sin 2 θ+9Para′ yz1 =9cos 2 θ+9Para x ' z1 =9+9Para′ yz1 +9Para x ' z1 (25)

[0123]

[0124] Because Para x 'z1 、Para′ yz1 are both greater than or equal to 0, so the equal signs in equation (24) cannot hold simultaneously. Therefore, we know that θ 01 ≠θ 02 So the θ obtained by solving equation (21) and θ 01 ,θ 02 Compare (i.e. if θ = θ 01 , then θ 01 Corresponding is the final relative pitch angle, if θ=θ 02 , then θ 02 Corresponding is the final relative pitch angle), which is uniquely determined

[0125] Specific embodiment 10: This embodiment describes an ellipse fitting positioning system based on a rotating permanent magnet magnetic beacon, the system comprising a positioning model construction module and a target position solution module, wherein:

[0126] The positioning model construction module is used to construct a positioning model;

[0127] The specific process of positioning model construction is:

[0128] The rotating permanent magnet magnetic beacon rotates around the z-axis of the three-dimensional rectangular coordinate system at an angular frequency ω. The rotating permanent magnet magnetic beacon is derived from the magnetic dipole model at the measurement point. Quasi-static magnetic field distribution at :

[0129]

[0130] in, Indicates that the rotating permanent magnet magnetic beacon is at the measuring point The quasi-static magnetic field distribution at B x express The projection coordinate in the x-axis direction of the three-dimensional rectangular coordinate system, B y express The projection coordinate in the y-axis direction of the three-dimensional rectangular coordinate system, B z express The projection coordinates in the z-axis direction of the three-dimensional rectangular coordinate system, M represents the magnetic moment of the rotating permanent magnet magnetic beacon, μ0 is the magnetic permeability of the air, r0 is the relative distance between the rotating permanent magnet magnetic beacon and the measuring point, represents the relative pitch angle between the rotating permanent magnet beacon and the measurement point, θ0 represents the relative azimuth angle between the rotating permanent magnet beacon and the measurement point, φ represents the initial phase of the rotating permanent magnet beacon, and t represents time;

[0131] According to the quasi-static magnetic field distribution The projection coordinates in the x-axis direction and the projection coordinates in the z-axis direction fit the ellipse parametric equation of the xoz plane to obtain the ellipse parametric equation coefficients Para of the xoz plane xz1 、Para xz2 and Para xz3 ;

[0132] According to the quasi-static magnetic field distribution The projection coordinates in the y-axis direction and the projection coordinates in the z-axis direction fit the ellipse equation of the yoz plane to obtain the ellipse parameter equation coefficients Para of the yoz plane yz1 、Para yz2 and Para yz3 ;

[0133] The coefficients of the ellipse equation according to the xoz plane are Para xz1 、Para xz2 and Para xz3 Construct column vector Para xz , according to the coefficient of the ellipse equation of the yoz plane Para yz1 、Para yz2 and Para yz3 Construct column vector Para yz , then based on the column vector Para xz and column vector Para yz Construct positioning model:

[0134]

[0135] in, Para θ and Para r All are intermediate variables;

[0136] The target position calculation module is used to calculate the target point position according to the positioning model;

[0137] The working process of the target position solution module is:

[0138] Use target points The magnetic sensor at the location collects the quasi-static magnetic field distribution of the rotating permanent magnet magnetic beacon

[0139]

[0140] Where θ represents the relative azimuth angle between the rotating permanent magnet beacon and the target point, r is the relative distance between the rotating permanent magnet beacon and the target point, is the relative pitch angle between the rotating permanent magnet magnetic beacon and the target point;

[0141] According to the quasi-static magnetic field distribution The projection coordinates in the x-axis direction and the projection coordinates in the z-axis direction are fitted to the ellipse equation of the xoz plane, and the coefficients of the ellipse equation are obtained as follows:

[0142]

[0143] Among them, Para x ' z1 、Para x ' z2 and Para x ' z3 According to the target point The xoz plane elliptic equation coefficients fitted from the quasi-static magnetic field distribution at

[0144] According to the quasi-static magnetic field distribution The ellipse equation of the yoz plane is fitted with the projection coordinates in the y-axis direction and the projection coordinates in the z-axis direction. The coefficients of the ellipse equation are:

[0145]

[0146] Among them, Para′ yz1 、Para′ yz2 and Para′ yz3 According to the target point The coefficients of the YOZ plane ellipse equation fitted from the quasi-static magnetic field distribution at ;

[0147] Calculating intermediate variables Para′ θ and Para′ θ :

[0148]

[0149] Para′ θ and Para′ θ Substitute the constructed positioning model to calculate the relative azimuth and distance between the rotating permanent magnet beacon and the target point:

[0150]

[0151] The two relative pitch angles calculated in equation (34) are respectively expressed as and Then and Substituting into equation (35), we can get The corresponding relative azimuth angle θ 01 , The corresponding relative azimuth angle θ 02 :

[0152]

[0153] If θ 01 is equal to the relative azimuth angle θ calculated in equation (34), then we can determine is the relative pitch angle between the rotating permanent magnet magnetic beacon and the target point;

[0154] If θ 02 is equal to the relative azimuth angle θ calculated in equation (34), then we can determine is the relative pitch angle between the rotating permanent magnet magnetic beacon and the target point.

[0155] Simulation part

[0156] The positioning algorithm based on ellipse fitting of the present invention is simulated and verified, and the method of the present invention is compared with the traditional positioning method based on characteristic vectors. The permanent magnet rotates around the z-axis at a speed of 240 rpm, the magnetic sensor sampling frequency is 5000 Hz, there is an interference magnetic field with a mean of 45000 nT and a white noise with an amplitude of 5 nT, and the magnetic permeability of air is 4π×10 -7 H / m, the simulation results are as follows Figure 4a 、 Figure 4b 、 Figure 5 and Figure 6 shown.

[0157] Simulation results show that the traditional eigenvector method has an average pitch error of 0.125°, an average azimuth error of 0.131°, an average distance error of 0.040m, and an average algorithm solution time of 16.9 milliseconds, while the ellipse fitting method of the present invention has an average pitch error of 0.105°, an average azimuth error of 0.107°, an average distance error of 0.033m, and an average algorithm solution time of 3.9 milliseconds. Therefore, compared with the traditional eigenvector-based positioning algorithm, the ellipse fitting-based positioning algorithm of the present invention improves positioning accuracy and optimizes data processing efficiency.

[0158] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

Claims

1. An ellipse fitting positioning method based on a rotating permanent magnet magnetic beacon, characterized in that: The method specifically comprises the following steps: Step 1: Establish a three-dimensional rectangular coordinate system with the center of the rotating permanent magnet magnetic beacon as the coordinate origin. The rotating permanent magnet magnetic beacon rotates around the z-axis of the three-dimensional rectangular coordinate system at an angular frequency ω. The rotating permanent magnet magnetic beacon is deduced at the measurement point Quasi-static magnetic field distribution at According to the quasi-static magnetic field distribution The projection coordinates in the x-axis direction and the projection coordinates in the z-axis direction are fitted with the ellipse equation of the xoz plane, according to the quasi-static magnetic field distribution The projection coordinates in the y-axis direction and the projection coordinates in the z-axis direction are fitted to the ellipse equation of the yoz plane; Step 2: Construct column vector Para based on the coefficients of the ellipse equation of the xoz plane xz , according to the coefficients of the ellipse equation of the yoz plane, the column vector Para is formed yz , and based on the column vector Para xz and column vector Para yz Construct positioning model; Step 3: Use the target point The magnetic sensor at the target point collects the quasi-static magnetic field distribution of the rotating permanent magnet magnetic beacon and The quasi-static magnetic field distribution at is projected onto the xoz and yoz planes, and then the elliptic equations of the xoz and yoz planes are fitted respectively. The coefficients of the elliptic equations are then substituted into the positioning model constructed in step 2 to calculate the position of the target point.

2. The ellipse fitting positioning method based on a rotating permanent magnet magnetic beacon according to claim 1, characterized in that: The rotating permanent magnet magnetic beacon is at the measuring point Quasi-static magnetic field distribution at for: in, Indicates that the rotating permanent magnet magnetic beacon is at the measuring point The quasi-static magnetic field distribution at B x express The projection coordinate in the x-axis direction of the three-dimensional rectangular coordinate system, B y express The projection coordinate in the y-axis direction of the three-dimensional rectangular coordinate system, B z express The projection coordinates in the z-axis direction of the three-dimensional rectangular coordinate system, M represents the magnetic moment of the rotating permanent magnet magnetic beacon, μ0 is the magnetic permeability of the air, r0 is the relative distance between the rotating permanent magnet magnetic beacon and the measuring point, represents the relative pitch angle between the rotating permanent magnet beacon and the measurement point, θ0 represents the relative azimuth angle between the rotating permanent magnet beacon and the measurement point, represents the initial phase of the rotating permanent magnet magnetic beacon, and t represents time.

3. The ellipse fitting positioning method based on a rotating permanent magnet magnetic beacon according to claim 2, characterized in that: According to the quasi-static magnetic field distribution The projection coordinates in the x-axis direction and the projection coordinates in the z-axis direction fit the ellipse equation of the xoz plane; specifically: For B in formula (2) x and B z Perform ellipse fitting and obtain the fitting equation: B x 2 +For xz1 B z 2 +For xz2 B x B z =For xz3 (3) Among them, the fitting equation coefficient Para xz1 、Para xz2 and Para xz3 They are:

4. The ellipse fitting positioning method based on a rotating permanent magnet magnetic beacon according to claim 3, characterized in that: According to the quasi-static magnetic field distribution The projection coordinates in the y-axis direction and the projection coordinates in the z-axis direction fit the ellipse equation of the yoz plane; specifically: For B in formula (8) y and B z Perform ellipse fitting and obtain the fitting equation: B y 2 +For yz1 B z 2 +For yz2 B y B z =For yz3 (9) Among them, the coefficient of the fitting equation Para yz1 、Para yz2 and Para yz3 They are:

5. The ellipse fitting positioning method based on a rotating permanent magnet magnetic beacon according to claim 4, characterized in that: The column vector Para is formed based on the ellipse equation coefficients of the xoz plane xz , specifically: Among them, Para xz1 、Para xz2 and Para xz3 Both are column vectors Para xz Elements in .

6. The ellipse fitting positioning method based on a rotating permanent magnet magnetic beacon according to claim 5, characterized in that: The column vector Para is formed according to the coefficients of the ellipse equation of the yoz plane yz , specifically: Among them, Para yz1 、Para yz2 and Para yz3 Both are column vectors Para yz Elements in .

7. The ellipse fitting positioning method based on a rotating permanent magnet magnetic beacon according to claim 6, characterized in that: The column-based vector Para xz and column vector Para yz Construct a positioning model; specifically: in, Para θ and Para r All are intermediate variables.

8. The ellipse fitting positioning method based on a rotating permanent magnet magnetic beacon according to claim 7, characterized in that: The ellipse equation fitting adopts the least square method.

9. The ellipse fitting positioning method based on a rotating permanent magnet magnetic beacon according to claim 8, characterized in that: The specific process of step three is: Step 3.

1. Use the target point The magnetic sensor at the location collects the quasi-static magnetic field distribution of the rotating permanent magnet magnetic beacon Where, θ represents the relative azimuth angle between the rotating permanent magnet beacon and the target point, r is the relative distance between the rotating permanent magnet beacon and the target point, is the relative pitch angle between the rotating permanent magnet magnetic beacon and the target point; Step 32: Based on the quasi-static magnetic field distribution The projection coordinates in the x-axis direction and the projection coordinates in the z-axis direction fit the ellipse equation of the xoz plane, and the obtained ellipse equation coefficients are related to θ, r and The relationship is: Among them, Para x ' z1 、Para x ' z2 and Para x ' z3 According to the target point The xoz plane elliptic equation coefficients fitted from the quasi-static magnetic field distribution at; Step 3: According to the quasi-static magnetic field distribution The ellipse equation of the yoz plane is fitted with the projection coordinates in the y-axis direction and the projection coordinates in the z-axis direction, and the coefficients of the ellipse equation are obtained as follows: Among them, Para′ yz1 、Para′ yz2 and Para′ yz3 According to the target point The coefficients of the YOZ plane ellipse equation fitted from the quasi-static magnetic field distribution at ; Step 3 and 4: Calculate the intermediate variables according to formula (18) and formula (19) Para′ θ and Para′ θ : Step 35: Para′ θ and Para′ θ Substitute the positioning model constructed in step 2 to calculate the relative azimuth and distance between the rotating permanent magnet beacon and the target point: The two relative pitch angles calculated in equation (21) are respectively expressed as and Then and Substituting into equation (22), we can get The corresponding relative azimuth angle θ 01 , The corresponding relative azimuth angle θ 02 : If θ 01 If the relative azimuth angle θ is equal to the one calculated in equation (21), then we can determine is the relative pitch angle between the rotating permanent magnet magnetic beacon and the target point; If θ 02 If the relative azimuth angle θ is equal to the one calculated in equation (21), then we can determine is the relative pitch angle between the rotating permanent magnet magnetic beacon and the target point.

10. An ellipse fitting positioning system based on a rotating permanent magnet magnetic beacon, characterized in that: The system includes a positioning model construction module and a target position solution module, wherein: The positioning model construction module is used to construct a positioning model; the specific process of positioning model construction is: The rotating permanent magnet magnetic beacon rotates around the z-axis of the three-dimensional rectangular coordinate system at an angular frequency ω. It is deduced that the rotating permanent magnet magnetic beacon at the measurement point Quasi-static magnetic field distribution at in, Indicates that the rotating permanent magnet magnetic beacon is at the measuring point The quasi-static magnetic field distribution at B x express The projection coordinate in the x-axis direction of the three-dimensional rectangular coordinate system, B y express The projection coordinate in the y-axis direction of the three-dimensional rectangular coordinate system, B z express The projection coordinates in the z-axis direction of the three-dimensional rectangular coordinate system, M represents the magnetic moment of the rotating permanent magnet magnetic beacon, μ0 is the magnetic permeability of the air, r0 is the relative distance between the rotating permanent magnet magnetic beacon and the measuring point, represents the relative pitch angle between the rotating permanent magnet beacon and the measurement point, θ0 represents the relative azimuth angle between the rotating permanent magnet beacon and the measurement point, represents the initial phase of the rotating permanent magnet magnetic beacon, and t represents time; According to the quasi-static magnetic field distribution The projection coordinates in the x-axis direction and the projection coordinates in the z-axis direction fit the ellipse parametric equation of the xoz plane to obtain the ellipse parametric equation coefficients Para of the xoz plane xz1 、Para xz2 and Para xz3 ; According to the quasi-static magnetic field distribution The projection coordinates in the y-axis direction and the projection coordinates in the z-axis direction fit the ellipse equation of the yoz plane to obtain the ellipse parameter equation coefficients Para of the yoz plane yz1 、Para yz2 and Para yz3 ; According to the coefficient of the ellipse equation of the xoz plane Para xz1 、Para xz2 and Para xz3 Construct column vector Para xz , according to the coefficient of the ellipse equation of the yoz plane Para yz1 、Para yz2 and Para yz3 Construct column vector Para yz , then based on the column vector Para xz and column vector Para yz Construct positioning model: in, Para θ and Para r All are intermediate variables; The target position calculation module is used to calculate the target point position according to the positioning model; the working process of the target position calculation module is as follows: Use target points The magnetic sensor at the location collects the quasi-static magnetic field distribution of the rotating permanent magnet magnetic beacon Where, θ represents the relative azimuth angle between the rotating permanent magnet beacon and the target point, r is the relative distance between the rotating permanent magnet beacon and the target point, is the relative pitch angle between the rotating permanent magnet magnetic beacon and the target point; According to the quasi-static magnetic field distribution The projection coordinates in the x-axis direction and the projection coordinates in the z-axis direction are fitted to the ellipse equation of the xoz plane, and the coefficients of the ellipse equation are obtained as follows: Among them, Para x ' z1 、Para x ' z2 and Para x ' z3 According to the target point The xoz plane elliptic equation coefficients fitted from the quasi-static magnetic field distribution at According to the quasi-static magnetic field distribution The ellipse equation of the yoz plane is fitted with the projection coordinates in the y-axis direction and the projection coordinates in the z-axis direction, and the coefficients of the ellipse equation are obtained as follows: Among them, Para′ yz1 、Para′ yz2 and Para′ yz3 According to the target point The coefficients of the YOZ plane ellipse equation fitted from the quasi-static magnetic field distribution at ; Calculate intermediate variables Para′ θ and Para′ θ : Para′ θ and Para′ θ Substitute the constructed positioning model to calculate the relative azimuth and distance between the rotating permanent magnet beacon and the target point: The two relative pitch angles calculated in equation (34) are respectively expressed as and Then and Substituting into equation (35), we can get The corresponding relative azimuth angle θ 01 , The corresponding relative azimuth angle θ 02 : If θ 01 is equal to the relative azimuth angle θ calculated in equation (34), then we can determine is the relative pitch angle between the rotating permanent magnet magnetic beacon and the target point; If θ 02 is equal to the relative azimuth angle θ calculated in equation (34), then we can determine is the relative pitch angle between the rotating permanent magnet magnetic beacon and the target point.

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