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1. Enabling Small Anomaly Detection using Finite-Difference Magnetic Gradiometry

   Myers, Heidi; Lathrop, Daniel; Lekic, Vedran (March 2025, Geophysics)

   Magnetometry is used to detect ferrous objects at various scales, but detecting small-size, compact sources that produce small-amplitude anomalies in the shallow subsurface remains challenging. Magnetic anomalies are often approximated as dipoles or volumes of dipoles that can be located, and their source parameters (burial depth, magnetization direction, magnetic susceptibility, etc.) are characterized using scalar or vector magnetometers. Both types of magnetometers are affected by space weather and cultural noise sources that map temporal variations into spatial variations across a survey area. Vector magnetometers provide more information about detected bodies at the cost of extreme sensitivity to orientation, which cannot be reliably measured in the field. Magnetic gradiometry addresses the problem of temporal-to-spatial mapping and reduces distant noise sources, but the heading error challenges remain, motivating the need for magnetic gradient tensor (MGT) invariants that are relatively insensitive to rotation. Here, we show that the finite size of magnetic gradiometers compared to the lengthscales of magnetic anomalies due to small buried objects affects the properties of the gradient tensor, including its symmetry and invariants. This renders traditional assumptions of magnetic gradiometry largely inappropriate for detecting and characterizing small-size anomalies. We then show how the properties of the finite-difference MGT and its invariants can be leveraged to map these small sources in the shallow critical zone, such as unexploded ordnance (UXO), landmines, and explosive remnants of war (ERW), using both synthetic and field data obtained with a triaxial magnetic gradiometer (TetraMag). 

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2. GMAG: An open-source python package for ground-based magnetometers

   https://doi.org/10.3389/fspas.2022.1005061  

   Murphy, Kyle R.; Rae, I. Jonathan; Halford, Alexa J.; Engebretson, Mark; Russell, Christopher T.; Matzka, Jürgen; Johnsen, Magnar G.; Milling, David K.; Mann, Ian R.; Kale, Andy; et al (November 2022, Frontiers in Astronomy and Space Sciences)

   Magnetometers are a key component of heliophysics research providing valuable insight into the dynamics of electromagnetic field regimes and their coupling throughout the solar system. On satellites, magnetometers provide detailed observations of the extension of the solar magnetic field into interplanetary space and of planetary environments. At Earth, magnetometers are deployed on the ground in extensive arrays spanning the polar cap, auroral and sub-auroral zone, mid- and low-latitudes and equatorial electrojet with nearly global coverage in azimuth (longitude or magnetic local time—MLT). These multipoint observations are used to diagnose both ionospheric and magnetospheric processes as well as the coupling between the solar wind and these two regimes at a fraction of the cost of in-situ instruments. Despite their utility in research, ground-based magnetometer data can be difficult to use due to a variety of file formats, multiple points of access for the data, and limited software. In this short article we review the Open-Source Python library GMAG which provides rapid access to ground-based magnetometer data from a number of arrays in a Pandas DataFrame, a common data format used throughout scientific research. 

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3. Citizen science: Development of a low-cost magnetometer system for a coordinated space weather monitoring

   https://doi.org/10.1016/j.ohx.2024.e00580  

   Kim, Hyomin; Witten, David; Madey, Julius; Frissell, Nathaniel; Gibbons, John; Engelke, William; Liddle, Anderson; Muscolino, Nicholas; Visone, Joseph; Cao, Zhaoshu (September 2024, HardwareX)

   As part of Ham Radio Science Citizen Investigation (HamSCI) Personal Space Weather Station (PSWS) project, a low-cost, commercial off-the-shelf magnetometer has been developed to provide quantitative and qualitative measurements of the geospace environment from the ground for both scientific and operational purposes at a cost that will allow for crowd-sourced data contributions. The PSWS magnetometers employ a magneto-inductive sensor technology to record three-axis magnetic field variations with a field resolution of ~3 nT at a 1 Hz sample rate. The measurement range of the sensor is +/-1.1e6 nT) and is valid over a temperature range of −40 °C to +85 °C. Data from the PSWS network will combine these magnetometer measurements with high frequency (HF, 3–30 MHz) radio observations to monitor large-scale current systems and ionospheric disturbances due to drivers from both space and the atmosphere. A densely-spaced magnetometer array, once established, will demonstrate their space weather monitoring capability to an unprecedented spatial extent. Magnetic field data obtained by the magnetometers installed at various locations in the US are presented and compared with the existing magnetometers nearby, demonstrating that the performance is very adequate for scientific investigations. 

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4. Investigation of geomagnetic reference models based on the Iridium$$^{\circledR }$$ constellation

   https://doi.org/10.1186/s40623-022-01574-w  

   Califf, Samuel; Alken, Patrick; Chulliat, Arnaud; Anderson, Brian; Rock, Kenneth; Vines, Sarah; Barnes, Robin; Liou, Kan (February 2022, Earth, Planets and Space)

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

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5. Online Three-Axis Magnetometer Hard-Iron and Soft-Iron Bias and Angular Velocity Sensor Bias Estimation Using Angular Velocity Sensors for Improved Dynamic Heading Accuracy

   https://doi.org/10.55417/fr.2022033  

   Spielvogel, Andrew; Shah, Abhimanyu; Whitcomb, Louis (March 2022, Field Robotics)

   This article addresses the problem of dynamic online estimation and compensation of hard-iron and soft-iron biases of three-axis magnetometers under dynamic motion in field robotics, utilizing only biased measurements from a three-axis magnetometer and a three-axis angular rate sensor. The proposed magnetometer and angular velocity bias estimator (MAVBE) utilizes a 15-state process model encoding the nonlinear process dynamics for the magnetometer signal subject to angular velocity excursions, while simultaneously estimating nine magnetometer bias parameters and three angular rate sensor bias parameters, within an extended Kalman filter framework. Bias parameter local observability is numerically evaluated. The bias-compensated signals, together with three-axis accelerometer signals, are utilized to estimate bias-compensated magnetic geodetic heading. Performance of the proposed MAVBE method is evaluated in comparison to the widely cited magnetometer-only TWOSTEP method in numerical simulations, laboratory experiments, and full-scale field trials of an instrumented autonomous underwater vehicle in the Chesapeake Bay, Maryland, USA. For the proposed MAVBE, (i) instrument attitude is not required to estimate biases, and the results show that (ii) the biases are locally observable, (iii) the bias estimates converge rapidly to true bias parameters, (iv) only modest instrument excitation is required for bias estimate convergence, and (v) compensation for magnetometer hard-iron and soft-iron biases dramatically improves dynamic heading estimation accuracy. 

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