CN113866688B - Error calibration method for three-axis magnetic sensor under condition of small attitude angle - Google Patents
Error calibration method for three-axis magnetic sensor under condition of small attitude angle Download PDFInfo
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Abstract
The invention discloses an error calibration method of a triaxial magnetic sensor under the condition of a small attitude angle, wherein the triaxial magnetic sensor has three errors of triaxial nonorthogonal, inconsistent sensitivity and zero drift due to the imperfect current manufacturing process; the traditional scalar calibration method needs to rotate a sensor along three sensitive axes in a large-range angle, record output values of the sensor under each posture in real time, and then use collected data and an established model to finish calibration. However, when the range of the attitude change of the sensor is limited, it is difficult to achieve a desired calibration effect using the conventional method. The invention establishes an error combined calibration model based on the total geomagnetic level and the vertical component by combining the attitude information of the sensor, adopts an optimization algorithm, and can still accurately solve error parameters when the attitude of the sensor is variable within a small range so as to finish the error calibration of the sensor.
Description
Technical Field
The invention belongs to the technical field of sensors, and particularly relates to an error calibration method for a three-axis magnetic sensor.
Background
The currently more common error calibration method for the three-axis magnetic sensor in practice is based on the principle that the modulus of the magnetic field vector at one point in space is not changed, i.e. scalar calibration. This method requires, when executed, a number of extensive changes of the attitude of the sensor (specifically operating with a number of rotations of the sensor along its three sensitive axes) and recording the magnetic field data of the sensor in each attitude. And then, estimating error parameters by using the data and the established error model, and finally compensating the acquired data by using the solved error parameters to finish calibration. However, when the magnetic sensor is installed on a large-scale motion platform such as a ship, an airplane or an aircraft, it is particularly difficult to change the attitude angle of the carrier, particularly the pitch angle and the roll angle, in a large range, and only a small range of change can be performed. This results in a large correlation of the acquired magnetic field data, and if the estimated parameters are trained using these strongly correlated data, the calibration effect will deviate significantly from the ideal. Aiming at the problems existing in the method, the general solution idea is to project the acquired data to a horizontal plane by combining with the attitude information of the magnetic sensor, and then obtain error parameters by utilizing ellipse fitting, wherein the calibration model is called as a two-dimensional total amount model. However, since the measured magnetic field value contains noise and changes with the change of the yaw angle, the combination of the measured magnetic field value and the zero offset cannot be regarded as a constant in the model, and therefore, even if the roll and the yaw angle are fixed by the training sample, the LM or PSO method adopted by the model cannot achieve a good effect for the two-dimensional total quantity model.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides an error calibration method of a three-axis magnetic sensor under the condition of a small attitude angle, wherein three errors of three-axis non-orthogonality, inconsistent sensitivity and zero drift exist in the three-axis magnetic sensor due to the imperfect current manufacturing process; the traditional scalar calibration method needs to rotate a sensor along three sensitive axes in a large range of angles, record output values of the sensor under each posture in real time, and then use collected data and an established model to finish calibration. However, when the range of the attitude change of the sensor is limited, it is difficult to achieve a desired calibration effect using the conventional method. The invention establishes an error joint calibration model based on the geomagnetic horizontal total quantity and the vertical component by combining the attitude information of the sensor, and adopts an optimization algorithm, so that when the attitude of the sensor is variable in a small range, error parameters can be accurately solved, and the error calibration of the sensor is completed.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: establishing an error model:
factors influencing the measurement accuracy of the three-axis magnetic sensor comprise three errors of three-axis non-orthogonality, inconsistent scale factors and zero offset;
step 1-1: the non-orthogonal error is expressed in that the actual sensitive axes of the three-axis magnetic sensor are not completely orthogonal in pairs due to the limitation of the manufacturing process;
defining O-XYZ to represent an ideal orthogonal coordinate system; defining O-X ' Y ' Z ' as a coordinate system where three sensitive axes of the actual three-axis magnetic sensor are located, and the coordinate system is called as a sensor coordinate system;
suppose that: (1) The OZ' axis of the sensor coordinate system is coincident with the OZ axis of the ideal orthogonal coordinate system; (2) A Z ' OY ' plane of a sensor coordinate system is coplanar with a ZOY plane of an ideal orthogonal coordinate system, and an included angle between an OY ' axis and an OY axis is alpha; (3) The OX ' axis of the sensor coordinate system deviates downwards from the XOY plane, OX ' is defined as the projection of OX ' on the XOY plane, the included angle between the OX ' axis and the sensor coordinate system is beta, and the included angle between the OX ' axis and the OX axis of the ideal orthogonal coordinate system is gamma;
the relationship between the ideal orthogonal coordinate system and the sensor coordinate system is expressed as:
step 1-2: the inconsistent scale factors show that when the three components of the magnetic field are the same, the magnetic field values output by the three shafts of the three-shaft magnetic sensor are different in size and can be represented by a theoretical value multiplied by a diagonal matrix;
step 1-3: the zero offset is represented by that the three axes have zero offset due to the residual magnetism of the magnetic core, the drift of the amplifying and conditioning part of the internal circuit and the external temperature change factors, so that different magnetic fields can be superposed and fixed in the three-axis direction when the three-axis magnetic sensor is used for measurement;
step 1-4: when the three errors are comprehensively considered, the relationship between the actual output value and the theoretical value of the three-axis magnetic sensor is expressed as follows:
B m ＝RB+b p (2)
wherein, B = [ B = x ,B y ,B z ]For an ideal magnetic field value, B m ＝[B mx ,B my ,B mz ]Magnetic field values, error matrix for actual three-axis magnetic sensor output
k x k y And k z Scale factors representing three axes, respectively, b p ＝[b x b y b z ] T Zero offset error for a three-axis magnetic sensor;
further derivation yields a true error-free magnetic field representation as:
B＝R'(B m -b p ) (3)
wherein R' is the inverse of the error matrix R and is an upper triangular matrix;
and 2, step: establishing a geomagnetic model;
establishing a geographic coordinate system: the coordinate origin is located at the intersection point of a connecting line of a carrier provided with the three-axis magnetic sensor and the earth center and the earth surface, the x axis points to the geographical north, the y axis points to the geographical east, and the z axis points to the earth center vertically; the projections of the earth magnetic field intensity T on the x, y and z axes are respectively north components B N East component B E And a vertical component B D ，B H D and I are respectively a geomagnetic declination and a geomagnetic inclination; t, B N 、B E 、B D 、B H D and I are collectively called as seven elements of the geomagnetic field, and the magnetic field value of any point on the earth surface is described and expressed by seven elements of the geomagnetic field;
the relationship between seven elements of geomagnetism is expressed as:
and step 3: establishing an error calibration model of a three-axis magnetic sensor;
when triaxial magnetic sensor error calibration is performed using the geomagnetic field, equation (3) is written as:
in the formula (I), the compound is shown in the specification,
is the geomagnetic field value in the sensor coordinate system;
the conversion relation between the geographical coordinate system and the sensor coordinate system is described by the connected multiplication of the attitude matrix, so that
Expressed as:
wherein
Gamma, theta and psi are roll, pitch and yaw, respectively; .
Continuing with the derivation formula (6) to obtain:
wherein ψ' = ψ -D,
k 11 ，k 12 …k 33 the matrix K is an element of the matrix K, and the matrix K can change along with the change of the roll angle and the pitch angle and is not an upper triangular or symmetrical matrix any more;
when the output values of N ≧ 12 groups of sensors under different postures are known, equation (7) is converted into a multi-objective function problem:
wherein the variable having the superscript ^' represents the geomagnetic field component represented by the formula (8), B H And B D Respectively representing the horizontal component modulus and the vertical component of the local real geomagnetic field;
and 4, step 4: estimating parameters;
estimating error parameters by adopting an optimization algorithm according to the established error estimation model formula (8);
and 5: and (5) compensating the magnetic field value with the error by using the parameter solved in the step (4) to finish calibration.
Preferably, the horizontal component module and the vertical component of the local real geomagnetic field in the step 3 can be obtained according to a world magnetic field model, and the average value of the measured values is used as a substitute in the experiment.
Preferably, the optimization algorithm in the step 5 is a Levenberg Marquardt algorithm or a particle swarm algorithm.
The invention has the following beneficial effects:
1. under the condition of a small range of attitude angles (the variation range of the pitch angle and the roll angle is less than +/-15 degrees), the method can still accurately estimate error parameters, and is more suitable for error correction of airborne or shipborne triaxial magnetic sensors compared with the existing large-scale calibration method based on the total magnetic field.
2. Compared with a two-dimensional total amount calibration method (magnetic field values are projected to a horizontal plane by using a known attitude angle, and then ellipse fitting is carried out to solve error parameters), the method provided by the invention has a better calibration effect.
Drawings
Fig. 1 is a non-orthogonal error model of a three-axis fluxgate sensor.
FIG. 2 is a diagram of geomagnetic elements in accordance with the present invention.
FIG. 3 is a diagram comparing a conventional method with the method of the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
In order to solve the problem that the existing magnetic field total amount calibration method based on the total amount cannot accurately estimate error parameters due to strong correlation among data when the change range of an attitude angle is limited, the invention provides a mixed calibration method based on the horizontal total amount and the vertical component of a magnetic field by combining pitching information and rolling information.
A method for calibrating errors of a three-axis magnetic sensor under the condition of a small attitude angle comprises the following steps:
step 1: establishing an error model:
factors influencing the measurement accuracy of the three-axis magnetic sensor comprise three errors of three-axis non-orthogonality, inconsistent scale factors and zero offset;
step 1-1: the non-orthogonal error is expressed in that the actual sensitive axes of the three-axis magnetic sensor are not completely orthogonal in pairs due to the limitation of the manufacturing process;
FIG. 1 shows a model diagram of non-orthogonal errors of a three-axis fluxgate sensor, defining O-XYZ to represent an ideal orthogonal coordinate system; defining O-X ' Y ' Z ' as a coordinate system of three sensitive axes of the actual three-axis magnetic sensor, and calling the coordinate system as a sensor coordinate system;
suppose that: (1) The OZ' axis of the sensor coordinate system is coincident with the OZ axis of the ideal orthogonal coordinate system; (2) A Z ' OY ' plane of a sensor coordinate system is coplanar with a ZOY plane of an ideal orthogonal coordinate system, and an included angle between an OY ' axis and an OY axis is alpha; (3) The OX ' axis of the sensor coordinate system deviates downwards from the XOY plane, OX ' is defined as the projection of OX ' on the XOY plane, the included angle between the OX ' axis and the sensor coordinate system is beta, and the included angle between the OX ' axis and the OX axis of the ideal orthogonal coordinate system is gamma;
the relationship between the ideal orthogonal coordinate system and the sensor coordinate system is expressed as:
step 1-2: the inconsistent scale factors show that when the three components of the magnetic field are the same, the magnetic field values output by the three shafts of the three-shaft magnetic sensor are different in size and can be represented by a theoretical value multiplied by a diagonal matrix;
step 1-3: the zero offset is represented by that the three axes have zero offset due to the residual magnetism of the magnetic core, the drift of the amplifying and conditioning part of the internal circuit and the external temperature change factors, so that different magnetic fields can be superposed and fixed in the three-axis direction when the three-axis magnetic sensor is used for measurement;
step 1-4: when the three errors are comprehensively considered, the relationship between the actual output value and the theoretical value of the three-axis magnetic sensor is expressed as follows:
B m ＝RB+b p (2)
wherein, B = [ B = x ,B y ,B z ]Ideal magnetic field value, B m ＝[B mx ,B my ,B mz ]Magnetic field values, error matrix for actual three-axis magnetic sensor output
k x k y And k z Scale factors representing three axes, respectively, b p ＝[b x b y b z ] T Zero offset error of the three-axis magnetic sensor;
further derivation yields a true error-free magnetic field representation as:
B＝R'(B m -b p ) (3)
wherein R' is the inverse of the error matrix R and is an upper triangular matrix; 6 elements for solving R' accurately and b p The 3 elements of the vector are the key to the magnetic sensor error calibration problem. The invention establishes a new error solving model, so that the 9 parameters can be accurately estimated even under the condition of a small-range attitude angle.
And 2, step: establishing a geomagnetic model;
the invention utilizes the earth magnetic field to carry out error calibration. As shown in fig. 2, a geographical coordinate system is established: the origin of coordinates is located at the intersection point of a connecting line of the carrier and the earth center and the earth surface, the x axis points to the geographical north, the y axis points to the geographical east, and the z axis points to the earth center vertically; the projections of the earth magnetic field intensity T on the x, y and z axes are north direction components B respectively N East component B E And a vertical component B D ，B H D and I are respectively a geomagnetic declination angle and a geomagnetic inclination angle; t, B N 、B E 、B D 、B H D and I are collectively called as seven elements of the geomagnetic field, and the magnetic field value of any point on the earth surface is described and expressed by seven elements of the geomagnetic field;
the relationship between seven elements of geomagnetism is expressed as:
and step 3: establishing an error calibration model of a three-axis magnetic sensor;
when using the geomagnetic field to perform error calibration of the three-axis magnetic sensor, equation (3) is written as:
in the formula (I), the compound is shown in the specification,
is the geomagnetic field value in the sensor coordinate system;
the transformation relationship between the geographic coordinate system and the sensor coordinate system is described by a connected multiplication of the attitude matrix, so that
Expressed as:
wherein
Gamma, theta and psi are roll, pitch and yaw, respectively; .
Continuing with the derivation formula (6) to obtain:
wherein ψ' = ψ -D,
k 11 ，k 12 …k 33 the matrix K is an element of the matrix K, and the matrix K can change along with the change of the roll angle and the pitch angle and is not an upper triangular or symmetrical matrix any more;
when the output values of N ≧ 12 groups of sensors under different postures are known, equation (7) is converted into a multi-objective function problem:
wherein the variable having the superscript ^' represents the geomagnetic field component represented by the formula (8), B H And B D The horizontal and vertical components, respectively, representing the local true earth magnetic field, can be obtained from the World Magnetic Model (WMM), and the average of the measurements is used as a substitute in the experiment.
And 4, step 4: estimating parameters;
according to the established error estimation model formula (8), a proper optimization algorithm (such as a Levenberg Marquardt algorithm, a particle swarm optimization algorithm and the like) is selected to estimate error parameters (6 elements of R' and b) p 3 elements of the vector).
And 5: and (5) compensating the magnetic field value with the error by using the parameter solved in the step (4) to finish calibration.
The specific embodiment is as follows:
1. example data preparation
The present embodiment considers a scenario in which errors of a three-axis magnetic sensor are calibrated in the context of a geomagnetic field, assuming that the total geomagnetic field is 48000nT, and the geomagnetic declination angle D and the inclination angle I are-5 ° and 5 °, respectively. Error matrix containing quadrature error and scale factor
Zero offset is set as b p ＝[2000 3000 4000] T . According to the settingThe parametric simulation of (1) yields earth magnetic field values for 20 sets of sensors theoretically error-free and actually measured with errors at different attitudes, wherein the pitch and roll angle variation ranges of the sensors are limited to within ± 15 ° to simulate the case of a small range of attitude angles. The structure formula of the earth magnetic field component theoretical value is as follows:
the output value of the actual magnetic sensor is constructed by the formula:
2. estimating error parameters according to the model provided by the invention;
the generated magnetic field data is brought into the established objective function,
the 6 elements of R' and b are estimated by using the Levenberg Marquardt algorithm p 3 elements of the vector. In order to show that the method provided by the invention has better calibration effect than a total amount-based method, the generated magnetic field data is simultaneously brought into a three-dimensional total amount method, and a communicated parameter solving algorithm is adopted to carry out error parameter estimation and comparison. To quantitatively compare the merits of the two methods, the error parameters estimated by the two methods are averaged for absolute deviation (MAD), which is defined as:
wherein x is i Represents the set R' and b p Value, c i Representing the values estimated by both models. Table 1 gives the MAD values for both methods.
TABLE 1 comparison of error calibration results for two methods
As can be seen from table 1, the MAD of the error parameters obtained by the method proposed by the present invention is small, while the large MAD of the parameters obtained by the total-amount-based calibration method indicates that the estimated parameters deviate significantly from the true values.
3. Test data error calibration
And (3) according to the simulation data set in the step 1, constructing 360 groups of test data under any posture, and correcting the 360 groups of test data by using the error parameters estimated by the two methods in the step 2. The correction formula is as follows: b = R' (B) m -b p ). The data before and after correction are plotted to compare the calibration effect (as shown in fig. 3). As can be seen from the figure, the magnetic field values (indicated by the lines marked with an "x" in the figure) actually output by the magnetic sensor deviate significantly from the true values (indicated by the straight lines in the figure) when the attitude of the sensor changes due to the presence of errors. The fluctuation range of the magnetic field component calibrated by the two methods is reduced, particularly, the magnetic field component (shown by a line with an "o" mark in the figure) calibrated by the method provided by the invention is very close to a theoretical value, and the calibration effect of the traditional method based on the total amount under the condition of a small range of attitude angles is obviously reduced. The result of the embodiment shows that the calibration method provided by the invention still has good error calibration capability under the condition of limited change range of the attitude angle of the sensor.
Claims (3)
1. A method for calibrating errors of a three-axis magnetic sensor under a small attitude angle condition is characterized by comprising the following steps:
step 1: establishing an error model:
factors influencing the measurement accuracy of the three-axis magnetic sensor comprise three errors of three-axis non-orthogonality, inconsistent scale factors and zero offset;
step 1-1: the non-orthogonal error is expressed in that the actual sensitive axes of the three-axis magnetic sensor are not completely orthogonal in pairs due to the limitation of the manufacturing process;
defining O-XYZ to represent an ideal orthogonal coordinate system; defining O-X ' Y ' Z ' as a coordinate system where three sensitive axes of the actual three-axis magnetic sensor are located, and the coordinate system is called as a sensor coordinate system;
suppose that: (1) The OZ' axis of the sensor coordinate system is coincident with the OZ axis of the ideal orthogonal coordinate system; (2) A Z ' OY ' plane of a sensor coordinate system is coplanar with a ZOY plane of an ideal orthogonal coordinate system, and an included angle between an OY ' axis and an OY axis is alpha; (3) The OX ' axis of the sensor coordinate system deviates downwards from an XOY plane, OX is defined as the projection of OX ' on the XOY plane, the included angle between the OX ' axis of the sensor coordinate system and the OX ' axis of the sensor coordinate system is beta, and the included angle between the OX ' axis and the OX axis of an ideal orthogonal coordinate system is gamma;
the relationship between the ideal orthogonal coordinate system and the sensor coordinate system is expressed as:
step 1-2: the inconsistent scale factors show that when the three components of the magnetic field are the same, the magnetic field values output by the three shafts of the three-shaft magnetic sensor are different in size and can be represented by a theoretical value multiplied by a diagonal matrix;
step 1-3: the zero offset is represented by that the three axes have zero offset due to the residual magnetism of the magnetic core, the drift of the amplifying and conditioning part of the internal circuit and the external temperature change factors, so that different magnetic fields can be superposed and fixed in the three-axis direction when the three-axis magnetic sensor is used for measurement;
step 1-4: when the three errors are comprehensively considered, the relationship between the actual output value and the theoretical value of the three-axis magnetic sensor is expressed as follows:
B m ＝RB+b p (2)
wherein, B = [ B = x ,B y ,B z ]Ideal magnetic field value, B m ＝[B mx ,B my ,B mz ]Magnetic field values, error matrix for actual three-axis magnetic sensor output
k x k y And k z Scale factors representing three axes, respectively, b p ＝[b x b y b z ] T Zero offset error for a three-axis magnetic sensor;
further derivation yields a true error-free magnetic field representation as:
B＝R'(B m -b p ) (3)
wherein R' is the inverse of the error matrix R and is an upper triangular matrix;
and 2, step: establishing a geomagnetic model;
establishing a geographic coordinate system: the coordinate origin is located at the intersection point of a connecting line of a carrier provided with the three-axis magnetic sensor and the earth center and the earth surface, the x axis points to the geographical north, the y axis points to the geographical east, and the z axis points to the earth center vertically; the projections of the earth magnetic field intensity T on the x, y and z axes are north direction components B respectively N East component B E And a vertical component B D ，B H D and I are respectively a geomagnetic declination and a geomagnetic inclination; t, B N 、B E 、B D 、B H D and I are collectively called as seven elements of the geomagnetic field, and the magnetic field value of any point on the earth surface is described and expressed by the seven elements of the geomagnetic field;
the relationship between seven elements of geomagnetism is expressed as:
and step 3: establishing a three-axis magnetic sensor error calibration model;
when using the geomagnetic field to perform error calibration of the three-axis magnetic sensor, equation (3) is written as:
in the formula (I), the compound is shown in the specification,
is the geomagnetic field value in the sensor coordinate system;
the conversion relation between the geographic coordinate system and the sensor coordinate system is described by the attitude matrix multiplicationThus, therefore, it is
Expressed as:
wherein
Gamma, theta and psi are roll, pitch and yaw, respectively;
continuing with the derivation formula (6) to obtain:
wherein ψ' = ψ -D,
k 11 ，k 12 …k 33 the matrix K is an element of the matrix K, and the matrix K can change along with the change of the roll angle and the pitch angle and is not an upper triangular or symmetrical matrix any more;
when the output values of N ≧ 12 groups of sensors under different postures are known, equation (7) is converted into a multi-objective function problem:
wherein the variable having the superscript ^' represents the geomagnetic field component represented by formula (8), B H And B D Respectively representing the horizontal component modulus and the vertical component of the local real geomagnetic field;
and 4, step 4: estimating parameters;
estimating error parameters by adopting an optimization algorithm according to the established error estimation model formula (8);
and 5: and (4) compensating the magnetic field value with the error by using the parameter solved in the step (4) to finish calibration.
2. The method for calibrating errors of a three-axis magnetic sensor under the condition of small attitude angle as claimed in claim 1, wherein the horizontal component module and the vertical component of the local real geomagnetic field in the step 3 can be obtained according to a world magnetic field model, and the average value of the measured values is used as a substitute in the experiment.
3. The method for calibrating the error of the three-axis magnetic sensor under the condition of small attitude angle according to claim 1, wherein the optimization algorithm in the step 5 is a Levenberg Marquardt algorithm or a particle swarm algorithm.
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