Magnetic field based heading estimation for pedestrian navigation environments

Most portable systems like smart-phones are equipped with low cost consumer grade sensors, making them useful as Pedestrian Navigation Systems (PNS). Measurements of these sensors are severely contaminated by errors caused due to instrumentation and environmental issues rendering the unaided navigation solution with these sensors of limited use. The overall navigation error budget associated with pedestrian navigation can be categorized into position/displacement errors and attitude/orientation errors. Most of the research is conducted for tackling and reducing the displacement errors, which either utilize Pedestrian Dead Reckoning (PDR) or special constraints like Zero velocity UPdaTes (ZUPT) and Zero Angular Rate Updates (ZARU). This article targets the orientation/attitude errors encountered in pedestrian navigation and develops a novel sensor fusion technique to utilize the Earth’s magnetic field, even perturbed, for attitude and rate gyroscope error estimation in pedestrian navigation environments where it is assumed that Global Navigation Satellite System (GNSS) navigation is denied. As the Earth’s magnetic field undergoes severe degradations in pedestrian navigation environments, a novel Quasi-Static magnetic Field (QSF) based attitude and angular rate error estimation technique is developed to effectively use magnetic measurements in highly perturbed environments. The QSF scheme is then used for generating the desired measurements for the proposed Extended Kalman Filter (EKF) based attitude estimator. Results indicate that the QSF measurements are capable of effectively estimating attitude and gyroscope errors, reducing the overall navigation error budget by over 80% in urban canyon environment.

The article discusses a field geophysical complex that includes the Earth's gravity and magnetic fields parameters meters — an digital zenith camera (DZC), a relative gravimeter, onboard quantum magnetometer and ground magnetovariation station. This complex allows determining such parameters of the Earth's gravity field as acceleration and anomalies of gravity, plumb line deviations, horizontal components of the acceleration of gravity and gravitational gradients, and parameters of the Earth's magnetic field — absolute and anomalous values of induction. Maps of the Earth's gravity and magnetic fields can be used in various fields, in particular, in the creation and testing of integrated autonomous navigation systems using the parameters of these fields. The paper presents examples of parameter maps created using this complex. The measurement error of acceleration and gravity anomaly is 10 µGal, plumb line deviation is ≈ 0.2″, horizontal components of gravity acceleration are ≈ 1 mGal, gravitational gradients are 10 Eötvös at a distanc

Robust attitude and heading estimation with respect to a known reference is an essential component for indoor localization in robotic applications. Affordable Attitude and Heading Reference Systems (AHRS) are typically using 9-axis solid-state MEMS-based sensors. The accuracy of heading estimation on such a system depends on the Earth's magnetic field measurement accuracy. The measurement of the Earth's magnetic field using MEMS-based magnetometer sensors in an indoor environment, however, is strongly affected by external magnetic perturbations. This paper presents a novel approach for robust indoor heading estimation based on skewed-redundant magnetometer fusion. A tetrahedron platform based on Hall-effect magnetic sensors is designed to determine the Earth's magnetic field with the ability to compensate for external magnetic field anomalies. Additionally, a correlation-based fusion technique is introduced for perturbation mitigation using the proposed skewed-redundant configuration. The proposed fusion technique uses a correlation coefficient analysis for determining the distorted axis and extracts the perturbation-free Earth's magnetic field vector from the redundant magnetic measurement. Our experimental results show that the proposed scheme is able to successfully mitigate the anomalies in the magnetic field measurement and estimates the Earth's true magnetic field. Using the proposed platform, we achieve a Root Mean Square Error of 12.74° for indoor heading estimation without using an additional gyroscope.

The effect of various combinations of conditions, i.e., presence of the Earth's magnetic field during and after deformation on the distribution of stray magnetic field of S355 steel sample, which is locally deformed, was investigated. Some of the stages of the experiment were carried out in zero magnetic field. Compensation of the Earth's magnetic field was obtained by the application of a pair of Helmholtz coils. These coils are able to produce homogeneous field compensating Earth's magnetic field over the full length of the sample. Stray magnetic field measurements were carried out along the longest dimension of the sample using the probe consisting of mutually perpendicular sensors allowing the simultaneous measurement of two magnetic field components, i.e., tangential and normal to a surface of the sample. Research has shown that there is a correlation between the level of plastic deformation of the investigated sample and the distribution of stray magnetic field. It was found that the nature of stray magnetic field of the sample depends on presence of external magnetic field during unloading. An attempt was also made, with the finite-element analysis, to verify experimentally obtained stray magnetic field distribution of undeformed sample.

The magnetic field of Earth, Be, is an intriguing topic in the introductory physics curriculum that engages students’ curiosity and inspires numerous speculations about the nature of this phenomenon. There are several methods for measuring Earth’s magnetic field. Probably, the most widespread and visual method of measuring the field in student lab experiments utilizes a tangent galvanometer. Recently, PASCO scientific suggested to use a magnetic field sensor for this goal, in a procedure where a magnetic field sensor combined with a rotary motion sensor is rotated in a 2-D plane containing the magnetic field vector of Earth. In this case, the magnetic field detected by the magnetic field sensor is a component of the magnetic field vector oriented relative to the direction of the magnetic field sensor probe (radial component of magnetic field). This means that the detected magnetic field considered as a function of the angle of rotation of the sensor will be a sinusoidal function. The amplitude of this function is the magnitude of Earth’s magnetic field. In conducting this experiment, initially the sensor is set to zero by placing it in a Zero Gauss Chamber (mu-metal). The equipment setup of the experiment is depicted in the figure shown in Ref. 9. The described experiment requires the use of a dip needle that is a compass pivoted to move in the plane containing the magnetic field vector of Earth. The dip needle shows the dip angle θ (inclination) that Earth’s magnetic field makes with the horizontal. Besides the previously mentioned devices, this experiment requires the use of an aluminum table clamp, adjustable angle clamp, and angle indicator to ensure proper alignment of the rotary motion sensor in a 2D plane containing the magnetic field vector.

Magnetoreception

Magnetic observations, and in particular those necessary for the control of magnetograph records, at stations in high magnetic latitudes have been greatly handicapped, because of unfavorable magnetic conditions as well as temperature conditions at such stations, for lack of a suitable instrument to determine rapidly and with precision the vertical intensity of the Earth's magnetic field. The establishment of the Godhavn Magnetic Observatory in Greenland, where the magnetic inclination is about 82°, led the author to consider electrical methods of determining the magnetic vertical‐intensity of the Earth's field. An experimental apparatus was used during a trip to Greenland in 1925 to select a site for the Observatory, and as a result of these experiments a new type of vertical‐intensity magnetometer was developed and was sent in August 1926, after trial at the Rude Skov and Potsdam observatories, to the Godhavn Observatory for use there regularly.The essential part of the new instrument is a precise standard for mutual inductance, that is, an inductor with two sets of windings, and very strongly built, By rotaiing the standard 180° on a horizontal axis the vertical intensity of the Earth's magnetic field gives rise to electromotive forces in the windings. One winding is connected with a ballistic galvanometer which, through the arrangement described below, measures the induced effect; the sensitivity of the galvanometer is such that rotating the inductor 180° would cause a deflection quite beyond the scale‐limit of the galvanometer, for example, at Rude Skov for a scale‐distance of 2 meters, a deflection of 10 meters. This arrangement, a sort of zero‐method, by which the deflection of the galvanometer never exceeds a few centimeters even for highest sensitivity of the apparatus, utilizes an accurately determined electric current which, during the turning of the inductor, may be made or broken in the second winding. The making or breaking in this current through the second winding induces an electromotive force in the winding connected with the galvanometer, and the connections are such that the electromotive force induced by the variation of the “compensating current” is opposite to the electromotive force induced by the vertical component of the Earth's magnetic field during a turn of the inductor. Thus, the resulting deflection of the galvanometer corresponds to the difference of the two induced electromotive forces. By again turning the coil and using some other compensating current, a second galvanometer reading is obtained. By means of two such readings the strength of a compensating current, which should give just the zero‐deflection of the galvanometer, is readily computed.

The theory of a new primary standard for measuring any component of the Earth's magnetic field is developed. The magnetometer consists of a Helmholtz‐Gaugain coil which provides a standard field opposed to that component of the Earth's magnetic field which is to be measured, and a rotating coil used as a null detector. The voltage generated in the rotating coil is detected by an alternating‐current amplifier. The constant of the Helmholtz‐Gaugain coil is computed from the formulas developed by C. Snow from the mutual inductance between two concentric cylinders. Corrections are computed for the fact that the Helmholtz‐Gaugain coils are helices, for the axial components of current, for the effect of the lead‐in wires, and for non‐uniformities in winding. The finite size of the detector is not a limitation on the accuracy since it is taken into account in the computation. Consequently, the accuracy of the coil‐constant of the new standard depends only upon constructional accuracy. Inhomogeneity in the field of the Helmholtz‐Gaugain coil necessitates the use of small correction‐terms to the voltage of fundamental frequency generated in the detector and produces odd harmonics of the fundamental frequency in the detector. The errors in orientating the Helmholtz‐Gaugain coil are also examined. The limiting sensitivity of the detector is calculated from the thermal agitation of electricty in the coil of the detector.

Summary It is shown that variable amplitudes in seismic signals received at a station need have no relation to the conductivity structure under that station. In particular, Eskdalemuir amplitude variations are satisfactorily explained with the most recent amplitude/distance curves, in which substantial modifications are made to the original Gutenberg-Richter curves. Osemeikhian & Everett (1968) studied magnetic field variations in South Scotland and Northern Ireland. They were particularly concerned with regions in which the vertical component of the Earth's magnetic field in the period band from a minute to several hours was ' anomalous '. Defining ' anomalous ' in the exploration of a new area is difficult, but they were able to distinguish two areas in Southern Scotland in which the variations in the vertical component of the Earth's magnetic field in the period range from 20min to 1 h were much smaller in amplitude than the variations at other stations. This they attributed to a region of high conductivity within 100 km of the surface in south-western Scotland. A magnetotelluric survey by Jain & Wilson (1967) indicates a layer approximately 10 km thick at a depth of 25-30 km with a high conductivity (50 times that of the overlying material). This layer might be equated with the sub-continental basaltic layer which is observed on occasions but which is difficult to derive from seismic refraction surveys. Agger & Carpenter (1964) hint that such a layer may exist beneath Eskdalemuir but are non-committal. One feature of Osemeikhian & Everett's paper is disturbing: they say at the beginning that seismic waves ' from North America ' are smaller in amplitude than similar signals received at Paris whereas signals ' from Russia ' are of comparable amplitude at Eskdalemuir and at Paris. I assume that they are referring to nuclear explosions at the Nevada Test Site and the Eastern Kazakh Test Site, as underground explosions would be the only suitably predictable sources on which to base such a statement. They therefore propose absorption of seismic waves, probably near Eskdalemuir, on their path from North America. In the absence of any disclaimer elsewhere in the paper one is led to assume that the authors equate the seismic absorption with the high conductivity found in the area. The implications are sufficiently serious to be examined in greater detail. To the casual reader this suggests: (a) that high conductivity (and maybe associated high temperatures) produce observable seismic absorption; (b) that the Eskdalemuir seismic array is badly located, being over a region of variable absorptive properties.

The order of magnitude of increased growth, multiplication rate, and decreased sporulation of Bacillus subtilis after exposure to nanotesla magnetic fields (MFs) relative to control samples were observed experimentally. Earth's total magnetic field intensity was reduced from 47.9 ± 0.4 μT to cover the range from 97.5 ± 1.7 nT to 1115 ± 158 nT in eight subsequent experiments by using three pairs of Helmholtz coils combined with Mu-metal shielding. The growth, multiplication rate, sporulation, and potassium content were measured in the probe and control containing B. subtilis cultures after 24 h of exposure to nanotesla and Earth's magnetic fields, respectively. The observed effect is discussed with regard to its possible repercussions on Earth's living species during geomagnetic reversals that occurred when the magnetic field was much weaker than the field that exists today. In addition, effects on future manned voyages into deep space, an environment with reduced magnetic field intensity, are considered.

Migratory birds are known to use the Earth's magnetic field as an orientation cue on their tremendous journeys between their breeding and overwintering grounds. The magnetic compass of migratory birds relies on the magnetic field's inclination, i.e. the angle between the magnetic field lines and the Earth's surface. As a consequence, vertical or horizontal field lines corresponding to 0 or 90 deg inclination should offer no utilizable information on where to find North or South. So far, very little is known about how small the deviations from horizontal or vertical inclination are that migratory birds can detect and use as a reference for their magnetic compass. Here, we asked: what is the steepest inclination angle at which a migratory bird, the Eurasian blackcap (Sylvia atricapilla), can still perform magnetic compass orientation in Emlen funnels? Our results show that blackcaps are able to orient in an Earth's strength magnetic field with inclination angles of 67 and 85 deg, but fail to orient in a field with 88 deg inclination. This suggests that the steepest inclination angle enabling magnetic compass orientation in migratory blackcaps tested in Emlen funnels lies between 85 and 88 deg.

We investigate magnetic effects in correspondence of the Mw6.1 L'Aquila earthquake. Magnetic and seismic records are analyzed. Rapid and distinct changes and an offset can be seen in magnetic field components after the main shock. We show that these effects result from electromagnetic induction due to the movement of the sensors through the Earth's magnetic field and from a permanent displacement of the sensors from their original position caused by the passing seismic waves. A transient signal in total field data from an overhauser magnetometer apparently occurs in correspondence with the earthquake. Our analysis shows that the transient was not observed by other sensors that were operating in close proximity to the overhauser. Thus, the transient signal in the total magnetic field data, and the offset in the magnetic field components, cannot be associated with a hypothetical underground electric current generated by the earthquake, as suggested by Nenovski (2015).

Detecting a weak physical signal immersed in overwhelming noises entails separating the two, a task for which machine learning is naturally suited. In principle, such a signal is generated by a nonlinear dynamical system of intrinsically high dimension for which a mathematical model is not available, rendering unsuitable traditional linear or nonlinear state-estimation methods that require an accurate system model (e.g., extended Kalman filters). We exploit the architectures of reservoir computing and feed-forward neural networks (FNNs) with time-delayed inputs to solve the weak-signal-detection problem. As a prototypical example, we apply the machine-learning schemes to Earth's magnetic anomaly field-based navigation. In particular, the time series are collected from the interior of the cockpit of a flying aircraft during different maneuvering phases, where the overwhelmingly strong noise background is the result of other components of Earth's magnetic field and the fields generated by the electronic devices in the cockpit. We demonstrate that, when combined with the traditional Tolles-Lawson model for Earth's magnetic field, the articulated machine-learning schemes are effective for accurately detecting the weak anomaly field from the noisy time series. The schemes can be applied to detecting weak signals in other domains of science and engineering.

Introduction: Natural earth’s magnetic field (EMF) is promoter of mother cell division into two daughter cells. Cancer is a cell that divides unlimited and destroys the body. Aim: Measurements presented in this paper show that malignant diseases are formed in anomalous magnetic fields (AMF) in patient’s beds. Removal of patients from AMF explains the etiological uncertainties in the medical literature. Methods: Measuring of AMF in patients’ beds was performed by proton magnetometer. Measuring points are on square net, 10 × 10 cm. The results are shown with contour lines on drawings. The health status of residence in the Earth’s natural magnetic field (EMF) was monitored. The etiologic data from the literature are explained. Results: Research lasted 25 years. AMF were measured in 1500 patients’ beds. There was a correlation between AMF and location of the diseased organ. AMF surfaces were shown in beds where the diseased organ is, on the contrary, there were natural values of EMF in the rest of the bed surface. Furthermore, the results found that three cases of breast cancer with metastases survived after surgical interventions and subsequent removal into natural EMF in contrast to 26 cases with the same diagnosis and surgical interventions who died after short period and staying in AMF. Another example was brain malignancy, which was decreased by living in natural EMF for one year. Conclusion: Based on the results of measurement of AMF, the medical condition of the patient when staying in a natural EMF, and explanation of uncertainties etiologies, the main conclusion was: AMF is the main cause of the malignant diseases.

This article describes both the setup and the use of a system for magnetic resonance imaging (MRI) in the Earth's magnetic field. Phase instability caused by temporal fluctuations of Earth's field can be successfully improved by using a reference signal from a separate Earth's field nuclear magnetic resonance (NMR) spectrometer/magnetometer. In imaging, it is important to correctly determine the phase of the NMR signal. A reference signal of a fixed‐frequency oscillator cannot be used since the Larmor frequency changes with time, following temporal fluctuations of Earth's magnetic field. The reference signal frequency and phase, provided by a separate NMR spectrometer, change in the same way as Earth's field, creating thereby, a stable rotating frame of reference for the measured signal. In principle, excellent homogeneity of the magnetic field enables scanning of very large volume samples. Reduction in S/N ratio due to the weak magnetic field can be partly compensated by the receiving coil design and shielding of electromagnetic pick‐up in audio frequency (AF) range. The smallest voxel examined so far is on the order of 50 mm3. Unlike in the case of strong magnetic fields, detection and processing of low frequency signal are less demanding for the electronics. The techniques used and the results of measurements are briefly presented.