Magnetometer Error Research Articles

Calibration of strapdown magnetic vector measurement systems based on a plane compression method

The strapdown magnetic vector measurement system, which can measure the magnetic vector and the attitude of a magnetometer simultaneously, has wide applications in geophysical prospecting, etc. Calibration of systematic errors, including magnetometer errors and misalignment errors, is essential for this system. Traditional methods calibrate these two errors separately, with the problem of cumbersome steps and being dependent on special data acquisition methods, such as rotation. An original method that combines a plane compression method with an ellipsoid fitting method is proposed in this paper, which can simultaneously complete the calibration calculation of magnetometer error and misalignment error in one experiment. The calculation can be performed using the spatial scatter point data required by the traditional attitude-independent magnetometer calibration method, and no additional mechanical equipment is required. A mathematical analysis of this method is performed to study the elements decreasing the measurement accuracy of the system, and numerical simulation and field experiments are performed to validate the analysis. The results indicate that the method can contribute to the accuracy improvement of magnetic vector measurement systems.

Real-time estimation of roll angles by magnetometer based on two-step adaptive Kalman filter

The geomagnetic field vector information is critical to the navigation and positioning in the magnetic measurement of satellites, ships, and aircraft, however, suffers from the internal inherent error and the internal error interfering magnetic fields. Most real-time geomagnetic correction algorithms based on the specific ellipsoid fitting typically lead to the difficulty in real-time acquisition of the attitude roll angle of the projectile and the estimation accuracy. Herein, we propose a novel real-time estimation algorithm based on Magnetometer measurement involved two-step adaptive Kalman filter. The first-step adaptive Kalman filter algorithm is proposed for online error compensation of the magnetometer by using the error model and ellipsoid model of the magnetometer. The robust estimation theory is proposed to apply to the first-step adaptive Kalman filtering for ellipsoid fitting. The capability of preprocessing data and the adaptive observation vector's covariance matrix enable the real-time separation and correction of outliers. In addition, a vector-dot product invariant method is proposed to estimate the 12 coefficients in the magnetometer error model, solving the problem that the traditional method cannot ultimately determine the coefficients of the error matrix. Furthermore, the second-step adaptive Kalman is utilized to adaptively real-time estimate the roll angle. In particular, the results of the simulations and experiments show that the algorithm's parameters tend to be stable, beginning since 3 s for the data collection; and the accuracy range of the roll angle is boost to between ±0.4°. Moreover, the error parameters of the magnetometer are fully calibrated, and the estimation accuracy of roll angle is improved by 1/2 with regard to that of conventional methods. The results demonstrate the capability of compensating for the random magnetic field error caused by the motor. The results show that the two-step adaptive Kalman filter algorithm can reduce the estimation error of roll angle and could be extended to practical engineering applications.

Investigation of geomagnetic reference models based on the Iridium^{circledR } constellation

The World Magnetic Model (WMM) is a geomagnetic main field model that is widely used for navigation by governments, industry and the general public. In recent years, the model has been derived using high accuracy magnetometer data from the Swarm mission. This study explores the possibility of developing future WMMs in the post-Swarm era using data from the Iridium satellite constellation. Iridium magnetometers are primarily used for attitude control, so they are not designed to produce the same level of accuracy as magnetic data from scientific missions. Iridium magnetometer errors range from 30 nT quantization to hundreds of nT errors due to spacecraft contamination and calibration uncertainty, whereas Swarm measurements are accurate to about 1 nT. The calibration uncertainty in the Iridium measurements is identified as a major error source, and a method is developed to calibrate the spacecraft measurements using data from a subset of the INTERMAGNET observatory network producing quasi-definitive data on a regular basis. After calibration, the Iridium data produced main field models with approximately 20 nT average error and 40 nT maximum error as compared to the CHAOS-7.2 model. For many scientific and precision navigation applications, highly accurate Swarm-like measurements are still necessary, however, the Iridium-based models were shown to meet the WMM error tolerances, indicating that Iridium is a viable data source for future WMMs.Graphical

Attitude-Independent Magnetometer Calibration Based on Adaptive Filtering

In order to calibrate the tri-axis magnetometer errors, an attitude-independent calibration method based on adaptive filtering is proposed. This method can estimate all the error parameters precisely without the need of external equipment to provide stable magnetic field and reference attitude information. In this paper, incremental meta-learning Incremental Delta-Bar-Delta (IDBD) algorithm is applied to adaptive filtering to achieve magnetometer calibration instead of the traditional least squares (LS) algorithm. The results of this calibration method will be compared with the classical calibration method in the earth’s magnetic field as well. The experiments show that the sensor error after calibration by the proposed method is significantly suppressed and reduced by more than 93 % compared with that before calibration and the calibration effect of IDBD algorithm is much better than that of LS algorithm. The proposed method in this paper can not only effectively improves the measurement accuracy of the tri-axis fluxgate sensor, but also is potentially applicable to various kinds of three-axis sensors.

Modernizatsiya izmeritel'nogo kompleksa «Sigma-1» dlya issledovaniya tsirkulyatsiy Lengmyura i obrusheniy poverkhnostnykh voln v Chernom more

The purpose of this article is to describe modernization of SIGMA-1 measuring complex. The modernization was performed to improve the quality of research of the wave breaking mechanisms and Langmuir circulations at the stationary oceanographic platform MHI. The article deals with the effects of natural oscillations of the device and changes in the housing position on the measured components of the flow velocity vector. The device natural oscillations are recorded by a position monitoring system consisting of a set of sensors: accelerometers and a magnetometer. A model study of permissible rotations and maximum tilt angles showed that in the absence of an angular velocity sensor, the uncorrected measured components of the flow velocity vector can differ significantly from the actual ones. To solve this problem, MPU-9250 module with an accelerometer, gyroscope and magnetometer was chosen; Arduino Nano was used as a microcontroller system. Based on the theory of calculating spatial angles, a program for correcting the measured components of velocity pulsations for the new module was developed in Arduino IDE programming environment. The optimal program (Magneto) for calibrating the magnetometer was selected as the most accurate and satisfying the conditions of use at the oceanographic platform. The main stages of sensor calibration are described. The flow velocity components measured in the device coordinate system are adjusted for the values of tilt angles, angular and linear velocities, the calculation is performed using the eddy correlation method. The developed system has been tested on specialized equipment in laboratory setting and has the following characteristics: within the range –30…+30° the maximum pitch error is 0.31°; the maximum roll error is 0.42°; the maximum magnetometer error is 2.09°. The achieved characteristics allow significant increase in the accuracy of measuring the velocity vector and reliability estimate of influence of various physical processes on the vertical exchange.

PocketQube Pico-Satellite Attitude Control: Implementation and Testing

Attitude control for CubeSats and small satellites has been widely researched. Nonetheless, most of the literature is based on simulations, with limited availability of actual implementation results. This article tries to fill this gap by highlighting implementation difficulties and proposing appropriate workable solutions. The difficulty of direct reaction wheel (RW) torque feedback for attitude control of a 1p PocketQube (PQ) pico-satellite is noted and addressed. A simple control strategy implementable on a microcontroller is then proposed, showing how direct RW torque control can be achieved through angular velocity measurement without using derivative feedback. A linear quadratic Gaussian controller with integral action in quaternion formulation is used for attitude control, and a reference input boundary caused by the use of the standard integral action scheme is highlighted. A simple solution is then proposed, showing how using the error quaternion removes this boundary. An extended Kalman filter in quaternion formulation is used for attitude determination by fusing data from three sensors, namely, a magnetometer, solar cells, and a gyroscope. An accelerometer is used in place of the solar cells for simplified laboratory testing. Magnetometer error due to surrounding interference is addressed through calibration. A string-suspended model of the UoMBSat-1 PocketQube pico-satellite is used for attitude control testing. Preliminary single-axis tests are performed using a PID controller to determine the satellite parameters and actuators verification. The proposed linear quadratic Gaussian controller is then tested and validated experimentally in the laboratory setting.

Compensation Method for Diurnal Variation in Three-Component Magnetic Survey

Considering that diurnal variation interferes with three-component magnetic surveys, which inevitably affects survey accuracy, exploring an interference compensation method of high-precision is particularly desirable. In this paper, a compensation method for diurnal variation is proposed, the procedure of which involves calibrating the magnetometer error and the misalignment error between magnetometer and non-magnetic theodolite. Meanwhile, the theodolite is used to adjust the attitude of the magnetometer to unify the observed diurnal variation into the geographic coordinate system. Thereafter, the feasibility and validity of the proposed method were verified by field experiments. The experimental results show that the average error of each component between the observed value of the proposed method and that of Changchun Geomagnetic station is less than 1.2 nT, which indicates that the proposed method achieves high observation accuracy. The proposed method can make up for the deficiency that traditional methods cannot meet the requirements of high accuracy diurnal variation compensation. With this method, it is possible for us to set up temporary diurnal variation observation station in areas with complex topography and harsh environment to assist aeromagnetic three-component survey.

Attitude estimation and magnetometer calibration using reconfigurable TRIAD+filtering approach

This paper proposes using TRIAD and Unscented Kalman Filter (UKF) algorithms in a sequential architecture as a part of a small satellite attitude estimation algorithm. This TRIAD+UKF approach can both provide accurate attitude estimates for the satellite and calibrate the magnetometers in real-time. A complete calibration model for the magnetometers, considering bias, scale factor, soft iron and nonorthogonality errors, is assumed. In the algorithm's first stage, the TRIAD uses the available vector measurements (e.g. from Sun sensor and magnetometers) to estimate a coarse attitude. In the second stage, these estimated values are used as quaternion measurements in the UKF algorithm, together with the angular rate measured by a triad of gyros. The state vector for the UKF is composed of the attitude parameters, gyro biases and the magnetometer error terms. In result, we get fine attitude estimate for the satellite by calibrating the magnetometers in real-time. Rather high computational load of the algorithm, mainly due to the additional states, is decreased by filter reconfiguration. We evaluate the algorithm for a hypothetical nanosatellite by numerical simulations. The results show that the attitude of the satellite can be estimated with accuracy better than 0.5deg and the magnetometers can be fully calibrated.

A Calibration Method for the Misalignment Error Between Inertial Navigation System and Tri-Axial Magnetometer in Three-Component Magnetic Measurement System

In order to calibrate the misalignment error between inertial navigation system and tri-axial magnetometer in the three-component magnetic measurement system, a novel calibration method is proposed in the paper. Considering that the magnetometer error is inevitable, the calibration of which is the prerequisite to misalignment error calibration. Therefore, the calibration models of magnetometer error and misalignment error are established firstly, based on which, the objective function is constructed to calibrate the misalignment error. The magnetometer error calibration is based on the principle that the norm of the magnetic survey data keeps constant during the process of solving the objective function. Hence, the objective function solving problem is considered as the equality constrained nonlinear optimization problem, that is, the MATLAB's FMINCOM function is used to solve the objective function. The feasibility and validity of the proposed method were verified by simulation and field experiment, the results of which indicate high accuracy in misalignment error calibration. In the field experiment, the range of x, y, z components are decreased to 1.34%, 1.75% and 1.77% while the absolute errors are reduced to 2.13%, 2.11% and 3.47% respectively after calibration. Method comparisons indicate that the proposed method is superior to traditional methods, which can guarantee the accuracy for three-component magnetic measurement.

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.

Method of current distribution parameters measuring with using reference magnetic field source

The method for measurement of current distribution parameters is described in this work. Main feature of the method is compensation of magnetometer errors by using reference distribution. The measurement errors are compensated by using the error model parameters. The parameters are fitted on reference current distribution data. The method was tested on 3-axis Hall magnetometer with motorized positioning system. Its absolute accuracy is about 5 µm and dynamic range is 20 × 200 × 300 mm3. Sensitivity of the magnetometer is about 1 nT on averaging time of 5 s. Measurement error coordinate and magnetic moment of a circular current loop are not more than 5 µm by and 10–8 A⋅m2 accordingly.

An Attitude Filtering and Magnetometer Calibration Approach for Nanosatellites

We propose an attitude filtering and magnetometer calibration approach for nanosatellites. Measurements from magnetometers, Sun sensor and gyros are used in the filtering algorithm to estimate the attitude of the satellite together with the bias terms for the gyros and magnetometers. In the traditional approach for the attitude filtering, the attitude sensor measurements are used in the filter with a nonlinear vector measurement model. In the proposed algorithm, the TRIAD algorithm is used in conjunction with the unscented Kalman filter (UKF) to form the nontraditional attitude filter. First the vector measurements from the magnetometer and Sun sensor are processed with the TRIAD algorithm to obtain a coarse attitude estimate for the spacecraft. In the second phase the estimated coarse attitude is used as quaternion measurements for the UKF. The UKF estimates the fine attitude, and the gyro and magnetometer biases. We evaluate the algorithm for a hypothetical nanosatellite by numerical simulations. The results show that the attitude of the satellite can be estimated with an accuracy better than 0.5 $${^{\circ }}$$ and the computational load decreases more than 25% compared to a traditional UKF algorithm. We discuss the algorithm’s performance in case of a time-variance in the magnetometer errors.

A survey of calibration algorithms for small satellite magnetometers

Magnetometers are an integral part of attitude determination system for the low-Earth orbiting small satellites as they are lightweight, inexpensive and reliable. Yet using magnetometers for attitude determination is not straightforward because of the sensor errors. These errors limit the overall achievable attitude determination accuracy. Thus far different methods to cope with magnetometer errors and calibrate the magnetometers have been proposed. A new research field is the specific errors for magnetometers onboard the small satellites and their time-variation characteristics. In accordance, algorithms which consider also the time-varying error terms are proposed. This paper reviews the recent calibration algorithms for small satellite magnetometers. The survey mainly covers batch and recursive estimation algorithms which are capable of estimating the time-varying magnetometer error terms. It presents the foundation of each algorithm and covers issues about the algorithm design, application and performance. In the end possible directions in this research field are briefly discussed.

Integrated Calibration for the Cross Magnetic Gradiometer

The magnetic gradiometer onboard a maneuverable vehicle is subjected to not only magnetometer errors and misalignment errors but also magnetic interference of vehicle. Measurement precision of the magnetic gradiometer is greatly affected by those errors, so an integrated error calibration method is proposed in this paper. Firstly, considering vector magnetometer errors and magnetic interference, an integrated error calibration model for vector magnetometer is established, and ellipsoid fitting parameters are calculated by the least square algorithm under ellipsoid restriction, then the error calibration matrices are solved by the Cholesky factorization. Secondly, the misalignment error calibration matrices are obtained by solving the Orthogonal Procrustes problem. Finally, simulations and experiments with a cross magnetic gradiometer are performed to verify effectiveness and robustness of the proposed method. Results show that the proposed method can effectively calibrate the cross magnetic gradiometer, and measurement accuracy of the cross magnetic gradiometer is increased greatly.

A Fast Calibration Method for Magnetometer Array and the Application of Ferromagnetic Target Localization

The vector magnetometer array is commonly used in ferromagnetic target detection and localization. Due to technological limitations, the accuracy of measurements is restricted by magnetometer errors, misalignment errors between magnetometers and the interference of soft iron and hard iron. In order to correct the measurement errors, a calibration method with less computation time is proposed. A magnetometer array is designed for ferromagnetic target detection and localization, which is calibrated by the proposed method. The results of our empirical evaluations confirm that the proposed method outperforms conventional calibration method both in terms of computation cost and accuracy. Different test specimens are used to test the detection range and the localization accuracy of the system. The array system compensated by the proposed method has a larger detection range.

Magnetometer Error Models of Low-Cost Land Vehicle Navigation System

This article implies a method of magnetometer error determination. Using solid-state magnetic sensors, vehicle odometer and GPS sensor, low-cost complex navigation system for land vehicles can be realized. The methods and algorithms of magnetometer calibration are shown. Results of magnetometer calibration experiments and possibility to detect magnetometer error parameters in process of car driving are analysed. To acquire vehicle heading output, navigation system described here is developed. DOI: http://dx.doi.org/10.5755/j01.eie.22.6.17225

Advanced numerical study of the three-axis magnetic attitude control and determination with uncertainties

Attitude motion of a satellite equipped with magnetic control system is considered. System comprises of three magnetorquers and one three-axis magnetometer. Satellite is stabilized in orbital reference frame using PD controller and extended Kalman filter. Three-axis attitude is analyzed numerically with advanced assumptions: inertia tensor uncertainty, disturbances of unknown nature, magnetometer errors are taken into account. Stabilization and determination accuracy dependence on orbit inclination is studied.

Magnetometer calibration improvement using wavelet and genetic algorithm

Three‐axis magnetometer error and measurement noise influence the accuracy of magnetic measurements. Genetic algorithm (GA) is proposed to calibrate the magnetometer error, and wavelet is proposed for noise cancellation. The noise of a Mag3300 magnetometer and a DM magnetometer were tested within a horizontal barrel shield equipment. Five kinds of wavelet analysis and two kinds of wavelet package were used for noise cancellation, and the performance of different wavelets was compared. Noise of the Mag3300 magnetometer and DM magnetometer were suppressed from 29.6 and 2.3466 to 3.7 and 1.0789 nT, respectively. The scalar error of the Mag3300 magnetometer was tested using a two‐dimensional nonmagnetic rotation equipment and a GSM‐19T proton magnetometer. Scalar calibration performances of the unscented Kalman filter (UKF), the two‐step algorithm, and GA were compared. Experimental results show that GA provides less error intensity (about 370 and 70 nT) than UKF and the two‐step algorithm. In addition, the influence of wavelet on scalar calibration using UKF, the two‐step algorithm, and GA was analyzed. Results show that wavelet improved the scalar calibration performance. Mean error of the Mag3300 magnetometer scalar was 795.5 nT. When combined with the wavelet package, the error was suppressed to −22.3, 3.3, and −0.4 nT using UKF, the two‐step algorithm, and GA, respectively. The results suggest an effective way for magnetometer calibration using GA and wavelet. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Online three-axis magnetometer calibration for a pedestrian navigation system using a foot-mounted inertial navigation system

Foot-mounted inertial navigation systems(INS)having inexpensive micro electro mechanical system(MEMS)-based inertial sensors are widely used for pedestrian navigation.A foot-mounted INS can be combined with a magnetometer to constrain the heading angle error,but the magnetometer needs to be calibrated before use.This paper presents a magnetometer error model and an online calibration algorithm based on the foot-mounted INS characteristics.The magnetometer error characteristics and the foot-mounted INS mobility characteristics are used to develop a state equation and a magnetometer error measurement equation.An extended Kalman filter(EKF)is used for the online estimation and real-time calibration of the three-axis magnetometer errors with the zero velocity update(ZUPT)algorithm and a magnetic heading angle constraint algorithm for error constraint.The algorithm is validated by walking in a square playing ground.The results show that the online estimation and calibration algorithm reduce the end position error of the east direction from-110.7to 1.8mand the end position error of the north direction from 37.8to 5.2m compared to the system without calibration. This algorithm provides online calibration of magnetometer errors and significantly improves the positioning accuracy of pedestrian navigation.

Calibration and Compensation of Geomagnetic Vector Measurement System and Improvement of Magnetic Anomaly Detection

The magnetometer error and distortion magnetic field of an inertial navigation system are the major two factors influencing the measurement accuracy of geomagnetic vector information measurement systems. The calibration and compensation methods are proposed in this letter. As a first step, a calibration model for a three-axis magnetometer is established, and a nonlinear least square algorithm is used to estimate thoroughly the error parameters. Then, a distortion compensation model based on relative attitude information is proposed, in which only four groups of attitude information are needed to estimate precisely the distortion parameters. Finally, the whole system is used for magnetic anomaly detection. Experimental results suggest that the magnetometer error can be accurately calibrated, and the magnetic field distortion can be suppressed significantly. After calibration and compensation, the intensity and magnetic anomaly vectors such as west vector, south vector, and vertical vector can be accurately measured by the geomagnetic vector measurement system. It demonstrates that the proposed method can effectively improve the accuracy of the geomagnetic vector measurement system.