Magnetometer Output Research Articles

Spectral analysis of spin noise in an optically spin-polarized stochastic Bloch equation driven by noisy magnetic fields

We theoretically analyze an optically spin-polarized collection of atoms, which serves as a basis for atomic sensors. Assuming that the intrinsic atomic spin projection noise is negligible, we provide the closed-form autocorrelation function and the power spectral density (PSD) of the solution to a noisy version of an optically pumped Bloch equation, wherein each component of the external magnetic field is subjected to white noise. We conclude that noise in the bias B-field direction does not affect the autocorrelation function, up to first order in white noise covariance amplitudes. Moreover, the noise terms for the remaining two axes make different contributions to the magnetic noise-driven spin PSD; in particular, the contribution corresponding to noises perpendicular to the probing direction dominates at high frequencies. Some results concerning the second (and higher)-order terms are given. In particular, we anticipate a decrease in the effective Larmor frequency despite an increase in the magnetic field magnitude in the case of anisotropic transversal B-field noises. The analytic results are supported by Monte Carlo simulations employing the Euler–Maruyama method. The analytic methodology is applied to the case of a Bell–Bloom magnetometer, which reveals a non-linearity in the PSD of the magnetometer output and also a broadening effect due to magnetic field noise.

Design of NV Centers Integrated Magnetometer and High-Resolution Output Module Based on the ODMR System

In recent years, magnetic sensing based on the nitrogen-vacancy (NV) centers in diamonds has been considered to be a promising candidate for highly sensitive, spatial resolution solid-state quantum sensors. With the advancement of technology, scholars are committed to the introduction of miniaturized, highly integrated NV magnetometers. In this article, we integrate a focus system in the traditional laboratory into the sensor, propose a dual-focus magnetometer module (DFM), and design a signal-processing module (SPM) to perform current/voltage conversion–subtraction–amplification and filtering on the output signal of the DFM. Comparing the signal directly output by the DFM with the signal output after passing through the SPM the magnetic sensitivity and resolution are improved by 419 times and 256 times, respectively, and the magnetic resolution of the entire sensor reaches 24.6 nT in an area of 10.6 cm2. It has achieved a breakthrough in the resolution limit of integrated magnetometers in smaller volumes.

Numerical simulation of the sensor output on Macau Science Satellite-1

Macau Science Satellite-1 (MSS-1) will be launched at the early of 2023 into a near-circular orbit. The mission is designed to measure the Earth’s geomagnetic field with unpreceded accuracy through a new perspective. The most important component installed on the satellite, to ensure high accuracy, is the deployable boom (Optical Bench). A Vector Field Magnetometer (VFM), an Advanced Stellar Compass (ASC), and a Couple Dark State Magnetometers (CDSM) are deployed on the deployable boom. In order to maximize the mission’s scientific output, a numerical simulator on MSS-1’s deployable boom was required to evaluate the adaptability of all devices on the deployable boom and assist the satellite’s data pre-processing. This paper first briefly describes the synthesis of the Earth’s total magnetic field and then describes the method simulating the output of scalar and vector magnetometers. Finally, the calibration method is applied to the synthetic magnetometer data to analyze the possible noise/error of the relevant instruments. Our results show that the simulator can imitate the disturbance of different noise sources or errors in the measuring system, and is especially useful for the satellite's data processing group.

The Space Density Distribution of Alkali Metal Atoms in a SERF Atomic Magnetometer

The number density of alkali atoms in vaper cell is an important parameter for atomic magnetometer. The vapor cell is usually heated to a high temperature for the number density exceed to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">18</sup> m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> to achieve the spin-exchange-relaxation-free (SERF) process. The optical rotation of multichannel atomic magnetometers is affected by the number density distribution. We present an effective method for monitoring and analyzing the spatial distribution homogeneity of the atomic number density in the alkali metal cell within the SERF magnetometer. The numerical results from researching the model of electric heating films and ovens show that the temperature gradient increases with an increase in the cell temperature. This causes an nonuniform number density distribution based on the saturated vapor pressure curve. We present a laser absorption spectroscopy method by using the high-resolution beam profiling camera to record the power of the beam before and after the cell. An optimized optical system of the atomic magnetometer has been established by measuring the the number density variation in the spatial distribution in mm scale. The number density variation coefficient, which is introduced to evaluate the distribution homogeneity, increases from 0.0257 to 0.0333 when the temperature of the oven wall rises from 140°C to 190 °C, showing the same trend as the simulation results. The optical rotation distribution is calculated according to the magnetometer output signal formula. This study is of great interest for optimizing the oven structure and improving the stability of atomic spin polarization and sensitivity of the multichannel magnetometer.

Analysis and demonstration of the in-situ magnetometer for nuclear magnetic resonance gyroscopes

Rb atom serves as both polarization medium and an in-situ magnetometer in a nuclear magnetic resonance gyroscope. Analytical solution for the in-situ magnetometer output is obtained. The output gains and the decoupling phases for the transverse fields are developed analytically. A method to determine experimentally the decoupling phases for the x and y outputs by scanning the phases at different offsets of the magnetometer is proposed. Influence of magnetic field parameters on the output gains and the decoupling phases are analyzed by experiment and theoretical computations. It is found that the main static field B0 and the sinusoidal carrier amplitude Bc and their ratios have significant effects on the output gains and decoupling phases. Accurate determination of the decoupling phases needs careful minimization of the constant residual field. The performance of the in-situ magnetometer is evaluated by experiment with the coupled output characteristic bellow ±0.16 nT when the transverse input field is within ±100 nT and the transverse output sensitivity 0.01nT/Hz0.5 within the bandwidth except the low frequency part.

Precise Shearer Positioning Technology Using Shearer Motion Constraint and Magnetometer Aided SINS

The key technology to realize intelligent unmanned coal mining is the strapdown inertial navigation system (SINS); however, the gradual increase of cumulative error during the working process needs to be solved. On the basis of an SINS/odometer (OD)-integrated navigation system, this paper adds magnetometer (MAG)-aided positioning and proposes an SINS/OD/MAG-integrated shearer navigation system. The velocity observation equation is obtained from the speed constraints during shearer movement, and the yaw angle observation equation is obtained from the magnetometer output. The position information of the SINS output is calibrated using these two observations. In order to improve the fault tolerance of the integrated navigation system, an adaptive federated Kalman filter is established to complete the data fusion of the SINS. Experimental results show that the positioning accuracy of the SINS/OD/MAG-integrated navigation system is 75.64% and 74.01% higher in the east and north directions, respectively, than the SINS/OD-integrated navigation system.

Pose estimation by extended Kalman filter using noise covariance matrices based on sensor output

This paper presents an extended Kalman filter for pose estimation using noise covariance matrices based on sensor output. Compact and lightweight nine-axis motion sensors are used for motion analysis in widely various fields such as medical welfare and sports. A nine-axis motion sensor includes a three-axis gyroscope, a three-axis accelerometer, and a three-axis magnetometer. Information obtained from the three sensors is useful for estimating joint angles using the Kalman filter. The extended Kalman filter is used widely for state estimation because it can estimate the status with a small computational load. However, determining the process and observation noise covariance matrices in the extended Kalman filter is complicated. The noise covariance matrices in the extended Kalman filter were found for this study based on the sensor output. Postural change appears in the gyroscope output because the rotational motion of the joints produces human movement. Therefore, the process noise covariance matrix was determined based on the gyroscope output. An observation noise covariance matrix was determined based on the accelerometer and magnetometer output because the two sensors’ outputs were used as observation values. During a laboratory experiment, the lower limb joint angles of three participants were measured using an optical 3D motion analysis system and nine-axis motion sensors while participants were walking. The lower limb joint angles estimated using the extended Kalman filter with noise covariance matrices based on sensor output were generally consistent with results obtained from the optical 3D motion analysis system. Furthermore, the lower limb joint angles were measured using nine-axis motion sensors while participants were running in place for about 100 s. The experiment results demonstrated the effectiveness of the proposed method for human pose estimation.

Real‐time estimation of roll angle for trajectory correction projectile using radial magnetometers

An adaptive extend Kalman filter（EKF） is designed to estimate the roll angle for trajectory correction projectile only using radial magnetometers. By analysing the characteristics of the radial magnetometer output signal and the complex angular motion of the high-spin projectiles, the measurement equation is established. Two important measures, namely noise parameter adaptation and increasing system observation, are taken to improve the performance of the designed EKF. The novelty of this study is the proposed adaptive EKF has no requirements on the magnetometer measurement accuracy. That is the magnetometers used need not undergo a complicated calibration process. In addition, orthogonal difference method is introduced to adjust noise parameters. Finally, a series of numerical simulations and flight tests are carried out to verify the performance of the proposed method. The results show the designed adaptive EKF can effectively estimate the roll angle for the trajectory correction projectile and could be extended to practical engineering applications.

A SQUID Magnetometer-Based Readout System for an Inertial Navigation System

The characteristics of a SQUID magnetometer-based readout system for a superconducting gyroscope-based inertial navigation system (INS) are investigated. The transformation function of the rotation angle of the gyroscope simulator to the voltage at the magnetometer output with a value close to 6.5 mV/deg is calculated and measured. This value corresponds to 4.1 V/deg for a superconducting gyroscope with a rotor diameter of 30 mm. Zero voltage drifts with a duration of up to 8 h are measured on the SQUID magnetometer. A drift of $$10^{-6}$$ deg/h was detected.

Observability analysis and design of two nested filters for the satellite attitude estimation with magnetometer‐only

This study aims to propose a scenario for determining the attitude of a nano-satellite with only a magnetometer in the case of temporal failure or faults in other sensors of attitude determination subsystem. For the sake of this matter, two nested filters are employed. The first filter estimates the magnetic field derivative by an extended Kalman filter (EKF). This information is applied along with the magnetometer outputs to obtain the attitude in the second one. A proposed algorithm based on the Square-Root UnScented QUaternion Estimator has been carried out to guarantee the positiveness of the covariance matrices considering the restriction about the unit norm of the quaternion. Furthermore, the non-linear observability of these filters is investigated analytically accompanied by condition number studies to show the functionality of these filters for magnetometer-only attitude determination. Finally, Monte Carlo simulation results indicate better performance of this approach in comparison with the traditional method of multiplicative EKF, particularly with large initialisation errors.

How many solar wind data are sufficient for accurate fluxgate magnetometer offset determinations?

Abstract. Accurate magnetic field measurements by fluxgate magnetometers onboard spacecraft require ground and regular in-flight calibration activities. Therewith, the parameters of a coupling matrix and an offset vector are adjusted; they are needed to transform raw magnetometer outputs into calibrated magnetic field measurements. The components of the offset vector are typically determined by analyzing Alfvénic fluctuations in the solar wind if solar wind measurements are available. These are characterized by changes in the field components, while the magnetic field modulus stays constant. In this paper, the following question is answered: how many solar wind data are sufficient for accurate fluxgate magnetometer offset determinations? It is found that approximately 40 h of solar wind data are sufficient to achieve offset accuracies of 0.2 nT, and about 20 h suffice for accuracies of 0.3 nT or better if the magnetometer offsets do not drift within these time intervals and if the spacecraft fields do not vary at the sensor position. Offset determinations with uncertainties lower than 0.1 nT, however, would require at least hundreds of hours of solar wind data.

An Experimental Heuristic Approach to Multi-Pose Pedestrian Dead Reckoning Without Using Magnetometers for Indoor Localization

Pedestrian dead reckoning (PDR) is a potential technique for smartphone-based indoor localization using the built-in accelerometers and gyroscopes. However, most current PDR positioning approaches restrict the pose to carry a phone, such as holding it in front of the body during tracking. In addition, heading determination is the primary error sources in PDR systems, and hence, a magnetometer is normally required to reduce heading errors. However, in indoor environments, magnetometer outputs would be seriously distorted by magnetic disturbances from the building structures and electronics. In this paper, an experimental heuristic approach to multi-pose PDR (mpPDR) indoor positioning for structured environments has been proposed. Six poses and four modes to carry a phone could be recognized, and then, on the basis of different modes, an experimental approach to the heading determination without using magnetometers has been presented to reduce the heading error considering the effects of turning and hand-shaking events. The experimental results indicate that the proposed approach supports four smartphone modes with a high position accuracy of 97.99%.

Geomagnetic Compensation for the Rotating of Magnetometer Array During Magnetic Tracking

Based on a permanent magnet and a magnetometer array, magnetic tracking approach has some advantages such as wireless, real-time, and no line-of-sight problem. However, its tracking accuracy will be greatly deteriorated by the magnetometer array’s rotating during the tracking process. The reason lies in the relative variation of triaxial geomagnetic components, which should be calibrated before the tracking process. In this paper, we proposed an inertial sensor-based geomagnetic compensation method to reduce the intervention of the triaxial geomagnetic components for the magnetic tracking performance. An inertial measurement unit, which is situated on the magnetometer array, can capture the triaxial rotation of the magnetometer array in real time. As the vector sum of the triaxial geomagnetic components is constant, the rotation vector of the magnetometer array can be converted to the variation of the triaxial geomagnetic components. Thus, the triaxial geomagnetic components, which are included in the magnetometer outputs, can be separated from the sensing signals of permanent magnet even if the magnetometer array is rotating. The experimental results indicate that the magnetic tracking accuracy has been significantly improved. This method extends the application scope of the magnetic tracking approach because it enables both the magnetometer array and magnet to rotate during the tracking process.

Optimization-based gravity-assisted calibration and axis alignment of 9-degrees of freedom inertial measurement unit without external equipment

Applicable in numerous fields, low-cost micro-electromechanical system inertial measurement units often require on-sight calibration by the end user due to the existence of systematic errors. A 9-degrees of freedom inertial measurement unit comprises a tri-axis accelerometer, a tri-axis gyroscope, and a tri-axis magnetometer. Various proposed multi-position calibration methods can calibrate tri-axis accelerometers and magnetometers to a degree. Yet the full calibration of a tri-axis gyroscope and axis alignment of all the sensors still often requires equipment such as a rate table to generate a priori known angular velocities and attitudes or relies on the disturbance-prone magnetometer output as a reference. This study proposes an augmentation to the popular multi-position calibration scheme, capable of fully calibrating and aligning the sensor axes of the 9-degrees of freedom inertial measurement unit while eliminating the reliance on external equipment or magnetometer. The algorithm does not rely on the inertial measurement unit attitude during various stages of the multi-position data acquisition. Instead, it uses the gravity vector measured by the accelerometer to calibrate the gyroscope and align the magnetometer axes with the sensor body frame. Experimental results using a navigation module with factory calibration and extensive simulation results indicate the current method's ability in estimating large calibration parameters with relative errors below 0.5%.

Roll angle estimation of guided gun-launched projectile using MEMS angular rate gyro and magnetometer

The previous method to estimate roll angle of guided gun-launched projectile can be completely invalid in case of GPS is disabled in battlefield. To solve that problem, this paper proposes roll angle estimation used MEMS angular rate gyro and magnetometer. Comparing to the previous method with GPS, the addition of magnetometer outputs increases the measurement accuracy, but increases the dimension and nonlinearity of the measurement model. Therefore the Extended Kalman Filter is introduced. Through trajectory simulation, this study indicates that the absolute roll estimation error is less than 7 degrees after 3 seconds in whole flight trajectory, which is completely met the guided system requirement.

Advanced calibration of magnetometers on spin-stabilized spacecraft based on parameter decoupling

Abstract. Magnetometers are key instruments on board spacecraft that probe the plasma environments of planets and other solar system bodies. The linear conversion of raw magnetometer outputs to fully calibrated magnetic field measurements requires the accurate knowledge of 12 calibration parameters: six angles, three gain factors, and three offset values. The in-flight determination of 8 of those 12 parameters is enormously supported if the spacecraft is spin-stabilized, as an incorrect choice of those parameters will lead to systematic spin harmonic disturbances in the calibrated data. We show that published equations and algorithms for the determination of the eight spin-related parameters are far from optimal, as they do not take into account the physical behavior of science-grade magnetometers and the influence of a varying spacecraft attitude on the in-flight calibration process. Here, we address these issues. Based on decade-long developments and experience in calibration activities at the Braunschweig University of Technology, we introduce advanced calibration equations, parameters, and algorithms. With their help, it is possible to decouple different effects on the calibration parameters, originating from the spacecraft or the magnetometer itself. A key point of the algorithms is the bulk determination of parameters and associated uncertainties. The lowest uncertainties are expected under parameter-specific conditions. By application to THEMIS-C (Time History of Events and Macroscale Interactions during Substorms) magnetometer measurements, we show where these conditions are fulfilled along a highly elliptical orbit around Earth.

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-Based Phase Shifting Ratio Method for High Spinning Projectile’s Attitude Measurement

Accurate measurement of high spinning projectiles' attitude is the basis of guidance and control. In order to reduce the attitude measurement error and improve the attitude update rate, a magnetometer-based phase shifting ratio method is proposed in this paper. This method does not introduce additional installation errors as the existing methods, simplifies the calibration of the extreme value ratio-pitch angle curve, and makes full use of the measurement data of the sensors. The attitude update is synchronized with the magnetometer output without using the local geomagnetic information. Simultaneously, the local geomagnetic errors are avoided. The results of numerical simulation and semi-physical simulation experiments show that compared with the three orthogonal ratio method and the crest and trough method, the proposed algorithm in this paper can increase the attitude update rate by more than 2 times and the attitude calculation accuracy can be enhanced by 30%.

A Fast Calibration and Compensation Method for Magnetometers in Strap-Down Spinning Projectiles.

Attitude measurement is an essential technology in projectile trajectory correction. Magnetometers have been used for projectile attitude measurement systems as they are small in size, lightweight, and low cost. However, magnetometers are seriously disturbed by the artillery magnetic field during launch. Moreover, the error parameters of the magnetometers, which are calibrated in advance, usually change after extended storage. The changed parameters have negative effects on attitude estimation of the projectile. To improve the accuracy of attitude estimation, the magnetometers should be calibrated again before launch or during flight. This paper presents a fast calibration method specific for a spinning projectile. At the launch site, the tri-axial magnetometer is calibrated, the parameters of magnetometer are quickly obtained by optimal ellipsoid fitting based on a least squares criterion. Then, the calibration parameters are used to compensate for magnetometer outputs during flight. The numerical simulation results show that the proposed calibration method can effectively determine zero bias, scale factors, and alignment angle errors. Finally, a semi-physical experimental system was designed to further verify the performance of the calibration method. The results show that pitch angle error reduces from 3.52° to 0.58° after calibration. The roll angle error is reduced from 2.59° to 0.65°. Simulations and experimental results indicate that the accuracy of magnetometer in strap-down spinning projectile has been greatly enhanced, and the attitude estimation errors are reduced after calibration.

Development of an Attitude Determination System for Mobile Robots

This paper designs an attitude determination system based on a low-cost MEMS inertial measurement unit. By introducing an adaptive Kalman filter algorithm, the outputs of accelerometers, magnetometers, and gyroscopes are combined to solve the robot’s attitude angle in real time. The algorithm effectively eliminates the cumulative error of the gyro output. In addition, the output of the accelerometer is used to determine the motion state of the vehicle body, and the covariance matrix is adaptively adjusted to maintain a high-accuracy attitude output in both static and dynamic environments.