Magnetometer Calibration Research Articles

Real-Time Magnetic Field Calibration Method Based on Extended Kalman Filter

VINS makes roll and pitch observable because IMU is added, but if yaw also needs to be observable, the magnetometer needs to be used. But it is highly susceptible to interference from surrounding ferromagnetic materials. This paper first improves the traditional complementary filtering to eliminate the influence of linear acceleration during motion, then uses it fuses the accelerometer and gyroscope data to make more accurate prediction of the magnetometer data, and an Extended Kalman Filtering is used to implement magnetometer calibration. In the convenience experiment, our algorithm reduces the error RMS from 71.12uT to 11.77uT, while the ellipsoid fitting can’t calibrate correctly. In the calibration speed and accuracy experiment, our algorithm can realize the maximum value of the error distance after 5s is 0.42uT, which is better than the 0.98uT of the gyro-only compensation. In the stability experiment, within 10 minutes, the data calibrated by our algorithm drift only 4.12uT, which is better than 11.10uT of the gyro-only compensation. Finally, a convenient, accurate and stable real-time magnetometer calibration algorithm is realized. It has a wide range of functions in consumer electronics, VINS and military.

Multiple Accelerometers and Magnetometers Joint Calibration and Alignment

In this article, we introduce a computationally efficient algorithm for simultaneous joint calibration and axes alignment of multiple three-axis accelerometers or magnetometers. The proposed algorithm applies to ensembles of sensors of the same type, fixed to the same rigid platform. It compensates for all linear time-invariant distortions, such as scale factor, cross coupling, and offset, including the soft-iron and hard-iron distortions of the magnetometer. It can be implemented in a simple 12-step sequence and provides fast and accurate calibration without requiring any special piece of equipment.

An improved magnetometer calibration and compensation method based on Levenberg–Marquardt algorithm for multi-rotor unmanned aerial vehicle

In order to improvethe yaw angle accuracy of multi-rotor unmanned aerial vehicle and meet the requirement of autonomous flight, a new calibration and compensation method for magnetometer based on Levenberg–Marquardt algorithm is proposed in this paper. A novel mathematical calibration model with clear physical meaning is established. “Hard iron” error and “Soft iron” error of magnetometer which affect the yaw accuracy of unmanned aerial vehicle are compensated. Initially, Levenberg–Marquardt algorithm is applied to the process of sphere fitting for the original magnetometer data; the optimal estimation of sphere radius and initial “Hard iron” error are obtained. Then, the ellipsoid fitting is performed, and the optimal estimation of “Hard iron” error and “Soft iron” error are obtained. Finally, the calibration parameters are used to compensate for the magnetometer’s output during unmanned aerial vehicle flight. Traditional ellipsoid fitting based on least squares algorithm is taken as reference to prove the effectiveness of the proposed algorithm. Semi-physical simulation experiment proves that the proposed magnetometer calibration method significantly enhances the accuracy of magnetometer. Static test shows that the yaw angle error is reduced from 1.2° to 0.4° when using the proposed calibration model to calibrate magnetometers. In dynamic tests, the sensor MTi’s output is used as reference. The data fusion of magnetometer compensated by the proposed new calibration model based on Levenberg–Marquardt algorithm can accurately track the desired attitude angle. Experimental results indicate that the accuracy of magnetometer in the yaw angle estimation has been greatly enhanced. In the process of attitude estimated, the compensation magnetometer data given by this new method have faster convergence speed, higher accuracy, and better performance than the compensation magnetometer data given by traditional ellipsoid fitting based on least squares algorithm.

Calibration Method of Magnetometer Based on BP Neural Network

Due to the influence of processing technology and environmental factors, there are errors in attitude measurement with the three-axis magnetometer, and the change of parameters during the operation of the magnetometer in orbit will have a great impact on the measurement accuracy. This paper studies the calibration method of magnetometer based on BP neural network, which reduces the influence of model error on calibration accuracy. Firstly, the error model of the magnetometer and the structural characteristics of the BP neural network are analyzed. Secondly, the number of hidden layers and hidden nodes is optimized. To avoid the problem of slow convergence and low accuracy of basic BP algorithm, this paper uses the Levenberg Marquardt backpropagation training method to improve the training speed and prediction accuracy and realizes the on-orbit calibration of magnetometer through online training of the neural network. Finally, the effectiveness of the method is verified by numerical simulation. The results show that the neural network designed in this paper can effectively reduce the measurement error of magnetometer, while the online training can effectively reduce the error caused by the change of magnetometer parameters, and reduce the measurement error of magnetometer to less than 10 nT.

Localization with Magnetic Field Distortions and Simultaneous Magnetometer Calibration

Magnetic field localization utilizes position dependent and time persistent distortions of the earth magnetic field. These distortions are introduced by stationary ferromagnetic material in the environment and can be stored in a map to enable localization. Estimating the position of a magnetometer with these distortions requires a calibration of the sensor to enable the matching of the measurements to the map. Typically, the calibration is performed in a prior step and requires specific maneuvers like sensor rotations in a homogenous field. The goal of the maneuvers is to render the calibration parameters observable. For heavy platforms, e.g., cars, trains and driverless transport systems in factories, performing special maneuvers is cumbersome or even impossible. In addition they operate in an environment with an inhomogeneous magnetic field. To address this issue, this article proposes a novel method that exploits the magnetic field distortions to render the calibration parameters observable. To simplify the calibration process, the calibration parameters are estimated simultaneously with the position of the platform. The method employs a Rao-Blackwellized particle filter that reduces the computational complexity and enables real time processing. The feasibility of the method is shown in an evaluation with measurements of a magnetometer mounted on a model train. The results show a high accuracy of the position and calibration parameter estimation.

Magnetometer Calibration Using Ellipsoid Fitting Method

Considering various applications of magnetic sensors, it is of high importance to correctly calibrate them. Through the conducted experiment here, in order to approach to real conditions and to count for the effect of the environmental magnetic field, the magnetometer has been installed on a vehicle and is moved in a deserted area in Iran within a small radius. The values read by the sensor were then saved in a file and subsequently calibration has been applied using Ellipsoid Fitting Method and MATLAB software. In this paper we have first briefly explained about various magnetometer calibration methods and then the results of the experiments are studied and presented.

Interference-Compensating Magnetometer Calibration With Estimated Measurement Noise Covariance for Application to Small-Sized UAVs

This article proposes a new interference-compensating magnetometer calibration scheme aided by a gyroscope sensor, which could reduce the effect of induced magnetic interference due to nearby onboard current flow. By using the innovation process and a linear matrix inequality approach, mean and variance of the induced magnetic interference are estimated to ensure that their physical meaningful values are taken to be closest to the empirically measured ones. The values are reflected in the update step of the extended Kalman filter in order to accurately estimate the calibration parameters and the corresponding direction. Results of experiments performed using a real unmanned aerial vehicle (UAV) demonstrate that the proposed calibration scheme compensates well for the disturbing magnetic interference arising from the UAV's onboard current and hence reduces the estimation error of its yaw angle, or its heading direction, by approximately two-thirds of that obtained using the existing scheme.

Recurrent Implementation of Integral Magnetometer Calibration Algorithm Using the Measurements of a Three-Axis Gyro

The paper addresses the practical implementation of a calibration algorithm for a magnetometer integrated in an electronic device, using synchronous measurements of a gyroscope. Recurrent expressions have been derived for accumulating the intermediate matrices, due to which there is no need for accumulating the full set of primary measurements of vector counters. An algorithm has been formulated for determining the time point when accumulation stops and calculation of calibrated parameters starts.

A Stochastic Optimization Approach to Magnetometer Calibration With Gradient Estimates Using Simultaneous Perturbations

Triaxial magnetometers are indispensable part of every attitude sensing equipment for providing heading information. However, magnetometer measurements are affected by a number of error sources such as soft iron, hard iron, sensor nonorthogonality, and bias. These erroneous measurements, if not properly calibrated, deteriorate the quality of attitude estimates. In this paper, we present a new approach to calibrate triaxial magnetometer measurements by posing the calibration problem as a stochastic optimization problem. A scalar objective function is derived which involves magnetometer calibration parameters corresponding to all distortions. In order to recursively solve for optimized calibration parameters, a modified version of simultaneous perturbation stochastic approximation for the gradient is proposed for faster convergence. The proposed approach places no restrictions on the number of parameters involved and offers a complete solution by solving for all calibration parameters. The proposed approach is tested and validated using experimental data and the performance is compared against a reference approach.

A Novel Calibration Method for Magnetometer Array in Nonuniform Background Field

The measurement accuracy of the magnetometer system is closely related to the calibration effect. Available magnetometer calibration methods face the limitation on the assumption that the background magnetic field is uniform. The fact is that the experiment magnetic environment is inhomogeneous for the presence of human activities mainly. This problem could be partially addressed by an auxiliary large-scale triaxial Helmholtz coil to compensate the nonuniformity of magnetic field. This paper proposes a novel calibration method based on the tensor invariants in the nonuniform magnetic field without extra device. The inhomogeneity of background field implies a nonzero gradient field; a new correction model in the gradient field has been established. Calibration parameters are estimated to compensate the observed data using the concept of magnetic gradient tensor and the corresponding rotational tensor invariants, combined with the Levenberg Marquardt optimization. And after the calibration operation, the tensor invariants should be close to a constant. Numerical simulations have been designed and carried out, showing that the proposed algorithm had a good compensation performance with fast convergence, robustness in any gradient field. Field experiments with fluxgate magnetometer array were also conducted to verify this calibration procedure. The measured results are consistent with the simulation results. The root-mean-square (RMS) error is reduced from 616.239 to 1.608 nT/m, after calibration. In addition, the machining error of the frame, the time stability of the background field, the scale of gradient field, and robustness of this proposed method have been discussed.

MAG.I.C.AL.–A Unified Methodology for Magnetic and Inertial Sensors Calibration and Alignment

This paper introduces the MAGnetometer-Inertial sensors Calibration and ALignment (MAG.I.C.AL.) methodology for unified calibration and joint axes alignment of three-axis magnetometer, three-axis accelerometer, and three-axis gyroscope. MAG.I.C.AL. compensates for all linear time-invariant distortions such as scale-factor, cross-coupling, and offset, including the soft-iron and hard-iron distortions of the magnetometer. It introduces a new, computationally efficient, least-squares-based iterative algorithm for the calibration of the magnetometer and the accelerometer. It aligns their axes and introduces a new way to calibrate the gyroscope based on their joint data. MAG.I.C.AL. is implemented in a 15-step sequence achieving fast convergence and high accuracy without using any external piece of equipment and without requiring external attitude references. Simulation and experimental results using low-cost sensors are presented to support the accuracy, efficiency, and the applications of the algorithm.

An Efficient Method for Gyroscope-Aided Full Magnetometer Calibration

Due to the interference of the onboard magnetic material, the magnetometer intrinsic parameters differ from factory specification, and the cross-sensor misalignment between magnetometers and other sensors is distorted as well. This paper proposes an efficient full magnetometer calibration algorithm at the aid of gyroscopes by solving a homogeneous least-squared problem. The algorithm is able to accomplish both the intrinsic and cross-sensor calibration in a single step. It can serve as a coarse calibration method alone or be used as a good initial value for other fine algorithms for more accurate result.

Low Power In Situ AI Calibration of a Three-Axial Magnetic Sensor

Magnetic surveys are conventionally performed by scanning a domain with a portable scalar magnetic sensor. Unfortunately, scalar magnetometers are expensive, power consuming and bulky. In many applications, calibrated vector magnetometers can be used to perform magnetic surveys. In recent years algorithms based on artificial intelligence (AI) achieve state-of-the-art results in many modern applications. In this work we investigate an AI algorithm for the classical scalar calibration of magnetometers. A simple, low cost method for performing a magnetic survey is presented. The method utilizes a low power consumption sensor with an AI calibration procedure that improves the common calibration methods and suggests an alternative to the conventional technology and algorithms. The setup of the survey system is optimized for quick deployment in-situ right before performing the magnetic survey. We present a calibration method based on a procedure of rotating the sensor in the natural earth magnetic field for an optimal time period. This technique can deal with a constant field offset and non-orthogonality issues and does not require any external reference. The calibration is done by finding an estimator that yields the calibration parameters and produces the best geometric fit to the sensor readings. A comprehensive model considering the physical, algorithmic and hardware properties of the magnetometer of the survey system is presented. The geometric ellipsoid fitting approach is parametrically tested. The calibration procedure reduced the root-mean-squared noise from the order of 104 nT to less than 10 nT with variance lower than 1 nT in a complete 360 degrees rotation in the natural earth magnetic field.

Calibration of Integral Magnetometer Linear Model Coefficients Using Simultaneous Measurements of a Three-Axis Gyro

The paper considers a problem of calibration of a three-axis magnetometer integrated in a complex electronic device. Known methods of calibration based on the ellipsoid approximation of the geometric locus of magnetometer measurements provide only partial calibration and determine only the symmetrical part of the magnetic permeability matrix. The orthogonal part of the matrix remains undetermined. The proposed algorithm makes it possible to find the full matrix of magnetic permeability with the use of device rotation and additional measurements made by a three-axis gyro.

Calibration of triaxial magnetometer with ellipsoid fitting method

The accuracy of the triaxial strapdown magnetometer is limited by the scaling factor, three-axis orthogonality, offset errors, hard iron and soft iron effects of the platform, a calibration method of the triaxial strapdown magnetometer is proposed in this paper. Firstly, the integrated error model of the triaxial magnetometer is established without simplification, then the error calibration parameters are calculated by the ellipsoid fitting method, and the output of triaxial strapdown magnetometer can be calibrated by the calibration parameters. At last, simulation experiments are built for verification of the proposed calibration method. The simulation results show that the proposed method can reduce 94.6% of magnetometer errors and magnetic inference. The proposed calibration method can effectively calibrate the triaxial strapdown magnetometer.

Magnetometer Calibration and Field Mapping through Thin Plate Splines.

While the undisturbed Earth’s magnetic field represents a fundamental information source for orientation purposes, magnetic distortions have been mostly considered as a source of error. However, when distortions are temporally stable and spatially distinctive, they could provide a unique magnetic landscape that can be used in different applications, from indoor localization to sensor fusion algorithms for attitude estimation. The main purpose of this work, therefore, is to present a method to characterize the 3D magnetic vector in every point of the measurement volume. The possibility of describing the 3D magnetic field map through Thin Plate Splines (TPS) interpolation is investigated and demonstrated. An algorithm for the simultaneous estimation of the parameters related to magnetometer calibration and those describing the magnetic map, is proposed and tested on both simulated and real data. Results demonstrate that an accurate description of the local magnetic field using TPS interpolation is possible. The proposed procedure leads to errors in the estimation of the local magnetic direction with a standard deviation lower than 1 degree. Magnetometer calibration and magnetic field mapping could be integrated into different algorithms, for example to improve attitude estimation in highly distorted environments or as an aid to indoor localization.

Калибровка коэффициентов линейной модели интегрального магнитометра за счет использования измерений трехосного гироскопа

Калибровка коэффициентов линейной модели интегрального магнитометра за счет использования измерений трехосного гироскопа

Калибровка коэффициентов линейной модели интегрального магнитометра за счет использования измерений трехосного гироскопа

Калибровка коэффициентов линейной модели интегрального магнитометра за счет использования измерений трехосного гироскопа

Design and Development of a New Magnetometer Calibration Device

This paper describes the development of a new magnetometer calibration device using an active magnetic field compensation technique based on the base quantity of time rather than secondary standard field measurements. The proposed arrangement can be used as a laboratory calibration device that monitors and compensates the ambient dc magnetic field in a magnetically quiet environment. Furthermore, it can be developed to serve as a laboratory primary standard since it is based on the measurement of a base quantity, such as time. The proposed technique is based on the fluxgate magnetization principle and the measurement of the time difference between the two successive output pulses. The laboratory arrangement consists of a long solenoid for 1-D applications, which may be extended to 2-D and 3-D using Helmholtz coils, and a microcontroller for fast signal processing operations, which evaluate and compensate the detected ambient magnetic field using a closed-loop control algorithm. The proposed arrangement is used to obtain the calibration curves of a commercial Hall and a custom-made fluxgate sensor.

Рекуррентная реализация алгоритма калибровки интегрального магнитометра с использованием измерений трехосного гироскопа

Рекуррентная реализация алгоритма калибровки интегрального магнитометра с использованием измерений трехосного гироскопа