Magnetic Disturbances Research Articles

Effect of sub-micron deformations at opposing strain rates on the micromagnetic behaviour of non-oriented electrical steel

We are entering an era of re-electrification, seeking high-power density electrical machines with minimal resource use. Significant performance gains in electrical machines have been achieved through precise manufacturing processes, including the shaping/cutting of soft magnetic materials. However, most studies have evaluated magnetic performance at a macro level, focusing on components, while the fundamental mechanisms, e.g., how the micromagnetic behaviour is affected by mechanical interference, remain unclear. In this study, we examine the impact of sub-micron deformations at opposing strain rates (10−2 to 101 s−1) on the micromagnetic behaviour of soft magnetic non-oriented electrical steel. Using a diamond probe to indent within a single grain of polycrystalline material at different velocities, we induce quasi-static and dynamic mechanical loading. Our analysis, employing magnetic force microscopy, transmission Kikuchi diffraction, and scanning transmission electron microscopy with a pixelated detector, reveals that magnetic texture disturbances rely on the time-dependent dislocation dynamics of the Fe-BCC material. Additionally, we compress micro-pillars to further investigate these effects under bulk-isolated deformation. These findings highlight the importance of considering even ultra-small loads, such as nano-indentations and micro-pillar compressions, in the manufacturing of next-generation electric machines, as they can affect magnetic texture and performance.

Strong turbulence and magnetic coherent structures in the interstellar medium

Magnetic turbulence is classified as weak or strong based on the relative amplitude of the magnetic field fluctuations compared to the mean field. These two classes have different energy transport properties. The purpose of this study is to analyze turbulence in the interstellar medium (ISM) based on this classification. Specifically, we examined the ISM of simulated galaxies to detect evidence of strong magnetic turbulence and provide statistics on the associated magnetic coherent structures (MCoSs), such as current sheets, that arise in this context. We analyzed magnetohydrodynamic galaxy simulations with different initial magnetic field structures (either completely ordered or completely random) and recorded statistics on the magnetic field fluctuations ($ B/B_0$) and the MCoSs, which are defined here as regions where the current density surpasses a certain threshold. We also studied the MCoS sizes and kinematics. The magnetic field disturbances in both models follow a log-normal distribution, peaking at values close to unity; this distribution turns into a power law at large values ($ B/B_0 > 1$), which is consistent with strong magnetic turbulence The current densities are widely distributed, with non-power-law deviations from a log-normal at the largest values. These deviating values of the current density define MCoSs. We find that, in both models, MCoSs are fractally distributed in space, with a typical volume-filling factor of about 10 percent, and tend to coincide with peaks of star formation density. Their fractal dimension is close to unity on sub-kiloparsec scales, and between 2 and 3 on larger scales. These values are consistent with MCoSs having a sheet-like or filament-like morphology. Our work challenges the prevailing paradigm of weak magnetic turbulence in the ISM by demonstrating that strong magnetic disturbances can occur even when the initial magnetic field is completely ordered. This strong magnetic turbulence arises self-consistently from differential rotation and supernova feedback. Our findings provide a foundation for a magnetic turbulence description of the galactic ISM that includes strong fluctuations of the magnetic field.

Geomagnetic and ionospheric effects two consecutive strong earthquakes in Morocco on september 08, 2023

The geophysical effects of a strong seismic event in the form of two earthquakes of magnitude 6.8 and 4.9 that occurred on September 08, 2023 in Morocco at close times 22:11 and 22:30 UTC with an epicentral distance between the foci of ~ 4 km are considered. We used data from a number of observatories of the INTERMAGNET network and the results of magnetic registration at the Mikhnevo Geophysical Observatory of IDG RAS. It was shown that in the absence of significant global disturbances of the Earth’s magnetic field, earthquakes were accompanied by a series of three positive bay-shaped geomagnetic variations with maximum amplitudes from ~1 to ~10 nT, following each other after ~60 min. The maxima of the induced magnetic field variations were observed almost synchronously at distances from ~800 to ~10000 km. The delay time of the magnetic effect relative to the main shock of the first earthquake was ~70 min. Taking into account the almost planetary nature and high synchronicity of the magnetic field disturbances caused over a significant range of distances, as well as time delays corresponding in order of magnitude to the travel time of the seismic signal of a distance multiple of the size of the Earth, it is suggested that the magnetic effect of the seismic event in question was caused by a global source, which can serve as an excited geodynamo. The ionospheric effect of the seismic event under consideration is presented in the form of variations of the critical frequency f0F2 calculated from the data of the ground-based sounding station of the del Ebre Observatory.

Different origins of magnetic disturbances during substorm growth and expansion phases and insufficiency of the AL index as their sole measure

The paper examines the relationship between the PC index, characterizing the solar wind energy input into the magnetosphere, and the AL index, characterizing the magnetic substorm intensity for the expansion phase of isolated substorms recorded in 1998–2017. Magnetic disturbances in the course of the expansion phase are produced by the DP11 current system with a powerful westward electrojet disposed in the midnight auroral zone. It is generally accepted that this electrojet is generated by the “substorm current wedge” system of fieldaligned currents (SCW FAC) providing closure of the magnetotail plasma sheet currents through the auroral ionosphere. As this takes place, magnetic disturbances in the course of the substorm growth phase are produced by the DP12 current system with westward and eastward electrojets located, correspondingly, in the morning and evening sectors of the auroral zone, with the electrojets generated by the R1/R2 FAC system operating in the inner (closed) magnetosphere. The intensity of R1 currents is determined by the “coupling function” EKL, which represents the optimal combination of all geoeffective solar wind parameters affecting the magnetosphere. The DP2 magnetic disturbances generated by the R1 FAC system in polar caps forms the basis for estimating the PC index, which strongly follows the EKL field changes and correlates well with the development of magnetic substorms. Analyses performed in AARI revealed the principally distinctive character of the relationships between the PC index and AL index in the course of the substorm growth (DP12 disturbances) and explosive (DP11 disturbances) phases. The DP12 disturbances, generated by FAC systems in the closed magnetosphere, are developed in strong relation to the PC index. The DP11 disturbances, generated by the SCW FAC system, related to the magnetotail plasma sheet, show quite irregular character of relationship between the PC and AL values: the sudden jumps of the substorm intensity (ALpeaks) might occur, time and again, at any value of the PC index and with quite different delay times relative to sudden substorm onset. It means that the processes in the tail plasma sheet, leading to the formation of a “substorm current wedge” are determined by the state of the magnetotail plasma sheet itself. The solar wind influence (evaluated by the PC index) affects but does not control the processes in the magnetotail, unlike those in the inner magnetosphere. It should be noted in this connection that the intensity of magnetic DP12 and DP11 disturbances, observed in the course of the substorm growth and explosive phases, is estimated by a single AL index, in spite of the different origin of these disturbances (R1/R2 and SCW FAC systems). It is necessary to employ two separate indices characterizing DP12 and DP11 disturbances in order to allow for the effects of the solar wind on the processes in the inner magnetosphere and in the magnetotail.

Dayside Magnetic Depression Following Interplanetary Shock Arrivals During the February 1958 and July 1959 Superstorms

AbstractThe present study investigates mid‐ and low‐latitude ground magnetic disturbances observed following the arrival of three interplanetary (IP) shocks during the super‐geomagnetic storms of February 1958 and July 1959. One may expect that after IP shocks, the H (northward) magnetic component increases globally but especially on the dayside. However, in each event, the H component was depressed sharply for 1–2 hr in the dawn‐to‐noon sector, whereas it increased in other local time (LT) sectors. Observed magnetic deflections suggest that there existed field‐aligned currents (FACs) flowing into and out of the auroral zone around the western and eastern edges of the LT sector of the dayside H depression. These features strongly suggests that the observed H depression was a remote effect of a R1‐sense FAC system. It was previously reported that similar ground magnetic disturbances were observed after the SSC of the 2003 Halloween storm, which reveals striking similarities to the well‐known H depression observed at Colaba during the 1859 Carrington storm. It is therefore suggested that the external driving behind IP shocks, especially those associated with major storms, is most optimum for the sharp reduction of the dayside H component through the formation and intensification of the dayside FAC system. Associated magnetic disturbances are considered to be larger in magnitude with increasing magnetic latitude, and oriented azimuthally as well as meridionally. Such magnetic disturbances in dayside midlatitudes may not be discussed very often as a target of space weather, but their potential impacts on ground infrastructures probably require closer attention.

A Robust Tri-Electromagnet-Based 6-DoF Pose Tracking System Using an Error-State Kalman Filter.

Magnetic pose tracking is a non-contact, accurate, and occlusion-free method that has been increasingly employed to track intra-corporeal medical devices such as endoscopes in computer-assisted medical interventions. In magnetic pose-tracking systems, a nonlinear estimation algorithm is needed to recover the pose information from magnetic measurements. In existing pose estimation algorithms such as the extended Kalman filter (EKF), the 3-DoF orientation in the S3 manifold is normally parametrized as unit quaternions and simply treated as a vector in the Euclidean space, which causes a violation of the unity constraint of quaternions and reduces pose tracking accuracy. In this paper, a pose estimation algorithm based on the error-state Kalman filter (ESKF) is proposed to improve the accuracy and robustness of electromagnetic tracking systems. The proposed system consists of three electromagnetic coils for magnetic field generation and a tri-axial magnetic sensor attached to the target object for field measurement. A strategy of sequential coil excitation is developed to separate the magnetic fields from different coils and reject magnetic disturbances. Simulation and experiments are conducted to evaluate the pose tracking performance of the proposed ESKF algorithm, which is also compared with standard EKF and constrained EKF. It is shown that the ESKF can effectively maintain the quaternion unity and thus achieve a better tracking accuracy, i.e., a Euclidean position error of 2.23 mm and an average orientation angle error of 0.45°. The disturbance rejection performance of the electromagnetic tracking system is also experimentally validated.

Near-zero magnetic field disturbance suppression method based on adaptive filtering and quasi-proportional resonance control

The cardiac magnetic field used for magnetocardiographic (MCG) imaging must be detected in a stable near-zero magnetic field environment. In the hospital environment, there are mainly two kinds of magnetic field disturbances that affect the signal-to-noise ratio of cardiac magnetic field detection. One is the magnetic field disturbance with high power spectral density at a specific frequency, and the other is the random magnetic field disturbance with low frequency. To suppress magnetic field disturbances, this paper proposed a near-zero magnetic field disturbance suppression method that combined a PI controller with adaptive filtering and quasi-proportional resonance control (PI-APF-QPR). The magnetic field disturbance with high amplitude and specific frequency was extracted by the adaptive filter (APF) and suppressed by the quasi-proportional resonance (QPR) controller. Additionally, the low-frequency random disturbance was suppressed by the PI controller. The experimental results showed that compared with the PI controller, the peak-to-peak value of the magnetic field by the PI-APF-QPR controller was reduced by 39.1%, and the suppression ratio of the magnetic field noise by the PI-APF-QPR controller was improved by 29.5%, which verified the effectiveness of the proposed magnetic field disturbance suppression method.

On the Role of Physical Processes in Controlling Equatorial Plasma Bubble Morphology

AbstractIn this study, we present the results of an analysis of the morphological features of Equatorial Plasma Bubbles (EPBs) over South America. In this context, we analyzed data from the Disturbance Ionosphere indeX (DIX) maps calculated using around 450 Global Navigation Satellite System (GNSS) stations. To mitigate the influence of magnetic disturbances on bubble development, only data from geomagnetically quiet days were utilized. This study covered the period from the post‐peak of solar cycle 24 (2015) to the pre‐peak of solar cycle 25 (2023), totaling 1321 nights with EPB occurrences, representing the largest data set of EPBs ever compiled for South America. Our analysis unveiled several key findings regarding EPBs and their behavior over the South American region. First, we observed that the amplitude of plasma depletions, as reflected in the DIX values, and the EPB latitudinal development follow an approximately 11‐year cycle driven by solar radiation levels. Furthermore, our analysis highlights the significant influence of factors such as the angle between the solar terminator and the magnetic meridian (T‐M angle), which varies inversely with the vertical plasma drift velocity during the pre‐reversal enhancement (PRE). Additionally, we discuss the longitudinal variations associated with magnetic declination, as well as the saturation behavior of EPB development with extreme solar flux.

Adaptive current decoupling control scheme based on online multi-parameter identification for high-speed permanent magnet synchronous motor in fuel cell

The precise control of centrifugal hydrogen compressor (CHC) driven by high-speed permanent magnet synchronous motor (PMSM) is the key to the stable and efficient operation of hydrogen fuel cell (HFC). In this paper, an adaptive current deviation decoupling control (CDDC) strategy based on variable step size affine projection algorithm (VSS-APAs) is proposed to solve the high-speed PMSM control problem caused by current cross-coupling and parameter perturbation under complex operating conditions. Firstly, the step size is dynamically adjusted by VSS-APA through a normalized gradient descent to respond to system fluctuations, achieving rapid parameter identification during dynamic changes and accurate tracking in steady states. Secondly, stator inductance, magnetic flux linkage, stator resistance, and disturbance torque are identified in two-time-scale based on the characteristics of parameter changes, overcoming the rank deficiency in motor mathematical equations. Finally, utilizing online-identified motor parameters, the gains of the CDDC are adjusted, and compensation is applied for back electromotive force (BEMF) and disturbance torque, thereby ensuring the control accuracy of the motor under parameter perturbations and system disturbances. Experimental results demonstrate that the proposed method enhances the responsiveness and accuracy of the control strategy through efficient parameters identification. Consequently, it guarantees high-efficiency and stable performance of the CHC across different working conditions, markedly advancing the overall functionality and dependability of hydrogen energy system.

Dynamic Field Nulling Method for Magnetically Shielded Room Based on Padé Approximation and Generalized Active Disturbance Rejection Control

Magnetically shielded rooms (MSRs) provide a near-zero field environment for magnetoencephalography (MEG) research. Due to the high cost of high-permeability materials and the weak shielding capability against low-frequency magnetic disturbance, it is necessary to further design active compensation coils combined with a closed-loop control system to achieve dynamic nulling of environmental magnetic disturbance. To enhance the performance of the dynamic nulling system, this paper proposes a novel controller design method based on Padé approximation and generalized active disturbance rejection control (GADRC). First, a precise closed-loop model of the dynamic nulling system is established. On this basis, the delay element of the optically pumped magnetometer (OPM) is approximated using the Padé approximation method, and the controller is designed within the GADRC framework. The system’s stability and disturbance suppression capability are analyzed using frequency-domain methods. To validate the effectiveness of the proposed method, simulations and experiments are conducted, achieving a shielding factor greater than 40 dB at 0.1 Hz. After filtering out power frequency interference, the peak-to-peak field fluctuation is reduced from 320.3 pT to 1.8 pT.

Special Particle Precipitation Signatures Over Giant Auroral Undulations During the 7 September 2015 Geomagnetic Storm

AbstractGiant undulations (GUs) have been well established to be the optical manifestation of the plasmapause surface wave (PSW) where the wave‐particle interactions provide particle sources to generate auroras. However, their detailed particles precipitation signatures in the ionosphere remain unclear. Here we analyze multi‐satellite conjugated observations in the ionosphere during a prominent GUs event, revealing the two‐zone precipitation pattern including energetic proton precipitations responsible for the main body of GUs and low‐energy electron precipitations for the edge of GUs. Interestingly, the occurrence of GUs is also accompanied with high‐energy particles precipitations of hundreds of keV and magnetic disturbances of three components. The sizes of sawtooth in the GUs correlate positively with the strength of adjacent subauroral polarization streams (SAPS). The two‐zone precipitation pattern and high‐energy particles precipitation over GUs are potentially related to the plasma sheet and very‐low frequency wave (VLF) modulation of the PSW, respectively.

Conjugate aurora observations by the Gjøa and Discovery expeditions

Abstract. From 1901 to 1912 – known as the “heroic period” of Arctic and Antarctic exploration – great inroads were made (not only geographic but also scientific) to our knowledge of the continent. At Amundsen's Expedition through the Northwest Passage, measurements of the geomagnetic field and visual auroras were carried out for 19 months at Gjoa Haven (Gjøahavn in Norwegian; geographic coordinates 68°37′10′′ N, 95°53′25′′ W). Scott's Discovery Expedition – at Cape Armitage, McMurdo (coordinates 77.86° S, 166.69° E), Antarctica – carried out the same type of measurements. Their observations were carried out geomagnetically conjugate to Gjoa Haven, with both stations close to 78° magnetic latitude. In addition, measurements were overlapping in time during 1903–1904. However, these two stations are located at different longitudes, so there is a difference in local time between the stations of about 6.5 h. Gjoa Haven and Cape Armitage are conveniently located for separating disturbances in the polar cap regions caused by solar electromagnetic radiations or the solar wind. Auroras were observed during 7 months per year. This gave a unique possibility to compare conjugate characteristics of polar cap auroras. Comparing conjugate geophysical data introduces some difficulties. During the winter season at Gjoa Haven, they had a bright summer in Antarctica, and visa versa. Thus, simultaneous temporal and spatial ionospheric variations can be marked differently. Still, the average diurnal and seasonal variations were similar. The quantity of the auroral data from Cape Armitage was larger because there they had a continuous watch of the sky. The main findings regarding polar cap auroras are the following. Three different auroral forms dominate the polar cap. Low-intensity auroral bands – then called streamers – were the dominating auroral forms morning and afternoon. The number of auroral events in 1903 was nearly twice that in 1902 and 1904. A marked midwinter maximum was observed at both stations. Many displays were observed poleward of the oval. The large fraction was associated with weak magnetic disturbances. Some forms of polar cap aurora have special magnetic signatures and seem to be anti-correlated with Kp. They can be mapped even if they are not seen. According to recent satellite measurements (Newell et al., 2009), they are probably caused by polar rain and/or photoelectrons.

Data Quality Assessment of Gravity Recovery and Climate Experiment Follow-On Accelerometer.

Accelerometers are mainly used to measure the non-conservative forces at the center of mass of gravity satellites and are the core payloads of gravity satellites. All kinds of disturbances in the satellite platform and the environment will affect the quality of the accelerometer data. This paper focuses on the quality assessment of accelerometer data from the GRACE-FO satellites. Based on the ACC1A data, we focus on the analysis of accelerometer data anomalies caused by various types of disturbances in the satellite platform and environment, including thruster spikes, peaks, twangs, and magnetic torque disturbances. The data characteristics and data accuracy of the accelerometer in different operational states and satellite observation modes are analyzed using accelerometer observation data from different time periods. Finally, the data consistency of the accelerometer is analyzed using the accelerometer transplantation method. The results show that the amplitude spectral density of three-axis linear acceleration is better than the specified accuracy (above 10-1 Hz) in the accelerometer's nominal status. The results are helpful for understanding the characteristics and data accuracy of GRACE-FO accelerometer observations.

Adaptive Magnetic Disturbance Suppression of a Shaking Buoy and Magnetic Anomaly Detection

Adaptive Magnetic Disturbance Suppression of a Shaking Buoy and Magnetic Anomaly Detection

How the Ionosphere Responds Dynamically to Magnetospheric Forcing

AbstractGround magnetic field variations have been used to investigate ionospheric dynamics for more than a century. They are usually explained in terms of an electric circuit in the ionosphere driven by an electric field, but this is insufficient to explain how magnetic field disturbances are dynamically established. Here we explain and simulate how the ionosphere dynamically responds to magnetospheric forcing and how it leads to magnetic field deformation via Faraday's law. Our approach underscores the causal relationships, treating the magnetic field and velocity as primary variables (the B, v paradigm), whereas the electric field and current are derived, in contrast to the E, j paradigm commonly used in ionospheric physics. The simulation approach presented here could be used as an alternative to existing circuit‐based numerical models of magnetosphere‐ionosphere coupling.

Plasma Sheet Counterparts for Auroral Beads and Vortices in Advance of Fast Flows: New Evidence for Near‐Earth Substorm Onset

AbstractThe relationship between auroral, ground, and plasma sheet signatures in the late growth phase is crucial for understanding the sequence of events during a substorm expansion phase onset. Here we show conjugate ground‐auroral‐satellite observations of a substorm that occurred on 18 September 2021, between 04:45 and 05:00 UT, where four auroral activations were detected in the all‐sky imagers. An initial activation showed the brightening of an equatorward arc within the cutoff of the 630 nm emissions, indicating activity on closed field lines well inside the open‐closed field line boundary (OCFLB). During a second activation, auroral beads were observed on a brightening arc, equatorward and within the OCFLB, followed by the transformation from small‐scale to large‐scale vortices. The tail current sheet was highly disturbed during the auroral vortex evolution, including pressure and magnetic disturbances, an apparent broadening of a previously thin current sheet, and a breakdown of the frozen‐in condition. Our observations clearly show late growth phase dynamics, including arc brightenings, the formation of auroral beads, and auroral vortex development, can occur well in advance of fast Earthward flows in the tail. Indeed, it is only during that later activity that auroral breakup and strong Earthward flows, which we associate with magnetic reconnection further down the tail, are observed together with strong magnetic bays on the ground. The sequence of events is consistent with an inside‐to‐outside model at substorm expansion phase onset, most likely via a shear‐flow ballooning instability in the transition region from dipole to tail‐like fields in the near‐Earth plasma sheet.

Prediction of high latitude nightside Geomagnetic Field Disturbances (GGFDs) during the 9-March-2012 geomagnetic storm using Recurrent Neural Network (RNN)

Geomagnetically Induced currents (GICs) pose a potentially catastrophic threat to the safety and security of large-scale power distribution systems. Using a recurrent neural network, we predict high (≥60°) magnetic latitude (MLAT) and night side (06–18) magnetic local time (MLT) geomagnetic field disturbances (surface dBs/dt and vertical dBz/dt), the trigger of GICs, during a geomagnetic storms occurred on March 09, 2012. We use the high latitude geomagnetic field data from SuperMAG and the solar wind particle and magnetic field data from NASA-OMNIWeb. We divide the high latitude night side of Earth’s globe into multiple sectors and obtain a time series of maximum geomagnetic disturbances observed in each sector. We use the Long Short Term Memory (LSTM) network technique sector by sector on both, the solar wind data and the sectored geomagnetic field disturbance (10° geomagnetic latitude, 1-hour MLT) time series obtained from SuperMAG. Each sector prediction is plotted on a polar map to reveal high latitude night side geomagnetic disturbance patterns. This high latitude nigh side model has great potential. With solar wind input at a Lagrangian-1 point, and geomagnetic field data from SuperMAG, it can predict the peak magnetic disturbance at any given sector for couple of hours in advance. Our machine learning techniques provide the best set of solar wind input that gives the best disturbance prediction. This paper presents a prototype of the global geomagnetic disturbance model with low-resolution spatial grids and a subset of potential solar wind input parameters. Once matured, the global magnetic disturbance model will be provided to the public.

A novel sensor based on the composite mechanism of magnetic flux leakage and magnetic field disturbance for comprehensive inspection of defects with varying angles and widths

Ferromagnetic components are susceptible to various defects after prolonged service. The defects generated in these components are diverse and exhibit irregular orientation, which may impede comprehensive defect examination using a single magnetic testing method. This paper proposes a novel magnetic measurement sensor that integrates the principles of magnetic flux leakage (MFL) and magnetic field disturbance (MFD). The combined theory is analyzed and validated through the utilization of finite element method (FEM) simulations as well as experimental investigations. By comparing simulation results with experimental data, the composite nature of the signal acquired beneath a magnetic bridge is convincingly demonstrated. In comparison to conventional MFL and MFD methods, this innovative sensor exhibits superior defect detection performance for varying angles and widths, while also addressing some inherent limitations associated with MFL and MFD principles.

An optically pumped magnetic gradiometer for the detection of human biomagnetism

We realise an intrinsic optically pumped magnetic gradiometer based on non-linear magneto-optical rotation. We show that our sensor can reach a gradiometric sensitivity of 18 fT cm−1Hz−1 and can reject common mode homogeneous magnetic field noise with up to 30 dB attenuation. We demonstrate that our magnetic field gradiometer is sufficiently sensitive and resilient to be employed in biomagnetic applications. In particular, we are able to record the auditory evoked response of the human brain, and to perform real-time magnetocardiography in the presence of external magnetic field disturbances. Our gradiometer provides complementary capabilities in human biomagnetic sensing to optically pumped magnetometers, and opens new avenues in the detection of human biomagnetism.

Robust Orientation Estimation from MEMS Magnetic, Angular Rate, and Gravity (MARG) Modules for Human-Computer Interaction.

While the availability of low-cost micro electro-mechanical systems (MEMS) accelerometers, gyroscopes, and magnetometers initially seemed to promise the possibility of using them to easily track the position and orientation of virtually any object that they could be attached to, this promise has not yet been fulfilled. Navigation-grade accelerometers and gyroscopes have long been the basis for tracking ships and aircraft, but the signals from low-cost MEMS accelerometers and gyroscopes are still orders of magnitude poorer in quality (e.g., bias stability). Therefore, the applications of MEMS inertial measurement units (IMUs), containing tri-axial accelerometers and gyroscopes, are currently not as extensive as they were expected to be. Even the addition of MEMS tri-axial magnetometers, to conform magnetic, angular rate, and gravity (MARG) sensor modules, has not fully overcome the challenges involved in using these modules for long-term orientation estimation, which would be of great benefit for the tracking of human-computer hand-held controllers or tracking of Internet-Of-Things (IoT) devices. Here, we present an algorithm, GMVDμK (or simply GMVDK), that aims at taking full advantage of all the signals available from a MARG module to robustly estimate its orientation, while preventing damaging overcorrections, within the context of a human-computer interaction application. Through experimental comparison, we show that GMVDK is more robust to magnetic disturbances than three other MARG orientation estimation algorithms in representative trials.