Calibration Of Three-axis Magnetometers Research Articles

Attitude-Independent Magnetometer Calibration Using Nonlinear Least Squares

This paper presents a new formulation for attitude-independent calibration of three-axis magnetometers. The proposed solution employs a Non-Linear Least Squares (NLLS) estimator that uses the non-linear sensor model proposed by Foster and Elkaim in the well-known Extended Two-Step (ETS) algorithm. Our solution has several advantages over ETS and is more straightforward to implement than many subsequent algorithms. It enables the calculation of the calibration parameters’ uncertainties and does not require the assumption that all magnetometer measurements have a constant magnetic field magnitude. The former is essential for evaluating calibration quality, while the latter may be required for on-orbit magnetometer calibration. However, the NLLS has the drawback of requiring an initial parameter estimation to ensure convergence. Therefore, our work presents a new technique to calculate the scale factors and offsets for initializing the NLLS. Simulations and practical implementations demonstrate that our method performs similarly to a recently computed analytical solution of the ETS. Furthermore, a Monte Carlo simulation shows that the NLLS algorithm provides a slightly better estimation of the scale factors than the ETS, in addition to the abovementioned advantages.

Magnetometer Calibration Using Genetic Algorithms

This paper describes the method for threeaxis magnetometer calibration using genetic algorithms suitable for execution on industrial microcontrollers. Algorithm structure, description, simulation as well as field testing results are presented.

Calibration of three-axis magnetometers with alternative iteration looping optimization method

PurposeThis study aims to find a novel solution to the calibration of three-axis magnetometers to suppress errors of sensors. The nature of the calibration process is parameter estimation and hence the purpose of the paper is to calculate the error parameters and eliminate sensor errors and obtain the true value of the pure magnetic field.Design/methodology/approachThe paper puts forward a calibration method using an alternative iteration looping optimization (AILO) to estimate the parameters. The proposed method divided the parameters to be estimated into two parts: a portion less than one and the other greater than one. Parameters with different orders of magnitude are calculated respectively, which let one part to be a known quantity and the other part is derived by the known quantity; the derived quantity is used to calculate the known quantity again, and looping iteration multiple times until the iteration termination condition is satisfied.FindingsThe simulation and experimental results indicate that the calibration accuracy is improved at least by two orders by the proposed method compared to the two-step method and the linear decreasing weight particle swarm optimization (LDW-PSO) algorithm which proves the validity of the proposed method.Practical implicationsThe proposed method can improve the calibration accuracy of total magnetic field, which provides a reference to the calibration of three-axis magnetometers.Originality/valueA calibration method based on the AILO is proposed in this paper, which is used to improve the calibration accuracy of the three-axis magnetometer.

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.

On Calibration of Three-Axis Magnetometer

Magnetometer has received wide applications in attitude determination and scientific measurements. Calibration is an important step for any practical magnetometer use. The most popular three-axis magnetometer calibration methods are attitude-independent and have been founded on an approximate maximum likelihood (ML) estimation with a quartic subjective function, derived from the fact that the magnitude of the calibrated measurements should be constant in a homogeneous magnetic field. This paper highlights the shortcomings of those popular methods and proposes to use the quadratic optimal ML estimation instead for magnetometer calibration. Simulation and test results show that the optimal ML calibration is superior to the approximate ML methods for magnetometer calibration in both accuracy and stability, especially for those situations without sufficient attitude excitation. The significant benefits deserve the moderately increased computation burden. The main conclusion obtained in the context of magnetometer in this paper is potentially applicable to various kinds of three-axis sensors.

A Calibration Method of Three-Axis Magnetometer With Noise Suppression

This paper presents a new algorithm for the onboard calibration of three-axis magnetometers under noisy environment. The ordinary least squares (OLS) estimator is inconsistent for ellipsoid fitting problem. Proper corrections of the OLS estimator are derived, which can provide a consistent solution to the magnetometer's calibration parameters without noise preknown. Simulation and experimental results are presented and discussed, supporting the application of the algorithm in the noisy platform.

Improvement of magnetometer calibration using Levenberg-Marquardt algorithm

The algorithm, the model, and the measurement strategy are important for the calibration of three-axis magnetometers. A new calibration model with clear physical meaning is proposed, and scale factors, offsets, and nonorthogonal angles are directly illustrated. One limitation of traditional iteration calibration algorithms is the influence of the initial parameters. In this paper, the Levenberg–Marquardt algorithm is proposed to solve the troublesome procedure of initial parameter selection, so that it can improve the calibration performance of three-axis magnetometers. The validity of this method is proved by simulation, and the estimated parameters are found to be close to the prearranged parameters. The experimental system mainly consists of a three-axis fluxgate magnetometer (DM-050), two-dimensional nonmagnetic rotation equipment, and a proton magnetometer. The magnetic field intensity is obtained by the proton magnetometer. Experimental results show that the root-mean-square error is reduced from 84.177 to 4.076 nT. In addition, the influence of the initial parameters and measurement strategy is analyzed. Experimental results show that the Levenberg–Marquardt algorithm is not sensitive to the initial parameters and the 36 static measurements strategy is more reliable than the rotation measurement strategy. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Real-Time Attitude-Independent Three-Axis Magnetometer Calibration for Spinning Projectiles: A Sliding Window Approach

This brief deals with attitude-independent three-axis magnetometer calibration in real time. The first part of this note presents a new model used for real-time estimation without any knowledge of the attitude of the projectile. The second part describes the other main contribution, which consists of a new simple and useful filter used for parameters estimation. The latter is formulated within the framework of an extended Kalman filter (EKF), which includes previous measurements in order to increase the performance and stability of the estimator. Finally, numerical simulations support the contribution of the presented algorithm. A good performance is shown through a smart projectile example in a noisy context, without requiring much more computation time than the classical EKF.

Constrained total least-squares calibration of three-axis magnetometer for vehicular applications

Strapdown three-axis magnetometer is widely used to determine the heading angle of a vehicle to which it is attached. Unfortunately, the outputs of three-axis magnetometer are often distorted by various magnetic field sources. Therefore, a calibration procedure must be performed before it is used. This paper presents a new calibration algorithm to determine calibration parameters based on a constrained total least-squares (CTLS) technique. A Newton iteration method is utilized to determine the CTLS solution. Unlike existing calibration algorithms, the proposed algorithm yields efficient estimates without assuming a priori knowledge of the noise distribution. Thus, it is easily implemented and suitable for practical applications. The results of simulations and experiments reveal the superiority of the proposed algorithm to the compared algorithms.

Calibration of Three-Axis Magnetometer Using Stretching Particle Swarm Optimization Algorithm

In this paper, a stochastic optimization algorithm is proposed to calibrate the three-axis magnetometer onboard. The sensor errors, namely, hard iron, soft iron, nonorthogonality, scale factors, and bias, are taken into account. Particle swarm optimization (PSO) strategy is used to do the calibration, enhanced by the stretching technique to improve the accuracy and robustness. The performance of this algorithm is evaluated with a series of laboratory experiments and a field experiment of autonomous underwater vehicle. Comparisons with other analytical calibration methods are made. The results demonstrate that both the PSO and the stretched PSO algorithm can significantly compensate the magnetometer readings, and the latter algorithm has higher accuracy and more robustness.

Constrained Total Least Squares Algorithm Applied to Three-Axis Magnetometer Calibration

Strapdown three-axis magnetometer is becoming increasingly used in navigation systems and in biomedical applications. A calibration must be performed before the magnetometer can be used, because its outputs are often corrupted by various magnetic field sources. This paper presents a new calibration algorithm based on constrained total least squares (CTLS) to determine different calibration parameters such as sensor non-orthogonality, scale factors, offsets, hard iron and soft iron errors. The basic idea is to convert the calibration problem into an unconstrained nonlinear optimization problem. An iterative technique based on Newton’s method is applied to give a numerical solution. Simulation results show that the proposed CTLS algorithm gives more accurate solutions than compared algorithms.

Automatic Calibration of the 3D Vector Magnetometer

Embedded sensors are an emerging trend in mobile consumer devices. In this work a new algorithm is derived for the onboard calibration of three-axis magnetometers. The proposed calibration method is written in the sensor frame, and compensates for the combined effect of all linear time-invariant distortions, namely soft iron, hard iron, three-dimensional sensor non-orthogonally, scale factors, null-shift, arbitrary bias, among others. The new algorithm can be separated into two steps: In the first step, obtain the ellipsoid fitting parameters from comparing the difference between the measured value and the actual vector. In a second step, a calibration algorithm is adopted to compensate for magnetometers distortions. According to the model parameters the measured data is corrected to improve the precision of magnetometer. Simulation and experimental results with sensors data are presented and discussed, supporting the application of the algorithm to commercial and military platforms.

Spacecraft Attitude and System Identification Using Marginal Reduced UKF Utilizing the Sun and Calibrated TAM Sensors

This paper deals with attitude determination, parameter identification and reference sensor calibration simultaneously. A LEO satellite’s attitude, inertia tensor as well as calibration of Three-Axis-Magnetometer (TAM) are estimated during a maneuver designed to satisfy persistency of excitation condition. For this purpose, kinematic and kinetic state equations of spacecraft motion are augmented for the determination of inertia tensor and TAM calibration parameters including scale factors, misalignments and biases along three body axes. Attitude determination is a nonlinear estimation problem. Unscented Kalman Filter (UKF) as an advanced nonlinear estimation algorithm with good performance can be used to estimate satellite attitude but its computational cost is considerably larger than the widespread, low accuracy, Extended Kalman Filter (EKF). Reduced Sigma Points Filters provide good solutions and also decrease run time of UKF. However, in contrast to nonlinear problem of attitude determination, parameter identification and sensor calibration have linear dynamics. Therefore, a new Marginal UKF (MUKF) is proposed that combines the utility of Kalman Filter with Modified UKF (MMUKF). The proposed MMUKF utilizes only 14 sigma points to achieve the complete 25-dimensional state vector estimation. Additionally, a Monte Carlo simulation has demonstrated a good accuracy for concurrent estimation of attitude, inertia tensor as well as TAM calibration parameters in significantly less time with respect to sole utilization of the UKF.