Magnetometer calibration method for optimizing ellipsoid fitting based on Pauta criterion

Abstract

The invention discloses a magnetometer calibration method for optimizing ellipsoid fitting based on a Pauta criterion, and the method comprises the steps: S1, constructing a three-axis magnetometer ellipsoid fitting calibration model, so as to solve a magnetometer calibration coefficient matrix and a three-axis magnetometer calibration offset vector; s2, constructing a magnetometer gross error elimination model based on a Pauta criterion to obtain a three-axis magnetometer calibration offset vector subjected to secondary error calibration; s3, acquiring original magnetometer calibration data output by the magnetometer by adopting a splayed correction method; s4, processing the original magnetometer calibration data output by the magnetometer and obtained in the step S3 by using the method in the step S2 to obtain a three-axis magnetometer output vector after secondary error calibration; the magnetometer calibration method is high in reliability, strong in universality, high in algorithm operation efficiency, simple to operate, high in precision and good in practicability.

Description

Technical Field

[0001] The invention relates to the technical field of magnetometer error calibration, and in particular to a magnetometer calibration method based on Laida criterion optimization ellipsoid fitting. Background Art

[0002] The magnetometer is affected by itself and the external environment, resulting in unstable output of magnetometer calibration data. Before using the magnetometer data for magnetic heading calculation, the magnetometer needs to be recalibrated.

[0003] At present, the calibration methods of magnetometers are mainly divided into calibration methods based on ellipsoid fitting and calibration methods based on optimization. For example, the published patent CN112964278B provides a method, device, electronic device and storage medium for determining magnetometer calibration parameters, and calibrates the magnetometer based on the ellipsoid calibration model, but there are gross errors in the magnetometer calibration data collected by this method, and directly fitting the parameters will reduce the final magnetometer calibration accuracy. The published patent CN107656227B provides a magnetometer calibration method based on the Levenberg-Marquardt algorithm, which utilizes the simpler data structure of the magnetometer fitting and has better global quadratic convergence, but the calibration method based on optimization requires higher computing power, which increases the hardware cost of the system in a real-time operating system.

[0004] Therefore, in order to achieve high-precision magnetometer calibration in real-time systems, it is necessary to comprehensively consider the calibration accuracy and algorithm complexity to achieve high-precision magnetometer calibration with low computing power requirements. Summary of the invention

[0005] The purpose of the present invention is to provide a magnetometer calibration method based on the Laida criterion to optimize the ellipsoid fitting, which solves the problems of insufficient calibration accuracy of the existing magnetometer calibration method and excessive calibration algorithm computing power requirements.

[0006] To this end, the technical solution of the present invention is as follows:

[0007] A magnetometer calibration method based on Laida criterion optimization ellipsoid fitting, the steps are as follows:

[0008] S1. Construct a three-axis magnetometer ellipsoid fitting calibration model to solve the magnetometer calibration coefficient matrix S e and the three-axis magnetometer calibration offset vector h e ; Among them, the expression of the three-axis magnetometer ellipsoid fitting calibration model is:

[0009]

[0010] Where A is the ellipsoid fitting coefficient matrix; h e is the calibration offset vector of the three-axis magnetometer; is the actual output vector m of the three-axis magnetometer b The normalized vector of ; are the measured values ​​of the normalized vector of the magnetometer in the x-axis direction, y-axis direction and z-axis direction respectively; a 0 ~a 8 are the ellipsoid coefficients respectively;

[0011] S2. Construct a magnetometer gross error elimination model based on the Laida criterion to obtain a calibration offset vector of a three-axis magnetometer after secondary error calibration; wherein the expression of the magnetometer gross error elimination model based on the Laida criterion includes:

[0012] (1) Normalized three-axis magnetometer output vector m after the first ellipsoid fitting calibration t1 The expression is: m t1 =S e1 -1 (m b1 -h e1 ), where S e1 、m b1 and h e1 Substituting the original magnetometer calibration data into the three-axis magnetometer ellipsoid fitting calibration model in step S1, the calibration coefficient matrix S of the three-axis magnetometer is obtained e , the actual output vector m of the three-axis magnetometer b and the calibration offset vector h of the three-axis magnetometer e ;

[0013] (2) Magnetic vectors with a magnetic vector modulus outside the interval [-3σ, 3σ] are defined as abnormal magnetic vectors, and are removed from the original magnetometer calibration data of the magnetometer to obtain new magnetometer calibration data;

[0014] (3) Normalized three-axis magnetometer output vector m after the second ellipsoid fitting calibration t2 The expression is: m t2 =S e2 -1 (m t1 -h e2 ), where S e2 and h e2 Substitute the new magnetometer calibration data into the three-axis magnetometer ellipsoid fitting calibration model in step S1, and solve the calibration coefficient matrix S of the three-axis magnetometer e and the calibration offset vector h of the three-axis magnetometer e ;

[0015] S3, using the eight-character correction method to collect the original magnetometer calibration data output by the magnetometer;

[0016] S4. Using the method of step S2, the original magnetometer calibration data output by the magnetometer obtained in step S3 is processed to obtain the output vector of the three-axis magnetometer after secondary error calibration.

[0017] Furthermore, in step S1, the actual output normalized vector of the three-axis magnetometer The method for determining is:

[0018] Construct the error model of the three-axis magnetometer, and its expression is:

[0019] m b =S d S p m t +h e =S e m t +h e ,

[0020] In the formula, m b is the actual output vector of the three-axis magnetometer, S d is the scale factor error matrix of the three-axis magnetometer, S p is the soft magnetic error matrix of the three-axis magnetometer, m t is the output vector of the three-axis magnetometer after initial calibration, h e is the calibration offset vector of the three-axis magnetometer, S e is the calibration coefficient matrix of the three-axis magnetometer;

[0021] When the three-axis magnetometer works normally, the actual output vector m of the three-axis magnetometer b The modulus value is related to the local magnetic field m e Equal, the actual output normalized vector of the three-axis magnetometer The expression is:

[0022]

[0023] Furthermore, in step S1, the magnetometer calibration coefficient matrix S e and the three-axis magnetometer calibration offset vector h e The solution is:

[0024] Based on the three-axis magnetometer error model, the constraint relationship of magnetometer error correction is obtained, and its expression is:

[0025]

[0026] Where A is the ellipsoid fitting coefficient matrix, which is consistent with the calibration coefficient matrix S of the three-axis magnetometer e The relational expression is: h eis the calibration offset vector of the three-axis magnetometer, and its relationship with the ellipsoid fitting coefficient matrix A is expressed as:

[0027] The expression of the three-axis magnetometer ellipsoid fitting calibration model is rewritten into a vector form, and its expression is:

[0028]

[0029] Where M is the magnetometer calibration data vector; α is the coefficient vector, which is estimated using the least squares method and is expressed as: α = (M T M) -1 M;

[0030] Then, after solving for each ellipsoid coefficient, the magnetometer calibration coefficient matrix S can be calculated. e and the three-axis magnetometer calibration offset vector h e .

[0031] Furthermore, the specific implementation steps of step S3 are:

[0032] S301, powering on the three-axis magnetometer in a site with less magnetic interference to read and save the original magnetometer calibration data;

[0033] S302, placing the three-axis magnetometer in the air, and taking the current placement position of the three-axis magnetometer as the 0° position, drawing an "8" in the vertical direction, and collecting magnetometer calibration data of the current orientation for 1 minute;

[0034] S303, based on the 0° position of the three-axis magnetometer, the three-axis magnetometer is horizontally rotated clockwise to the 90° position, 180° position and 270° position respectively, and magnetometer calibration data is collected at the three positions in the same manner as step S302.

[0035] Compared with the prior art, the beneficial effect of the magnetometer calibration method based on the Laida criterion for optimizing ellipsoid fitting is that: a magnetometer calibration method based on the Laida criterion for optimizing ellipsoid fitting is provided, which solves the problems of insufficient calibration accuracy and excessive calibration algorithm computing power requirements of the prior magnetometer calibration method; the method first establishes a three-axis magnetometer ellipsoid fitting calibration model, and constructs a magnetometer gross error elimination model based on the Laida criterion to eliminate gross errors from the collected magnetometer calibration data, and then further ellipsoid fitting is performed based on the new magnetometer calibration data after the gross errors are eliminated, and an optimized three-axis magnetometer output vector is obtained based on the calculated magnetometer calibration coefficient matrix and calibration offset vector, and experimental verification shows that the method has high reliability, strong versatility, high algorithm operation efficiency, simple operation, high precision and good practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 The present invention provides a flowchart of a magnetometer calibration method for optimizing ellipsoid fitting based on the Laida criterion.

[0037] Figure 2 A comparison diagram of magnetic field distribution before and after a magnetometer is calibrated using a magnetometer calibration method based on the Laida criterion to optimize ellipsoid fitting provided by the present invention.

[0038] Figure 3 The present invention provides a comparison chart of the module error of a three-axis magnetometer after calibration using a magnetometer calibration method based on Laida criterion optimized ellipsoid fitting and an ellipsoid fitting method. DETAILED DESCRIPTION

[0039] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but the following embodiments are by no means intended to limit the present invention in any way.

[0040] See also Figure 1 The specific implementation steps of the magnetometer calibration method based on the Laida criterion to optimize the ellipsoid fitting are as follows:

[0041] S1. Construct a three-axis magnetometer ellipsoid fitting calibration model to solve the magnetometer calibration coefficient matrix S e and the three-axis magnetometer calibration offset vector h e .

[0042] The specific operation steps of step S1 are:

[0043] S101. Construct an error model of a three-axis magnetometer, which is expressed as follows:

[0044] m b =S d S p m t +h e =S e m t +h e ,

[0045] In the formula, m b is the actual output vector of the three-axis magnetometer, S d is the scale factor error matrix of the three-axis magnetometer, S p is the soft magnetic error matrix of the three-axis magnetometer, m t is the output vector of the three-axis magnetometer after initial calibration, h e is the calibration offset vector of the three-axis magnetometer, S e is the calibration coefficient matrix of the three-axis magnetometer;

[0046] S102, normalize the actual output vector of the three-axis magnetometer:

[0047] When the three-axis magnetometer works normally, the actual output vector m of the three-axis magnetometer is b The modulus value is related to the local magnetic field m e equal, that is, ||m b ||=m e ;

[0048] Furthermore, the actual output vector m of the three-axis magnetometer is b After normalization, the expression is:

[0049]

[0050] In the formula, is the actual output normalized vector of the three-axis magnetometer;

[0051] S103, combining the three-axis magnetometer error model constructed in step S101, obtaining the constraint relationship of magnetometer error correction, which is expressed as:

[0052]

[0053] Where A is the ellipsoid fitting coefficient matrix and satisfies:

[0054] In the actual space, the magnetic data is disturbed by the outside world, and the surface is stretched into an ellipsoid model. Based on this, the expression of the three-axis magnetometer ellipsoid fitting calibration model is:

[0055]

[0056] Where A is the ellipsoid fitting coefficient matrix; h e is the calibration offset vector of the three-axis magnetometer; are the measured values ​​of the normalized vector of the magnetometer in the x-axis direction, y-axis direction and z-axis direction respectively; a 0 ~a 8 are the ellipsoid coefficients respectively;

[0057] In the above expression, the ellipsoid fitting coefficient matrix A and the calibration coefficient matrix S of the three-axis magnetometer are e The relationship is further expanded into:

[0058]

[0059] Ellipsoid fitting coefficient matrix A and calibration offset vector h of the three-axis magnetometer e Satisfies the following expression:

[0060]

[0061] Furthermore, in order to solve the ellipsoid fitting coefficient matrix A and the calibration offset vector h of the three-axis magnetometer e , the quadratic surface equation of the ellipsoid, that is Rewritten in vector form, the expression is:

[0062]

[0063] Where M is the magnetometer data vector, α is the coefficient vector;

[0064] Among them, the coefficient vector α is estimated using the least squares method, and its expression is:

[0065] α=(M T M) -1 M,

[0066] Then, after solving the above equation to obtain the ellipsoid coefficients, the magnetometer calibration coefficient matrix S can be calculated. e and the three-axis magnetometer calibration offset vector h e .

[0067] S2. Construct a magnetometer gross error elimination model based on the Laida criterion to obtain the optimized three-axis magnetometer calibration offset vector through secondary error calibration.

[0068] The specific operation steps of step S2 are:

[0069] S201, calculate the normalized three-axis magnetometer output vector after the first ellipsoid fitting calibration, and its expression is:

[0070] m t1 =S e1 -1 (m b1 -h e1 ),

[0071] In the formula, m t1 S is the normalized output vector of the three-axis magnetometer after the first ellipsoid fitting calibration. e1 is the calibration coefficient matrix of the three-axis magnetometer calculated by ellipsoid fitting, m b1 is the actual output vector of the three-axis magnetometer, h e1 is the calibration offset vector of the three-axis magnetometer calculated by ellipsoid fitting;

[0072] In step S201, S in the above formula e1 、m b1 and h e1 Substituting the original data collected by the magnetometer into the three-axis magnetometer ellipsoid fitting calibration model in step S1, the calibration coefficient matrix S of the three-axis magnetometer is obtained by solving e , the actual output vector m of the three-axis magnetometer band the calibration offset vector h of the three-axis magnetometer e Then, the normalized three-axis magnetometer output vector m after the first ellipsoid fitting calibration is calculated in step S201. t1 , which is the output vector of the three-axis magnetometer obtained after the first error calibration;

[0073] S202, according to the Laida criterion, the abnormal magnetic vector is eliminated; specifically,

[0074] The magnetic vector whose modulus is outside the interval [-3σ, 3σ] is defined as an abnormal magnetic vector, and its expression is:

[0075] m a ∈{norm k ||norm k -1|>3σ},

[0076] In the formula, m a is the abnormal magnetic vector in the calibration data; norm k is the magnetic vector modulus at time k, σ is the standard deviation of the magnetic vector modulus of the calibration data;

[0077] Furthermore, when the modulus of the magnetic vector at any moment is outside the interval [-3σ, 3σ], the magnetic vector at that moment is judged as a gross error point and is removed;

[0078] S203, performing a second ellipsoid fitting on the residual magnetic vector to obtain a normalized three-axis magnetometer output vector after ellipsoid fitting calibration optimized by the Laida criterion; specifically,

[0079] (1) Substitute the residual magnetic vector data processed in step S202 into the three-axis magnetometer ellipsoid fitting calibration model in step S1 to obtain the three-axis magnetometer calibration coefficient matrix S optimized by the Laida criterion e2 and the three-axis magnetometer calibration offset vector h optimized by the Laida criterion e2 ;

[0080] (2) Calculate the normalized output vector of the three-axis magnetometer after the ellipsoid fitting calibration optimized by the Laida criterion, that is, the normalized output vector of the three-axis magnetometer after the second ellipsoid fitting calibration m t2 , whose expression is:

[0081] m t2 =S e2 -1 (m t1 -h e2 ),

[0082] In the formula, m t2 S is the normalized output vector of the triaxial magnetometer after calibration by ellipsoid fitting optimized by the Laida criterion.e2 is the calibration coefficient matrix of the three-axis magnetometer calculated by ellipsoid fitting optimized by the Laida criterion, m t1 is the normalized three-axis magnetometer output vector after the first ellipsoid fitting calibration obtained in step S201, h e2 The calibration offset vector for the three-axis magnetometer calculated by ellipsoid fitting optimized by the Laida criterion.

[0083] S3. Use the eight-character correction method to collect the original data output by the magnetometer.

[0084] The specific operation steps of step S3 are:

[0085] S301, powering on the three-axis magnetometer in a place with less magnetic interference to read and save data;

[0086] S302, placing the three-axis magnetometer in the air, and taking the current placement position of the three-axis magnetometer as the 0° position, drawing an "8" in the vertical direction, and collecting magnetometer calibration data of the current orientation for 1 minute;

[0087] S303, based on the 0° position of the three-axis magnetometer, the three-axis magnetometer is horizontally rotated in the clockwise direction to the 90° position, the 180° position and the 270° position, and the magnetometer calibration data is collected at the three positions in the same manner as step S302, that is, the magnetometer calibration data of the current orientation is collected for 1 minute during the process of the three-axis magnetometer drawing an "8" in the vertical direction;

[0088] Through the above steps S301 to S303, magnetometer calibration data of the three-axis magnetometer in four directions are collected in total, so that all the collected magnetometer calibration data can be approximately distributed on an ellipsoid.

[0089] S4, using the method of step S2 to process the raw data of the magnetometer output obtained in step S3, and through secondary error calibration, obtain the normalized three-axis magnetometer output vector m after ellipsoid fitting calibration optimized by the Laida criterion t2 , to achieve error compensation for the magnetometer.

[0090] Furthermore, in order to verify the effectiveness of the method of the present invention on the magnetometer calibration effect, a practical test was carried out. The performance parameters of the magnetometer in the experiment are listed in Table 1.

[0091] Table 1:

[0092] index Range noise Nonlinear Resolution parameter ±8Gs 1mGs 0.2％ 0.25mGs

[0093] Three sets of repeated actual measurement experiments were carried out using the calibration data collected by the magnetometer corresponding to Table 1. Then, the magnetometer was calibrated using the method of the present invention and the classical ellipsoid fitting calibration method, and the calibration effects were compared by calculating the modulus error; wherein the modulus error is the difference between the modulus of the output vector of the three-axis magnetometer after calibration and the ideal static normalized modulus: ||m t2 ||-1.

[0094] like Figure 2 The magnetic field distribution diagrams are shown in one group of experiments before and after the data are calibrated using the method of the present invention; Figure 2 It can be clearly seen that the magnetometer error caused by the calibration offset vector of the magnetometer has been effectively compensated. Figure 3 The figure shows the comparison of the modulus error of the three-axis magnetometer after calibration using the ellipsoid fitting and the method proposed by the present invention in the same group of experiments; Figure 3 It can be clearly seen that the magnetometer calibration method of the present invention has a lower three-axis magnetometer modulus error than the traditional ellipsoid fitting magnetometer calibration method. It can be seen that the calibration method of the present application has a better magnetometer error compensation effect.

[0095] The comparison of the standard deviation of the modulus error of the three-axis magnetometer calibrated by the two methods is shown in Table 2.

[0096] Table 2:

[0097]

[0098] From the comparison results of the standard deviation of the modulus error of the three-axis magnetometer after calibration in Table 2, it can be seen that the method provided by the present invention can achieve higher-precision magnetometer calibration. Compared with the traditional ellipsoid fitting magnetometer calibration method, the standard deviation of the modulus error of the three-axis magnetometer after calibration is reduced by about 25%, which effectively compensates for the error of the magnetometer. It can be seen that the method of the present invention is effective and correct in the magnetometer calibration effect, and has higher calibration accuracy than the traditional ellipsoid fitting calibration method.

[0099] Parts of the present invention that are not disclosed in detail belong to the common knowledge in the art. Although the above describes the illustrative specific embodiments of the present invention to facilitate the understanding of the present invention by those skilled in the art, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention defined and determined by the attached claims, these changes are obvious, and all inventions and creations using the concept of the present invention are protected.

Claims

1. A magnetometer calibration method based on Laida criterion optimization ellipsoid fitting, characterized in that: Here are the steps: S1. Construct a three-axis magnetometer ellipsoid fitting calibration model to solve the magnetometer calibration coefficient matrix S e and the three-axis magnetometer calibration offset vector h e ; Among them, the expression of the three-axis magnetometer ellipsoid fitting calibration model is: Where A is the ellipsoid fitting coefficient matrix; h e is the calibration offset vector of the three-axis magnetometer; is the actual output vector m of the three-axis magnetometer b The normalized vector of ; are the measured values ​​of the normalized vector of the magnetometer in the x-axis direction, y-axis direction and z-axis direction respectively; a0~a8 are the ellipsoid coefficients respectively; S2. Construct a magnetometer gross error elimination model based on the Laida criterion to obtain a calibration offset vector of a three-axis magnetometer after secondary error calibration; wherein the expression of the magnetometer gross error elimination model based on the Laida criterion includes: (1) Normalized three-axis magnetometer output vector m after the first ellipsoid fitting calibration t1 The expression is: m t1 =S e1 -1 (m b1 -h e1 ), where S e1 、m b1 and h e1 Substituting the original magnetometer calibration data into the three-axis magnetometer ellipsoid fitting calibration model in step S1, the calibration coefficient matrix S of the three-axis magnetometer is obtained by solving e , the actual output vector m of the three-axis magnetometer b and the calibration offset vector h of the three-axis magnetometer e ; (2) Magnetic vectors with a magnetic vector modulus outside the interval [-3σ, 3σ] are defined as abnormal magnetic vectors, and are removed from the original magnetometer calibration data of the magnetometer to obtain new magnetometer calibration data; (3) Normalized three-axis magnetometer output vector m after the second ellipsoid fitting calibration t2 The expression is: m t2 =S e2 -1 (m t1 -h e2 ), where S e2 and h e2 Substitute the new magnetometer calibration data into the three-axis magnetometer ellipsoid fitting calibration model in step S1, and solve the calibration coefficient matrix S of the three-axis magnetometer e and the calibration offset vector h of the three-axis magnetometer e ; S3, using the eight-character correction method to collect the original magnetometer calibration data output by the magnetometer; S4. Using the method of step S2, the original magnetometer calibration data output by the magnetometer obtained in step S3 is processed to obtain the output vector of the three-axis magnetometer after secondary error calibration.

2. The magnetometer calibration method based on Laida criterion optimization ellipsoid fitting according to claim 1 is characterized in that: In step S1, the actual output normalized vector of the three-axis magnetometer is The method to determine is: Construct the error model of the three-axis magnetometer, and its expression is: m b =S d S p m t +h e =S e m t +h e , In the formula, m b is the actual output vector of the three-axis magnetometer, S d is the scale factor error matrix of the three-axis magnetometer, S p is the soft magnetic error matrix of the three-axis magnetometer, m t is the output vector of the three-axis magnetometer after initial calibration, h e is the calibration offset vector of the three-axis magnetometer, S e is the calibration coefficient matrix of the three-axis magnetometer; When the three-axis magnetometer works normally, the actual output vector m of the three-axis magnetometer b The modulus of the local magnetic field m e Equal, the actual output normalized vector of the three-axis magnetometer The expression is:

3. The magnetometer calibration method based on Laida criterion optimization ellipsoid fitting according to claim 2 is characterized in that: In step S1, the magnetometer calibration coefficient matrix S e and the three-axis magnetometer calibration offset vector h e The solution is: Based on the three-axis magnetometer error model, the constraint relationship of magnetometer error correction is obtained, and its expression is: Where A is the ellipsoid fitting coefficient matrix, which is consistent with the calibration coefficient matrix S of the three-axis magnetometer e The relational expression is: h e is the calibration offset vector of the three-axis magnetometer, and its relationship with the ellipsoid fitting coefficient matrix A is expressed as: The expression of the three-axis magnetometer ellipsoid fitting calibration model is rewritten into a vector form, and its expression is: Where M is the magnetometer calibration data vector; α is the coefficient vector, which is estimated using the least squares method and is expressed as: α = (M T M) -1 M; Then, after solving for each ellipsoid coefficient, the magnetometer calibration coefficient matrix S can be calculated. e and the three-axis magnetometer calibration offset vector h e .

4. The magnetometer calibration method based on Laida criterion optimization ellipsoid fitting according to claim 1, characterized in that: The specific implementation steps of step S3 are: S301, powering on the three-axis magnetometer in a site with less magnetic interference to read and save the magnetometer calibration data; S302, placing the three-axis magnetometer in the air, and taking the current placement position of the three-axis magnetometer as the 0° position, drawing an "8" in the vertical direction, and collecting magnetometer calibration data of the current orientation for 1 minute; S303, based on the 0° position of the three-axis magnetometer, the three-axis magnetometer is horizontally rotated clockwise to the 90° position, 180° position and 270° position respectively, and magnetometer calibration data is collected at the three positions in the same manner as step S302.

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