Magnetometer Output Research Articles

Magnetometer and Gyroscope Calibration Method with Level Rotation.

Micro electro mechanical system (MEMS) gyroscopes and magnetometers are usually integrated into a sensor module or chip and widely used in a variety of applications. In existing integrated gyroscope and magnetometer calibration methods, rotation in all possible orientations is a necessary condition for a good calibration result. However, rotation around two or more axes is difficult to attain, as it is limited by the range of movement of vehicles such as cars, ships, or planes. To solve this problem, this paper proposes an integrated magnetometer and gyroscope calibration method with level rotation. The proposed method presents a redefined magnetometer output model using level attitude. New gyroscope and magnetometer calibration models are then deduced. In addition, a simplified cubature Kalman filter (CKF) is established to estimate calibration parameters. This method possesses important value for application in actual systems, as it only needs level rotation for real-time calibration of gyroscopes and magnetometers. Theoretical analysis and test results verify the validity and feasibility of this method.

A new method of fluxgate signal extraction

Using dedicated high-frequency measuring system the distribution of the Barkhausen jumps intensity along a reversal magnetization cycle was investigated for low noise fluxgate sensors of various core shapes. It is shown that Barkhausen (reversal magnetization) noise intensity is strongly inhomogeneous during an excitation cycle. In the traditional second harmonic fluxgate magnetometers the signals are extracted in the frequency domain, as a result, some average value of reversal magnetization noises is contributed to the output signals. In order to fit better the noise shape and minimize its transfer to the magnetometer output the new approach for demodulating signals of these sensors is proposed. The new demodulating method is based on information extraction in the time domain taking into account the statistical properties of cyclic reversal magnetization noises. This approach yields considerable reduction of the fluxgate magnetometer noise in comparison with demodulation of the signal filtered at the second harmonic of the excitation frequency.

Magnetic disturbance field compensation of a geomagnetic vector measuring instrument

Magnetic disturbance field from ferromagnetic structural parts is a dominant factor that influences the accuracy of a geomagnetic vector measuring instrument. In this paper, a new vector compensation method for a three‐axis magnetometer is proposed. In the first step, combined with posture information from inertial sensors, the dataset of the three‐axis magnetometer outputs in different postures is utilized to construct linear equations of the error parameters; then the soft‐iron parameters are determined with singular value decomposition. In the second step, the hard‐iron parameters are estimated by changing the fixing direction of the three‐axis magnetometer. Simulations and experiments are performed to assess the performance of the proposed method. The results show that the error parameters can be accurately estimated, and the measurement errors of geomagnetic field vectors and magnitude are suppressed greatly. After compensation, the standard deviations of the errors of the magnetic vector components decrease from hundreds of nT to tens of nT. The main advantages of this proposed method are as follows: (i) it can compensate not only the scalar error but also the vector error, and (ii) it compensates the errors of vectors and magnitude with higher accuracy. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Merging fluxgate and induction coil data to produce low-noise geomagnetic observatory data meeting the INTERMAGNET definitive 1 s data standard

Abstract. For frequencies above 30 mHz the instrument intrinsic noise level of typical fluxgate magnetometers used at geomagnetic observatories usually masks ambient magnetic field variations on magnetically quiet days. This is especially true for stations located at middle and low latitudes, where variations are generally smaller than at high latitudes. INTERMAGNET has set a minimum quality standard for definitive 1 s data. Natural field variations referred to as pulsations (Pc-1, Pc-2, Pi-1) fall in this band. Usually their intensity is so small that they rarely surpass the instrumental noise of fluxgate magnetometers. Moreover, high-quality magnetic field observations in the band 30 mHz–0.5 Hz contain interesting information, e.g., for the study of ionospheric electron interactions with electromagnetic ion cyclotron plasma waves. We propose a method to improve 1 Hz observatory data by merging data from the proven and tested fluxgate magnetometers currently in use with induction coil magnetometers into a single data stream. We show how measurements of both instruments can be combined without information loss or phase distortion. The result is a time series of the magnetic field vector components, combining the benefits of both instruments: long-term stability (fluxgate) and low noise at high frequencies (induction coil). This new data stream fits perfectly into the data management procedures of INTERMAGNET and meets the requirements defined in the definitive 1 s data standard. We describe the applied algorithm and validate the result by comparing power spectra of the fluxgate magnetometer output with the merged signal. Daily spectrograms from the Niemegk observatory show that the resulting data series reveal information at frequencies above 30 mHz that cannot be seen in raw fluxgate data.

In-orbit offline estimation of the residual magnetic dipole biases of the POPSAT-HIP1 nanosatellite

The nanosatellite POPSAT-HIP1 is a Cubesat-class spacecraft launched on the 19th of June 2014 to test cold-gas based micro-thrusters; it is, as of April 2015, in a low Earth orbit at around 600km of altitude and is equipped, notably, with a magnetometer. In order to increment the performance of the attitude control of nanosatellites like POPSAT, it is extremely useful to determine the main biases that act on the magnetometer while in orbit, for example those generated by the residual magnetic moment of the satellite itself and those originating from the transmitter.Thus, we present a methodology to perform an in-orbit offline estimation of the magnetometer bias caused by the residual magnetic moment of the satellite (we refer to this as the residual magnetic dipole bias, or RMDB). The method is based on a genetic algorithm coupled with a simplex algorithm, and provides the bias RMDB vector as output, requiring solely the magnetometer readings. This is exploited to compute the transmitter magnetic dipole bias (TMDB), by comparing the computed RMDB with the transmitter operating and idling.An experimental investigation is carried out by acquiring the magnetometer outputs in different phases of the spacecraft life (stabilized, maneuvering, free tumble). Results show remarkable accuracy with an RMDB orientation error between 3.6° and 6.2°, and a module error around 7%. TMDB values show similar coherence values.Finally, we note some drawbacks of the methodologies, as well as some possible improvements, e.g. precise transmitter operations logging. In general, however, the methodology proves to be quite effective even with sparse and noisy data, and promises to be incisive in the improvement of attitude control systems.

Extended Kalman Filter Based Gyroscope Aided Magnetometer Calibration for Consumer Electronic Devices

Magnetometers are low-cost sensors that are widely used for orientation sensing in consumer electronic devices. The sensor is affected by non-idealities that can be greatly compensated by proper calibration and determining parameters, such as bias, non-orthogonality, gain, and hard/soft iron. This paper presents a magnetometer calibration method, with the aid of a gyroscope. The algorithm is designed on a principle that the variation of magnetometer output should be aligned with device rotation, which can be sensed by the gyroscope. Based on this notion, an extended Kalman filter is established to estimate calibration parameters. The method evaluation is achieved by first running numerous simulations, followed by a series of experiments on real devices. The result shows that the proposed method can achieve within ten degrees of accuracy, with less than 5 s of convergence. Compared with least square ellipsoid fitting, our proposed method delivers five times better accuracy and avoids over fitting on ill-distributed calibration data sets. This advantage is especially useful for autonomous dynamic calibration in consumer electronic devices.

Step by step: reconstruction of terrestrial animal movement paths by dead-reckoning.

BackgroundResearch on wild animal ecology is increasingly employing GPS telemetry in order to determine animal movement. However, GPS systems record position intermittently, providing no information on latent position or track tortuosity. High frequency GPS have high power requirements, which necessitates large batteries (often effectively precluding their use on small animals) or reduced deployment duration. Dead-reckoning is an alternative approach which has the potential to ‘fill in the gaps’ between less resolute forms of telemetry without incurring the power costs. However, although this method has been used in aquatic environments, no explicit demonstration of terrestrial dead-reckoning has been presented.ResultsWe perform a simple validation experiment to assess the rate of error accumulation in terrestrial dead-reckoning. In addition, examples of successful implementation of dead-reckoning are given using data from the domestic dog Canus lupus, horse Equus ferus, cow Bos taurus and wild badger Meles meles.ConclusionsThis study documents how terrestrial dead-reckoning can be undertaken, describing derivation of heading from tri-axial accelerometer and tri-axial magnetometer data, correction for hard and soft iron distortions on the magnetometer output, and presenting a novel correction procedure to marry dead-reckoned paths to ground-truthed positions. This study is the first explicit demonstration of terrestrial dead-reckoning, which provides a workable method of deriving the paths of animals on a step-by-step scale. The wider implications of this method for the understanding of animal movement ecology are discussed.Electronic supplementary materialThe online version of this article (doi:10.1186/s40462-015-0055-4) contains supplementary material, which is available to authorized users.

Eye, head, and foot tracking during locomation over real-world complex terrain

Successful locomotion over complex terrain such as a rocky trail requires walkers to place each step on a safe foothold with high spatiotemporal precision while also taking the future terrain into account. We have previously shown that humans guide foot placement using a visual control strategy that exploits the physical dynamics of the bipedal gait cycle (e.g. Matthis, Barton & Fajen, 2014). However, this work was limited to locomotion over virtual terrain projected onto flat surfaces within the laboratory. In the current project, we develop a research protocol to allow accurate and integrated tracking of the eye, head, and feet during locomotion over real-world complex and rocky terrain, a protocol that has been previously limited by numerous technical challenges. This protocol allows us to test predictions derived from the results of previous lab-based studies on the visual control of foot placement in real-world terrains, and opens new opportunities to study the visual control of locomotion outside a laboratory setting. Our protocol utilizes a Positive Science mobile eye tracker with a GoPro scene camera and inertial measurement units (IMUs) attached to the head, trunk, and feet. Each IMU integrates the output of temperature-calibrated, tri-axial accelerometers, gyroscopes, and magnetometers to determine the sensor's orientation within a world-centered reference frame. The orientation quaternions produced by the head and trunk-mounted IMUs were used to rotate the gaze vectors recorded by the eye tracker in order to specify gaze fixations within a body-centered reference frame and relate gaze location to foot placement. In a pilot study, subjects walked across different types of real-world terrain while performing different distraction tasks. Preliminary results reveal that foot placement in complex terrain is highly demanding of attentional resources, and that the control strategies used to guide foot placement vary dramatically according to the difficulty of the terrain being traversed. Meeting abstract presented at VSS 2015. Language: en

Fundamental Mode Orthogonal Fluxgate Gradiometer

A new method based on the fundamental mode orthogonal fluxgate (FM-OFG) mechanism is proposed to build a gradiometer of flexible base line and a minimum set of electronics. A pair of thin sensor heads and an electronic circuit designed for a magnetometer can be used, in which pickup windings of a sensor head pair are connected in counter series to respond to the field gradient between two locations of the sensor heads. Furthermore, a fine tuning to get a good balance in sensitivity between two sensor heads can be made by adjusting a dc bias current to one of the sensor heads. Developed gradiometers show a high suppression performance to the uniform magnetic field, where the suppression ratio (gradiometer output)/(magnetometer output), reaches below 1/40 000 with the resolution of 100 pT/m/√Hz at 10 Hz.

Integrated calibration of magnetic gradient tensor system

Measurement precision of a magnetic gradient tensor system is not only connected with the imperfect performance of magnetometers such as bias, scale factor, non-orthogonality and misalignment errors, but also connected with the external soft-iron and hard-iron magnetic distortion fields when the system is used as a strapdown device. So an integrated scalar calibration method is proposed in this paper. In the first step, a mathematical model for scalar calibration of a single three-axis magnetometer is established, and a least squares ellipsoid fitting algorithm is proposed to estimate the detailed error parameters. For the misalignment errors existing at different magnetometers caused by the installation process and misalignment errors aroused by ellipsoid fitting estimation, a calibration method for combined misalignment errors is proposed in the second step to switch outputs of different magnetometers into the ideal reference orthogonal coordinate system. In order to verify effectiveness of the proposed method, simulation and experiment with a cross-magnetic gradient tensor system are performed, and the results show that the proposed method estimates error parameters and improves the measurement accuracy of magnetic gradient tensor greatly.

Linear calibration method of magnetic gradient tensor system

Based on the detailed analysis of systematic errors, mathematical model of error parameters is constructed and linear calibration method is proposed for magnetic gradient tensor system. Firstly, nonlinear mathematical model of error parameters for single vector magnetometer is constructed based on scalar calibration, and least square solution is deduced by two nonlinear conversions without any mathematical simplification. Then outputs of four tri-axial magnetometers are calibrated to sensor’s orthogonal coordinate respectively. Secondly, a least square estimation is proposed for the misalignment errors between different magnetometers according to the rotation matrix comprising conversion of different orthogonal coordinate system. After calibration, outputs of tri-axial magnetometers are acquired along the ideally platform frame-orthogonal coordinate system and these enable calibration of magnetic gradient tensor system. Simulations and experiments show that the proposed linear calibration method can accurately solve the detailed error parameters and decrease measurement errors of magnetic gradient tensor system remarkably.

Compensation of Crosstalk in Three-Axial Induction Magnetometers

A method for the compensation of crosstalk in three-axial induction magnetometers is developed theoretically and verified experimentally. The compensation is based on deriving crosstalk-free magnetometer outputs from a system of equations describing the magnetometer total outputs as a function of the applied field, the parameters of the magnetometer coils, and the crosstalk factors for the applied and secondary magnetic fluxes. Processing the total outputs of an experimental magnetometer has demonstrated an effective reduction of the crosstalk: it has been reduced below 0.5% in the whole magnetometer bandwidth, including the frequencies near resonance, where the crosstalk is especially strong (20%). In comparison, the reduction of the crosstalk by applying magnetic feedback is much less effective: the crosstalk has been reduced down to 6% at resonance, remained unchanged at low and high frequencies, and even increased just below resonance. Moreover, magnetic feedback flattens the frequency response and significantly reduces the magnetometer selectivity, which can be advantageous in many applications. Employing magnetic feedback also increases the magnetometer complexity and its power consumption.

DI3 - A New Procedure for Absolute Directional Measurements

The standard observatory procedure for determining a geomagnetic field's declination and inclination absolutely is the DI-flux measurement. The instrument consists of a non-magnetic theodolite equipped with a single-axis fluxgate magnetometer. Additionally, a scalar magnetometer is needed to provide all three components of the field. Using only 12 measurement steps, all systematic errors can be accounted for, but if only one of the readings is wrong, the whole measurement has to be rejected. We use a three-component sensor on top of the theodolites telescope. By performing more measurement steps, we gain much better control of the whole procedure: As the magnetometer can be fully calibrated by rotating about two independent directions, every combined reading of magnetometer output and theodolite angles provides the absolute field vector. We predefined a set of angle positions that the observer has to try to achieve. To further simplify the measurement procedure, the observer is guided by a pocket pc, in which he has only to confirm the theodolite position. The magnetic field is then stored automatically, together with the horizontal and vertical angles. The DI3 measurement is periodically performed at the Niemegk Observatory, allowing for a direct comparison with the traditional measurements.

A non-linear observer for attitude estimation of a fixed-wing unmanned aerial vehicle without GPS measurements

In this paper we propose a simple non-linear observer for attitude estimation based only on output from a typical inertial measurement unit (IMU) and dynamic pressure sensor embarked on a low-cost unmanned aerial vehicle. In particular, we aim to provide a good quality attitude estimate in the absence of global positioning system (GPS) ground truth and with potential low-frequency bias and high-frequency noise in the IMU sensor measurements. In addition, the case where the IMU only provides gyrometer and accelerometer outputs is considered; that is, there is no magnetometer output or it cannot be used due to local magnetic disturbances such as are common on a vehicle with electric motors. The proposed observer uses a simple centripetal force model (based on gyrometer and dynamic pressure measurements), augmented by a first-order dynamic model for angle of attack, to estimate non-inertial components of the acceleration. This estimate is used to correct the accelerometer output to provide a low-frequency estimate of the gravitational direction. This inertial direction, along with the gyrometer output, is then used to drive a fully non-linear attitude observer posed on the orthogonal group of rotation matrices SO(3). The observer is augmented with an integral state that ensures compensation of gyrometer bias. The resulting observer is simple to implement and fully non-linear. Experimental results are provided on a real-world data set and the performance of the filter is evaluated against the output from a full GPS/inertial navigation system (INS) that was available for the data set.

Magnetic Anomaly Detection Using a Three-Axis Magnetometer

Magnetic anomaly detection is a good method for detecting ferromagnetic objects, particularly hidden targets. In this work, we address the detection of a moving ferromagnetic target using a static three-axis referenced magnetometer. The analysis and the results are also applicable to the converse case of a static ferromagnetic target and a moving three-axis referenced magnetometer. We use the three magnetometer outputs to build a total magnetic field of the target. This signal is decomposed into a set of orthonormal basis functions, out of which the dominant basis function is chosen as the detector. The detector provides output responses to any target magnetic moment orientation. We support the analysis by a computer simulation and real-world experimental results. The high detection probability and the simple implementation of the proposed method make it attractive for real-time applications.

An adaptive unscented Kalman filter for quaternion‐based orientation estimation in low‐cost AHRS

PurposeThis paper aims to develop an adaptive unscented Kalman filter (AUKF) formulation for orientation estimation of aircraft and UAV utilizing low‐cost attitude and heading reference systems (AHRS).Design/methodology/approachA recursive least‐square algorithm with exponential age weighting in time is utilized for estimation of the unknown inputs. The proposed AUKF tunes its measurement covariance to yield optimal performance. Owing to nonlinear nature of the dynamic model as well as the measurement equations, an unscented Kalman filter (UKF) is chosen against the extended Kalman filter, due to its better performance characteristics. The unscented transformation of the UKF is shown to equivalently capture the effect of nonlinearities up to second order without the need for explicit calculations of the Jacobians.FindingsIn most conventional AHRS filters, severe problems can occur once the system suddenly experiences additional acceleration, resulting in erroneous orientation angles. On the contrary in the high dynamic accelerative mode of the new proposed filter the errors would not suddenly increase, since the additional to cruise accelerations are being continuously estimated resulting in substantially more accurate orientation estimation. This feature causes the associated filter errors to gradually increase, in the event of continuous vehicle acceleration, up to a point of zero additional acceleration that subsequently causes a subsidence of the error back to zero.Practical implicationsThe proposed filtering methodology can be implemented for orientation estimation of aircraft and UAV that are equipped with low‐cost AHRSs.Originality/valueTraditional AHRS algorithms utilize the accelerometers output for the computation of roll and pitch angles and magnetometer output for the heading angle. Moreover, these angles are also calculated from the gyroscopes output as well, but with errors that increase with time. Of course for some applications of AHRS system, orientation errors can be damped out with a proportional‐integral controller. In such a case, the filter cut‐off frequency is usually selected experimentally. But, for high accelerating vehicles utilizing AHRS, the system errors can become very large. A possible remedy to this problem could be to use more advanced nonlinear filter algorithms such as the one proposed.

Magnetometer Autocalibration Leveraging Measurement Locus Constraints

An autocalibration algorithm for calibration of magnetometer triads used to determine heading in small aerial vehicles is developed and its performance is analyzed. The algorithm estimates the 12 calibration parameters, which are elements of an affine transformation mapping measured, and thus, erroneous magnetometer measurements into corrected field measurements. The mapping corrects magnetometer output errors due to hard-iron biases, scale factor deviations, and nonorthogonality effects caused by soft irons or physical arrangement of the sensor axes. The correction mapping is determined by leveraging the fact that the locus of Earth's magnetic field vector as measured by a triad of magnetometers is an ellipsoid. The coefficients defining the ellipsoid are computed using a total least-squares estimator. It is shown that, generally, in such autocalibration algorithms, soft-iron errors and sensing axes nonorthogonality can result in an error mode that is unobservable. These conditions are identified and the algorithm incorporates a method for detecting them. In these instances, even though autocalibration can provide an estimate of only 9 of the 12 calibration parameters, it is shown that how external measurements from a triad of accelerometers and a global positioning system receiver can provide the information needed to estimate the unobservable error mode.

SQUID Nondestructive Testing System With Vibrating Normal Pick-Up Coil

A vibrating normal pick-up coil coupled to a superconducting quantum interference device (SQUID) magnetometer as a nondestructive testing system was studied. The vibrating normal pick-up coil measures the magnetic field gradient at a point. Output of the SQUID magnetometer is lock-in detected at the vibration frequency. The frequency of an excitation magnetic field can be set low to detect deep structural flaws. The use of a normal coil vibrated at 20 kHz with output voltage amplified by a low-noise amplifier enabled detection of a cylindrical defect in an aluminum plate with an excitation magnetic field at 40 Hz.

In-flight spacecraft magnetic field monitoring using scalar/vector gradiometry

Earth magnetic field mapping from planetary orbiting satellites requires a spacecraft magnetic field environment control program combined with the deployment of the magnetic sensors on a boom in order to reduce the measurement error caused by the local spacecraft field. Magnetic mapping missions (Magsat, Oersted, CHAMP, SAC-C MMP and the planned ESA Swarm project) carry a vector magnetometer and an absolute scalar magnetometer for in-flight calibration of the vector magnetometer scale values and for monitoring of the inter-axes angles and offsets over time intervals from months to years. This is done by comparing the two magnetometer outputs for several days and for as many different external field directions and amplitudes in the satellite frame as available. The vector and the scalar sensor may be placed of the order of 2 m apart and at the end of an about 10 m long boom counted from the spacecraft centre-of-gravity. In line with the classical dual vector sensors technique for monitoring the spacecraft magnetic field, this paper proposes and demonstrates that a similar combined scalar/vector gradiometry technique is feasible by using the measurements from the boom-mounted scalar and vector sensors onboard the Oersted satellite. For Oersted, a large difference between the pre-flight determined spacecraft magnetic field and the in-flight estimate exists causing some concern about the general applicability of the dual sensors technique.

Calibration of Strapdown Magnetometers in Magnetic Field Domain

This paper presents an algorithm for calibrating strapdown magnetometers in the magnetic field domain. In contrast to the traditional method of compass swinging, which computes a series of heading correction parameters and thus is limited to use with two-axis systems, this algorithm estimates magnetometer output errors directly. Therefore, this new algorithm can be used to calibrate a full three-axis magnetometer triad. The calibration algorithm uses an iterated, batch least-squares estimator that is initialized using a two-step nonlinear estimator. The algorithm is simulated to validate convergence characteristics and further validated on experimental data collected using a magnetometer triad. It is shown that the postcalibration residuals are small and result in a system with heading errors on the order of 1 to 2 degrees.