A high-precision calibration calculation method and system for the non-orthogonality of a triaxial vector magnetometer

Abstract

This application provides a high-precision calibration calculation method and system for the non-orthogonality of a triaxial vector magnetometer. The method includes: adjusting the pitch and direction axes of a non-magnetic turntable to rotate the triaxial vector magnetometer to be calibrated in multiple directions; recording the magnetic field vector readings and simultaneous scalar magnetometer readings in different directions; performing adjustments at least nine times; and calculating nine calibration parameters for the orthogonality calibration experiment using a set expression based on the magnetic field vector readings and simultaneous scalar magnetometer readings in different directions. The advantages of this application are: it directly provides analytical solutions without introducing additional errors; in addition to calculating the angles between the three non-orthogonal axes, it also simultaneously calculates six other magnetometer calibration parameters, such as the correction proportionality coefficient and zero bias; and if iterative calculation is performed, it can eliminate the error influence of unknown terms in the constant terms of the fitting equation, resulting in higher accuracy of the fitting results.

Description

Technical Field

[0001] This application belongs to the field of non-orthogonality calibration technology of triaxial vector magnetometers, specifically relating to a high-precision calibration calculation method and system for the non-orthogonality of triaxial vector magnetometers. Background Technology

[0002] The three magnetic field measurement axes of a triaxial vector magnetometer are usually non-orthogonal, requiring calibration experiments for correction. Existing methods for non-orthogonal calibration include two main approaches: One is the projection method, which uses a specific attitude angle to measure the projected magnetic field value to calculate the non-orthogonal deviation angle. This method typically involves adjusting the attitude to find the maximum or zero point of one axis and then recording the magnetic field measurement value of another axis. However, due to inherent errors in magnetic field measurement (including environmental fluctuations and other factors), the initial attitude direction is inherently flawed, which is then passed down to downstream calculations, resulting in insufficient calibration accuracy. Another approach is the ellipsoidal fitting method. This method assumes that when the detector rotates in place, the magnetic field vector, which should originally move along a sphere, becomes an ellipsoid due to the non-orthogonality of the measurement axes. After establishing the ellipsoidal equation, the coefficients of the equation are fitted using a large amount of measurement data, and the sensor coefficients are then calculated from these equation coefficients. These methods often employ different ellipsoidal equations due to variations in sensor coefficient models, leading to significant computational challenges. Additionally, the defined orthogonal deviation angles may not be triaxially symmetric, resulting in complex and irregular equations and further complicating the solution. Most methods simplify the equation coefficients using approximations, resulting in substantial calculation errors. Another type of method, the Kalman filter, leverages the dynamic convergence of the Kalman equations. Instead of directly solving for the sensor coefficients, it uses numerical approximation to obtain the correction value. This method is dynamic and adapts well to situations where orthogonality changes continuously, but its calibration performance is relatively low for structurally stable sensors.

[0003] In the non-orthogonality calibration test of a three-axis vector magnetic sensor, the projection method is traditionally used, but it has high environmental requirements and relatively poor calibration results. The Kalman filter method can be used in special environments such as satellites, but is rarely used in general ground tests. The ellipsoid method is relatively common, but its solution model usually uses a certain degree of approximation, which can further improve calibration accuracy. Rare high-precision calibration methods rarely disclose details, have high requirements for calibration tests, and are costly to implement. In actual production practice, there is a lack of a calculation scheme that is highly accurate, simple, and has low requirements for calibration tests. Summary of the Invention

[0004] The purpose of this application is to overcome the shortcomings of insufficient calibration accuracy in existing technologies.

[0005] To achieve the above objectives, this application proposes a high-precision calibration calculation method for the non-orthogonality of a triaxial vector magnetometer, comprising: Adjust the pitch and azimuth axes of the non-magnetic turntable to rotate the three-axis vector magnetometer to be calibrated in multiple directions, and record the magnetic field vector readings of the three-axis vector magnetometer in different directions and the scalar magnetometer readings at the same time; the number of adjustments is greater than or equal to 9. The three axes of the orthogonal coordinate system of the background magnetic field are defined as X0, Y0, and Z0; the three axes of the magnetometer to be calibrated are defined as X, Y, and Z. Specifically, X and X0 are set to be in the same direction, Y is located near the Y0 axis within the X0Y0 plane, and Z is located near the Z0 axis. The correction scaling factors for the XYZ axes are k, p, and r, respectively, and the zero biases are m, n, and l, respectively. The angles between any two axes of YZ, XZ, and XY are respectively... , , ; Substitute the recorded magnetic field vector readings and scalar magnetometer readings into the following formula to calculate the nine calibration parameters k, p, r, m, n, l, ... for the non-orthogonal calibration test. , and : ; Among them, parameters ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； ， ， These represent the magnetic field measurements of the magnetometer to be calibrated in the X, Y, and Z directions, respectively. This is a constant term.

[0006] As an improvement to the above method, the calculation result of the calibration parameters is expressed as follows: ; ; .

[0007] As an improvement to the above methodb Use measured values ; This indicates the reading of the scalar magnetometer.

[0008] As an improvement to the above method, if iterative calculation is used, starting from the second calculation... b use .

[0009] This application also provides a high-precision calibration calculation system for the non-orthogonality of a three-axis vector magnetometer, implemented based on the above method, the system comprising: The calibration parameter calculation module is used to calculate nine calibration parameters k, p, r, m, n, l, ..., ... for the orthogonal calibration test based on the magnetic field vector readings of the magnetometer in different directions and the scalar magnetometer readings at the same time, using set expressions. , and ; In this system, the three axes of the orthogonal coordinate system of the background magnetic field are defined as X0, Y0, and Z0; the three axes of the magnetometer to be calibrated are defined as X, Y, and Z. Specifically, X and X0 are set to be in the same direction, Y is located near the Y0 axis within the X0Y0 plane, and Z is located near the Z0 axis. The correction ratios for the XYZ axes are k, p, and r, respectively, and the zero biases are m, n, and l, respectively. The angles between any two axes of YZ, XZ, and XY are respectively... , , ; The setting expression is: ; Among them, parameters ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； ， ， These represent the magnetic field measurements of the magnetometer to be calibrated in the X, Y, and Z directions, respectively. This is a constant term.

[0010] Compared with existing technologies, the advantages of this application are: This application proposes a high-precision calibration method for the non-orthogonality of a triaxial vector magnetometer. It innovatively defines the non-orthogonality of the triaxial vector magnetometer using three interaxial angles, which are equally important and alternate, greatly simplifying the complexity of subsequent calculations and providing a complete analytical solution without introducing additional errors. In addition to calculating the three interaxial angles for non-orthogonality, it also simultaneously calculates six other magnetometer calibration parameters, including the correction proportionality coefficient and zero bias. An iterative process is added to eliminate the error influence of unknown terms in the constant terms of the fitting equation, resulting in higher accuracy of the fitting results. This calibration method theoretically reaches the error limit and can significantly advance the application level of this calibration experiment. Attached Figure Description

[0011] Figure 1 The diagram shown illustrates the definition of a non-orthogonal included angle. Detailed Implementation

[0012] The technical solution of this application will be described in detail below with reference to the accompanying drawings.

[0013] Triaxial vector magnetometers inevitably suffer from non-orthogonality. High-precision measurements necessitate non-orthogonal calibration experiments, and the calculation method for the calibration data determines the accuracy of the non-orthogonal calibration. The projection method introduces significant errors before calculation, resulting in lower relative errors, but it requires highly precise calibration procedures. The Kalman filter method, a gradually approximating numerical method, is often used in specific time-varying scenarios, but its performance in stable ground-based experimental environments is often inferior to the ellipsoidal method. The ellipsoidal method involves numerous calculation methods, typically pre-setting orthogonal deviation angles to characterize triaxial non-orthogonality, leading to complex and asymmetrical calculation equations. Approximate solutions are frequently used during the solution process, resulting in inconsistent calculation accuracy.

[0014] For the non-orthogonal calibration test of a triaxial vector magnetometer, this application proposes a high-precision, simple calibration calculation method based on the ellipsoid method, which does not have high test requirements. This method uses the complete ellipsoid equation instead of the simplified equation, thereby improving the model accuracy; it uses analytical solutions instead of approximate solutions, thereby improving the calculation accuracy; and it adopts an alternating model, so that the solution equation is both symmetrical and aesthetically pleasing and easy to calculate. At the same time, it has high compatibility with calibration test schemes. Its application in production practice not only improves calibration performance but also improves test efficiency.

[0015] The non-orthogonal calibration test of a triaxial vector magnetometer requires a stable standard magnetic field environment, which can be an open field environment or a magnetically shielded room, a standard magnetic field coil, or other equipment that can provide a stable standard magnetic field.

[0016] The equipment required for the non-orthogonality calibration test of a triaxial vector magnetometer includes: Non-magnetic turntable: A non-magnetic turntable has two rotation axes, one is the pitch axis and the other is the directional axis.

[0017] Scalar magnetometer, environmental magnetic field measurement equipment (optional).

[0018] A three-axis vector magnetometer device awaiting calibration.

[0019] Example 1 Non-orthogonal calibration methods for triaxial vector magnetometers include: Step 1: Start a stable standard magnetic field environment by placing the non-magnetic turntable in the uniform magnetic field region at its center.

[0020] Step 2: Fix the sensor of the triaxial vector magnetometer on the non-magnetic turntable, start the device to begin measurement and data reading.

[0021] Step 3: Place the scalar magnetometer in a uniform magnetic field area of ​​the test environment and monitor the changes in the background magnetic field environment.

[0022] Step 4: Adjust the pitch and azimuth axes of the non-magnetic turntable to make the three-axis vector magnetometer to be calibrated rotate in multiple directions.

[0023] Step 5: Record the magnetic field vector readings of the magnetometer in different directions as (B) xc B yc B zc The reading of the scalar magnetometer at the same time is recorded as B0.

[0024] Step 6: Record N≥9 sets of data. The more data, the better the calibration effect, and the more uniform the directional coverage, the better.

[0025] Step 7: Calculate the calibration parameters of the magnetometer to be calibrated based on the recorded values.

[0026] In the non-orthogonal calibration model of this application, let the true magnetic field components of the magnetometer to be calibrated be B in the X, Y, Z, and XYZ directions. x B y B z The magnetic field measurement value of the magnetometer to be calibrated is B. xc B yc B zc The correction scaling factors for the XYZ axes are k, p, r, respectively; the zero bias is m, n, l, respectively; and the included angles between any two YZ, XZ, and XY axes are respectively... , , Note that the orthogonal deviation angle between the measurement axis and the ideal orthogonal axis is not defined here, but the pairwise included angles are defined directly. This is because doing so preserves the equivalence between each axis and each angle, which simplifies the solution equation and calculation. , , k, p, r, m, n, and l constitute the nine calibration parameters for the non-orthogonal calibration experiment. The orthogonal coordinate system directions of the background magnetic field are then set as X0, Y0, and Z0, and the true magnetic field values ​​in the corresponding directions are set as B. x0 B y0 B z0 The X0Y0Z0 coordinate system is an orthogonal coordinate system adjacent to XYZ. Assume that X and X0 have the same direction, Y lies near the Y0 axis in the X0Y0 plane, and Z lies near the Z0 axis. The relationships between the directions and angles of each axis are as follows: Figure 1 As shown in the diagram, the coordinate system formed by the X0, Y0, and Z0 directions is orthogonal, while the coordinate system formed by the XYZ directions is non-orthogonal. O is the origin, and H is the perpendicular point of a point on the Z-axis to the XY plane. Defining the non-orthogonality of the three axes as the angles between them makes the three angles equally important, resulting in a cyclic expression in the subsequent results, greatly simplifying the computational complexity.

[0027] At this time, the measured magnetic field value in the XYZ direction satisfies the following condition as well as the actual magnetic field value in that direction: (1) The actual magnetic field values ​​in the XYZ directions satisfy the following relationship with the orthogonal magnetic field values ​​in the X0Y0Z0 directions: (2) (3) in, .

[0028] Considering that the scalar magnetic field measurement should be equal to the magnitude of the background vector magnetic field, that is (4) Substituting (1) and (3) into (4), we get: (5) Equation (5) is in the form of an ellipsoid equation, and the expressions for the undetermined coefficients of each term also follow the cyclical characteristics.

[0029] Equation (5) can be regarded as being of the form of (6) The equation, where ... Undetermined coefficients:

[0030]

[0031]

[0032]

[0033]

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[0035]

[0036]

[0037]

[0038] ， ， The values ​​of the nine independent variables are derived from measurements taken during the calibration process. This is a constant term, initially set to the measured value. After iteration, set to The method of this application does not have specific requirements for the angle and direction of the test data, will not cause a serious burden on the test process, will not introduce additional errors, and has strong compatibility with calibration tests. Since the equation has 9 undetermined coefficients, the calibration test must take at least 9 sets of data to form at least 9 equations. Then, equation (7) can be obtained by fitting the data to obtain the 9 undetermined coefficients, and then the 9 calibration parameters of the magnetometer can be solved.

[0039] Combining the simultaneous equations from multiple calibration results, equation (7) can be written in matrix form as follows: (7) Where M is A 1×9 matrix, where P is a 9×N matrix formed by the independent variables in equation (7) corresponding to the N sets of experimental data, in the form of... Q is a 1×N matrix formed by the constant terms in equation (7) corresponding to N sets of experimental data, in the form of... , b The initial value is set to After iteration, set to Solving equation (7) yields... (8) in, Representation matrix The transpose of the matrix, express The inverse matrix. Obtaining matrix M is equivalent to obtaining the inverse matrix. … The undetermined coefficients allow for the calculation of nine magnetometer calibration parameters. The derivation process is omitted; the calculation results can be expressed as follows: (9) (10) (11) (12) because The angles are all around 90°. The operation does not involve multiple solutions. The value is around 1. ， ， ， ， ， All are positive values, and the radical sign in equation (11) does not involve negative signs. In the initial calculation, equation (6) b Use measured values After calculating up to equation (12), iterate equations (6) to (12) again. At this point, equation (6) will be... b use This further improves the accuracy of the results. Ignoring the measurement error performance of the magnetometer itself, only the error introduced by this calculation method is calculated. Without iteration, the correction ratio for non-orthogonal angle error is 1× Within this range, the error ratio of the correction proportionality coefficients k, p, r is 1× Within a certain range, the error of the zero bias m, n, l is within 0.001nT. Even without iteration, its calibration accuracy is already very high and meets most calibration requirements. After one iteration, the error is only a computer numerical error and can be ignored.

[0040] The error sources of the calculation method in this application are only the measurement error of instrument performance, the measurement data error caused by calibration test operation, and the fitting error of the undetermined coefficients in equation (6) caused by them. In the subsequent calculation process, since the analytical solution is used completely and no other errors are introduced, the error limit has been reached in theory.

[0041] The method described in this application provides a complete definition, principle, derivation process, and calculation results, and can be used as a calculation scheme for high-precision non-orthogonal calibration tests of triaxial vector magnetometers.

[0042] The high-precision calculation method proposed in this application uses alternating inter-axis angles of equal status to characterize the non-orthogonality of the three axes, which simplifies the complexity of the calibration equation, provides complete analytical solution calculation results, and also provides six other calibration parameters such as the correction proportional coefficient and zero bias. The calculation results are symmetrical, aesthetically pleasing, concise and complete, without generating additional calculation errors. It has high compatibility with non-orthogonal calibration experiments without imposing excessive requirements, and can be used as a general calculation scheme for non-orthogonal calibration experiments, thereby reducing the threshold for calibration experiments and improving calibration accuracy.

[0043] Example 2 This application also provides a high-precision calibration calculation system for the non-orthogonality of a three-axis vector magnetometer, implemented based on the above method, the system comprising: The calibration parameter calculation module is used to calculate nine calibration parameters k, p, r, m, n, l, ..., ... for the orthogonal calibration test based on the magnetic field vector readings of the magnetometer in different directions and the scalar magnetometer readings at the same time, using set expressions. , and ; In this system, the three axes of the orthogonal coordinate system of the background magnetic field are defined as X0, Y0, and Z0; the three axes of the magnetometer to be calibrated are defined as X, Y, and Z. Specifically, X and X0 are set to be in the same direction, Y is located near the Y0 axis within the X0Y0 plane, and Z is located near the Z0 axis. The correction ratios for the XYZ axes are k, p, and r, respectively, and the zero biases are m, n, and l, respectively. The angles between any two axes of YZ, XZ, and XY are respectively... , , ; The setting expression is: ; Among them, parameters ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； ， ， These represent the magnetic field measurements of the magnetometer to be calibrated in the X, Y, and Z directions, respectively. This is a constant term.

[0044] The technical terms used in this application are explained as follows: A three-axis vector magnetometer is an instrument that measures the vector of a spatial magnetic field. When the directions of the three measuring axes are orthogonal, it can accurately describe the magnitude and direction of the spatial magnetic field vector.

[0045] Non-orthogonality: Due to the measurement principle and manufacturing process of magnetometers, the directions of their three measuring axes cannot be accurately known in advance, and therefore cannot be guaranteed to be orthogonal, thus exhibiting non-orthogonality.

[0046] Correction scaling factor: The scaling factor between the output value of the magnetometer and the true value of the magnetic induction intensity. It usually still has a deviation after the initial calibration in the laboratory, and can be further corrected in the non-orthogonal calibration test.

[0047] Zero bias: There is a fixed deviation between the zero point of the magnetometer's output value and the zero point of the true value of the magnetic induction intensity. Usually, there is still a deviation after preliminary calibration in the laboratory. Further correction can be obtained in non-orthogonal calibration experiments.

[0048] This application may also provide a computer device, including: at least one processor, memory, at least one network interface, and a user interface. The various components in this device are coupled together via a bus system. It is understood that the bus system is used to implement communication between these components. In addition to a data bus, the bus system also includes a power bus, a control bus, and a status signal bus.

[0049] The user interface can include a display, keyboard, or clicking device. Examples include a mouse, trackball, touchpad, or touchscreen.

[0050] It is understood that the memory in the embodiments disclosed in this application may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory may be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory may be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced Synchronous DRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). The memories described herein are intended to include, but are not limited to, these and any other suitable types of memory.

[0051] In some implementations, the memory stores elements such as executable modules or data structures, or subsets thereof, or extended sets thereof: operating systems and applications.

[0052] The operating system includes various system programs, such as the framework layer, core library layer, and driver layer, used to implement various basic business functions and handle hardware-based tasks. The application programs include various applications, such as media players and browsers, used to implement various application functions. Programs implementing the methods of the embodiments of this disclosure can be included in the application programs.

[0053] In the above embodiments, the processor can also invoke programs or instructions stored in memory, specifically programs or instructions stored in an application program, for the following purposes: Follow the steps described above.

[0054] The above methods can be applied to or implemented by a processor. The processor may be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above methods can be completed by integrated logic circuits in the processor's hardware or by software instructions. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic diagrams disclosed above. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the disclosed methods can be directly implemented by a hardware decoding processor, or by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0055] It is understood that the embodiments described in this application can be implemented using hardware, software, firmware, middleware, microcode, or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), general-purpose processors, controllers, microcontrollers, microprocessors, other electronic units for performing the functions described in this application, or combinations thereof.

[0056] For software implementation, the technology of this application can be implemented by executing the functional modules (e.g., procedures, functions, etc.) of this application. The software code can be stored in memory and executed by a processor. The memory can be implemented in the processor or outside the processor.

[0057] This application may also provide a non-volatile storage medium for storing a computer program. When the computer program is executed by a processor, it can implement the steps in the above method embodiments.

[0058] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit it. Although this application has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of this application do not depart from the spirit and scope of the technical solutions of this application, and should all be covered within the scope of the claims of this application.

Claims

1. A high-precision calibration calculation method for the non-orthogonality of a triaxial vector magnetometer, comprising: Adjust the pitch and azimuth axes of the non-magnetic turntable to make the triaxial vector magnetometer to be calibrated rotate in multiple directions, and record the magnetic field vector readings of the triaxial vector magnetometer in different directions and the scalar magnetometer readings at the same time. The number of adjustments is greater than or equal to 9; The three axes of the orthogonal coordinate system of the background magnetic field are defined as X0, Y0, and Z0; the three axes of the magnetometer to be calibrated are defined as X, Y, and Z. Specifically, X and X0 are set to be in the same direction, Y is located near the Y0 axis within the X0Y0 plane, and Z is located near the Z0 axis. The correction scaling factors for the XYZ axes are k, p, and r, respectively, and the zero biases are m, n, and l, respectively. The angles between any two axes of YZ, XZ, and XY are respectively... , , ; Substitute the recorded magnetic field vector readings and scalar magnetometer readings into the following formula to calculate the nine calibration parameters k, p, r, m, n, l, ... for the non-orthogonal calibration test. , and : ； Among them, parameters ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； ， ， These represent the magnetic field measurements of the magnetometer to be calibrated in the X, Y, and Z directions, respectively. This is a constant term.

2. The high-precision calibration calculation method for the non-orthogonality of a triaxial vector magnetometer according to claim 1, characterized in that, The calculation results of the calibration parameters are expressed as follows: ； ； 。 3. The high-precision calibration calculation method for the non-orthogonality of a triaxial vector magnetometer according to claim 2, characterized in that, b Use measured values ; This indicates the reading of the scalar magnetometer.

4. The high-precision calibration calculation method for the non-orthogonality of a triaxial vector magnetometer according to claim 3, characterized in that, If iterative calculation is used, start from the second calculation. b use .

5. A high-precision calibration calculation system for the non-orthogonality of a three-axis vector magnetometer, implemented based on the method described in any one of claims 1-4, characterized in that, The system includes: The calibration parameter calculation module is used to calculate the nine calibration parameters k, p, r, m, n, l, ..., ... for the orthogonal calibration test based on the magnetic field vector readings of the magnetometer in different directions and the scalar magnetometer readings at the same time, using set expressions. , and ; In this system, the three axes of the orthogonal coordinate system of the background magnetic field are defined as X0, Y0, and Z0; the three axes of the magnetometer to be calibrated are defined as X, Y, and Z. Specifically, X and X0 are set to be in the same direction, Y is located near the Y0 axis within the X0Y0 plane, and Z is located near the Z0 axis. The correction ratios for the XYZ axes are k, p, and r, respectively, and the zero biases are m, n, and l, respectively. The angles between any two axes of YZ, XZ, and XY are respectively... , , ; The setting expression is: ； Among them, parameters ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； parameter ； ， ， These represent the magnetic field measurements of the magnetometer to be calibrated in the X, Y, and Z directions, respectively. This is a constant term.

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