A magnetometer calibration method based on Laida criterion optimized ellipsoid fitting

Abstract

The invention discloses a magnetometer calibration method based on the Laida criterion optimized ellipsoid fitting, which comprises the following steps: S1, constructing a three-axis magnetometer ellipsoid fitting calibration model to obtain a magnetometer calibration coefficient matrix and a three-axis magnetometer calibration offset vector; S2, constructing a magnetometer gross error elimination model based on the Laida criterion to obtain a three-axis magnetometer calibration offset vector that has undergone quadratic error calibration; S3, adopting an eight-character correction method to collect original magnetometer calibration data output by the magnetometer; S4, adopting the method in step S2 to process the original magnetometer calibration data output by the magnetometer obtained in step S3 to obtain a three-axis magnetometer output vector that has undergone quadratic error calibration. The magnetometer calibration method has high reliability, strong versatility, high algorithm operation efficiency, simple operation, high precision and good practicality.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetometer error calibration, and in particular to a magnetometer calibration method based on Laida criterion optimized 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 magnetometer data for magnetic heading calculation, the magnetometer must be recalibrated.

[0003] Currently, magnetometer calibration methods 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. The magnetometer is calibrated based on an ellipsoid calibration model. However, the magnetometer calibration data collected by this method contains gross errors, and directly performing parameter fitting will reduce the final magnetometer calibration accuracy. The published patent CN107656227B provides a magnetometer calibration method based on the Levenberg-Marquardt algorithm. This method takes advantage of the simpler data structure of the magnetometer fitting and has good global quadratic convergence. However, the optimization-based calibration method 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 and excessive calibration algorithm computing power requirements of existing magnetometer calibration methods.

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

[0007] A magnetometer calibration method based on the Laida criterion to optimize the 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; a0~a8 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 the three-axis magnetometer after quadratic error calibration. 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 Substitute the original magnetometer calibration data into the three-axis magnetometer ellipsoid fitting calibration model in step S1, and calculate the calibration coefficient matrix S of the three-axis magnetometer 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) Define the magnetic vector whose modulus value is outside the interval [-3σ, 3σ] as an abnormal magnetic vector and remove it from the original magnetometer calibration data 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 calculate 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. Process the original magnetometer calibration data output by the magnetometer obtained in step S3 using the method of step S2 to obtain a three-axis magnetometer output vector after secondary error calibration.

[0017] Furthermore, in step S1, the actual output normalized vector of the three-axis magnetometer is 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] Where m b is the actual output vector of the three-axis magnetometer, S d is the scale coefficient 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] According to the actual output vector m of the three-axis magnetometer when it works normally, b The modulus of 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 follows:

[0027] The expression of the three-axis magnetometer ellipsoid fitting calibration model is rewritten into 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 the ellipsoid coefficients, 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 location with less magnetic interference to read and save original magnetometer calibration data;

[0033] S302: Place the three-axis magnetometer in the air, and draw an "8" in the vertical direction with the current placement position of the three-axis magnetometer as the 0° position, and collect 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 rotated horizontally in a clockwise direction to the 90° position, the 180° position, and the 270° position, and magnetometer calibration data is collected at the three positions in the same manner as step S302.

[0035] Compared with the existing technology, the magnetometer calibration method based on the Laida criterion for optimizing ellipsoid fitting has the following beneficial effects: providing a magnetometer calibration method based on the Laida criterion for optimizing ellipsoid fitting, solving the problems of insufficient calibration accuracy and excessive calibration algorithm computing power requirements of the existing 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, 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 based on the Laida criterion to optimize the ellipsoid fitting.

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

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

[0039] The present invention will be further described below with reference to 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 optimization 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 the 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] Where m b is the actual output vector of the three-axis magnetometer, S d is the scale coefficient 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 of 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] Where, is the actual output normalized vector of the three-axis magnetometer;

[0051] S103: Combine the three-axis magnetometer error model constructed in step S101 to obtain the constraint relationship for magnetometer error correction, which is expressed as follows:

[0052]

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

[0054] In real space, magnetic data is subject to external interference, 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; a0~a8 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 quadratic 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, the expression of which is:

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

[0071] Where m t1 is the normalized three-axis magnetometer output vector after the first ellipsoid fitting calibration, S 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 three-axis magnetometer calibration offset vector calculated by ellipsoid fitting;

[0072] In step S201, S in the above formula e1 、m b1 and h e1 Substitute the original data collected by the magnetometer into the three-axis magnetometer ellipsoid fitting calibration model in step S1, and calculate the calibration coefficient matrix S of the three-axis magnetometer 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 , that is, the output vector of the three-axis magnetometer obtained after the first error calibration;

[0073] S202, according to the Laida criterion, remove abnormal magnetic vectors; 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] Where 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 eliminated;

[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 triaxial magnetometer output vector after ellipsoid fitting calibration optimized by the Laida criterion, that is, the normalized triaxial magnetometer output vector m after the second ellipsoid fitting calibration t2 , whose expression is:

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

[0082] Where m t2 S is the normalized output vector of the three-axis magnetometer after calibration by the 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 raw data output by the magnetometer.

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

[0085] S301. Power on the three-axis magnetometer in a location with less magnetic interference to read and save data.

[0086] S302: Place the three-axis magnetometer in the air, and draw an "8" in the vertical direction with the current placement position of the three-axis magnetometer as the 0° position, and collect 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 rotated horizontally in a clockwise direction to 90°, 180°, and 270° positions, respectively. At each of the three positions, magnetometer calibration data is collected in the same manner as in step S302. That is, magnetometer calibration data of the current orientation is collected for 1 minute while the three-axis magnetometer draws 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, so that all 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 quadratic 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 calibration effect of the magnetometer, a practical experiment 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 field measurements were performed using the calibration data collected from the magnetometers corresponding to Table 1. The magnetometers were then calibrated using the method of the present invention and the classic ellipsoid fitting calibration method. The calibration results were compared by calculating the modulus error. 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: t2 ||-1.

[0094] like Figure 2 The figure shows the magnetic field distribution diagrams before and after the data are calibrated using the method of the present invention in one set of experiments; 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 method 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 after calibration using 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%, effectively compensating 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] Portions of the present invention not disclosed in detail are known in the art. Although the above description of illustrative embodiments of the present invention is intended to facilitate understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the specific embodiments. As long as various modifications are obvious to those skilled in the art within the spirit and scope of the present invention as defined and determined by the appended claims, all inventions and creations utilizing the concepts 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 the three-axis magnetometer after quadratic error calibration. 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 Substitute the original magnetometer calibration data into the three-axis magnetometer ellipsoid fitting calibration model in step S1, and calculate the calibration coefficient matrix S of the three-axis magnetometer 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) Define the magnetic vector whose modulus value is outside the interval [-3σ, 3σ] as an abnormal magnetic vector and remove it from the original magnetometer calibration data 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 calculate 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. Process the original magnetometer calibration data output by the magnetometer obtained in step S3 using the method of step S2 to obtain a three-axis magnetometer output vector after secondary error calibration.

2. The magnetometer calibration method based on Laida criterion optimization ellipsoid fitting according to claim 1, characterized in that: In step S1, the actual output normalized vector of the three-axis magnetometer The method for determining 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 , Where m b is the actual output vector of the three-axis magnetometer, S d is the scale coefficient 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; According to the actual output vector m of the three-axis magnetometer when it works normally, 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, 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 follows: The expression of the three-axis magnetometer ellipsoid fitting calibration model is rewritten into 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 the ellipsoid coefficients, 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 location with less magnetic interference to read and save magnetometer calibration data; S302: Place the three-axis magnetometer in the air, draw an "8" in the vertical direction with the current placement position of the three-axis magnetometer as the 0° position, and collect 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 rotated horizontally in a clockwise direction to the 90° position, the 180° position, and the 270° position, and magnetometer calibration data is collected at the three positions in the same manner as step S302.

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