941
1 INTRODUCTION
In recent decades, satellite-based navigation or GNSS
(Global Navigation Satellite System) has become the
standard in civil shipping. However, GNSS is
susceptible to jamming and other sources of
interference. This can lead to incorrect positioning
information, which can have devastating consequences
for ship and supply chain safety. In recent years,
conflicts have shown that satellite-based navigation
can be changed (spoofing) and/or jammed (e.g. in the
Baltic Sea region), or in the event of a conflict, the
spatial resolution can be reduced in certain regions.
Therefore, satellite-independent navigation systems
for civil shipping are essential to detect and mitigate
the effects of a disruption of GNSS-based systems and
to stabilize supply chains.
Accurate positioning without the use of GNSS is a
difficult engineering problem. Many alternative
technologies exist as summarized in Table 1, each with
their own limitations and benefits. Often, these
limitations restrict where and when the alternative
systems may be used. Ships can determine the position
via charts or external signals or determine a position
relative to a starting point with inertial sensors via
dead reckoning. Possible implementations of the
methods are shown in Table 1. Compared to direct
positioning, inertial sensors have the problem that the
drift of the sensors increases errors in positioning over
time. Very accurate inertial sensors have high costs and
often high complexity in maintenance. Inertial sensors
are advantageous in that they provide additional data
for positioning compared to map-based methods.
Therefore, it makes sense to use map-based methods
and inertial sensors in combination. However, in this
review we are concentrating on positioning via maps.
The different methods of positioning have different
advantages and disadvantages. While radio-based and
optical methods have passed their heyday in the
maritime world due to their limited range, magnetic
field and gravitational anomaly measurements are
relatively new, non-interference-prone methods for
which there is often not yet sufficient map material. Yet
there are early adopters with maritime surveys have
Review of Advantages and Disadvantages of
Magnetometer Types and Measuring Techniques to be
Used for GNSS-free PNT in the Maritime Environment
V. Bartsch, C. Bhattacharya, O. John, O. Rendel, A. Rizvanolli & O. Szal
Fraunhofer Center for Maritime Logistics and Services (CML), Hamburg, Germany
ABSTRACT: Reliable determination of position, navigation and timing (PNT) is essential for safe shipping traffic.
PNT using the Earth's magnetic anomaly field, which is always globally available, is a promising alternative to
satellite-based positioning which can be disturbed in case of conflicts. The aim of the review is to give an overview
of the advantages and disadvantages of magnetometer technologies and data gathering methods with respect to
positioning and their restrictions of the maritime environment such as specific setups, necessary accuracy and
sensitivity as well as measurement frequency to obtain the high frequency components of the earth magnetic
field.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 19
Number 3
September 2025
DOI: 10.12716/1001.19.03.28
942
already paved the way in the usage of this new
technology.
Table 1. Presentation of different methods for positioning
and inertial sensors
Dead reckoning via inertial
navigation sensors (INS)
Methods
- Rotation Sensors
- MEMS
- Fibre Optical Gyroscope
- Hemispherical Resonator
Gyroscope
- Ring Laser Gyroscope
- Accelerometers (MEMS)
Navigating with the Earth’s magnetic anomaly field
shows potential to overcome common limitations of
optical or radio-based positioning methods by always
being available, world-wide. The earth magnetic
field has a higher resilience to jamming than GNSS,
since it would take much more energy to disrupt the
earth’s magnetic field. Navigation accuracies within
hundreds of meters can be reached with accurate
magnetic field maps. However accurate maps with
sufficient sensitivity, spatial resolution and recordings
of high-frequency, daily and monthly variations of
magnetic field anomalies are not available for most
areas at sea. Hence, adequate magnetometers are
needed for both navigation and generation of more
accurate maps.
There are many theoretical papers on the topic of
map matching for navigation [1] [2] [3] [4] [5]. The
algorithms typically either use variations of Kalman
filters or particle filters or combinations of both. Most
algorithms can use multi-sensor data, e.g. from the INS
system and the magnetometers which improve the
navigation accuracy up to some point [1]. For these
algorithms to work, the errors related to positioning,
velocity and tilt of the INS systems as well as the
estimated temporal variation and accuracy errors of
the magnetometers need to be considered. We are
considering a navigational accuracy of a few hundred
meters to be sufficient for civilian seafaring.
2 MAPS OF THE EARTH MAGNETIC FIELD
Any physical observables outside controlled
laboratory situations are dependent on influences from
their surroundings which need to be considered. This
holds for the earth’s magnetic field which has
anomalies which cannot be modelled purely
mathematically. Concerning positioning with the earth
magnetic field, this has advantages and disadvantages.
On one hand these anomalies provide maps with
enough features to be able to navigate, on the other
hand some features cannot be modelled and contribute
to systematic background noise.
There exists a set of magnetic field maps which are
based on mathematical models as well as data from
satellites, observatories and surveys around the world
describing different components of the magnetic field.
Usually, these maps are used in combination with each
other to extract the exact value at a certain position.
E.g., the International Geomagnetic Reference Field
(IGRF) [1] is a standard mathematical description of the
Earth's main magnetic field. It is used widely in studies
of the Earth's deep interior, crust, ionosphere, and
magnetosphere, but does not consider anomalies
which arise from geological features. The earth
magnetic field anomalies are compiled in the EMAG2
map which considers data from satellite, ship and
airborne magnetic measurements [8]. The EMAG2 map
has a spatial resolution of 2-arcminutes. To reduce
navigation accuracies stemming from the low spatial
resolution, new measurements, e.g. from ships
carrying magnetometers can be used to incorporate
these data into the maps and therefore generate a self-
building map with a higher resolution. Thus,
magnetometers ca n be used for both positioning and
map building, at the same time.
To generate a self-building magnetic field map one
can use existing models of magnetic fields. The
modeling of magnetic anomaly fields is well
understood in the field of geophysics where magnetic
anomaly fields are routinely modeled for geological
studies and for oil and mineral exploration. This type
of modeling can be seen as an inverse problem, in
which a set of observations is used to solve a magnetic
source distribution to model the observed field. Several
methods with different advantages and disadvantages
can be used. E.g. the equivalent source dipole inversion
method [9] that represents the combined effect of a set
of magnetic dipoles or least-square collocation can be
used. While the first method is mathematically
instable, least-square collocation is often used for map
building [10]. Least square collocation calculates the
magnetic field value at a given point as the weighted
average of nearby observations. Least square
collocation often does not take physical effects into
account, however there are methods which use the
Maxwell equations and therefore are more
representative of reality [11]. However, these methods
need a vector field which typically is not available. For
aviation it has been shown that there is potential for a
huge improvement for existing magnetic field maps
when adding additional data taken in test flights [9].
To find the limits of sensitivity necessary in
magnetometers we have studied the gradients of the
magnetic field in the Baltic Sea area with the help of the
EMAG2 map. As can be seen in Figure 1 the gradients
are around 4-21nT between a nautical mile at a latitude
of 55.3 degree a longitude between 14.6 and 14.8
degrees in the Baltic Sea. Similar data can be taken at
other locations in the Baltic Sea. It is not possible to get
a better resolution due to the resolution of the map. To
get to a navigation accuracy of a few hundred meters,
we estimate that a sensitivity of the magnetometers a
few nT or even below is necessary if one uses the
magnet field map without considering information
from the INS or in case of measuring gradients between
two magnetometers which are located a few hundred
meters away from each other.
The maps have certain characteristics and
limitations for positioning: E.g. in the EMAG2 map
distinct patterns and magnetic signatures can be seen
in the oceans. They are attributed to the formation and
destruction of oceanic crusts and the alternating
polarity of the geomagnetic field. Figure 2 shows such
characteristic changes in the earth’s anomaly field at
the edge of tectonic plates.
943
Figure 1. Variation in total field intensity (F) at fixed latitude
of 55.3 degrees and longitude between 14.6 degrees to 14.8
degrees from IGRF-14 plus EMAGv3 data. The data has been
taken at an altitude of 4km.
Figure 2. Variation of magnetic field strength close to tectonic
plate edges (latitude 69 degrees and longitude between 306
and 320 degrees) from IGRF and EMAGv3 data.
3 TEMPORAL VARIATION OF THE EARTH
MAGNETIC FIELD
In addition to the limitations depending on the
magnitude of the anomalies, additional factors limit
the navigational accuracy. One limiting factor is the
temporal variation, where the yearly and monthly
variation can be modelled quite well, but the daily
variations are stochastic. A good way to suppress the
daily variations is with the help of a stationary
reference magnetometer. Values of the reference
stations are valid for a radius of about 100km
depending on the frequency of the magnetic field
variations [10]. The higher the frequency, the shorter
the propagation of the variations. There is data
available from a worldwide network of magnetometers
(e.g. the Intermagnet or the SuperMagnet network).
The existing stationary reference stations are mainly
located ashore or on islands. However, especially in
Europe there is a high density of magnetometers to be
found, so that there is good coverage of the Baltic Sea.
For high-sea areas there is no sufficient coverage of the
existing reference stations. Figure 3 shows the daily
variations in November 2020 at the InterMagnet
magnetometer in Wingst (near Hamburg). When
modelling the daily variation, one gets a variance in the
order of a few nT. Thus, lower accuracies of the
magnetometers only make sense when using real time
values from the reference stations which can consider
the stochastic changes or when measuring the
gradients between two magnetometers which are a few
hundred meters away from each other.
Figure 3. Daily variation of the InterMagnet magnetometer in
Wingst (near Hamburg) for several days in November 2020
from the InterMagnet dataset. Days which have a k index [9],
a parameter which measures the influence of the solar
activity on the earth magnetic field, lower than 3, have been
selected.
4 EFFECT OF THE VESSEL AND SEA WATER
To reduce the effects of the vessel on the earth’s
magnetic field one can envisage either to install the
magnetometer in a water-tight tow fish which is towed
behind the vessel or to carry the magnetometer on ship
as far away from electrical sources as possible and
compensate the effects of the vessel. For marine
surveys, often boats with small magnetic signatures
have been used. In such settings an error of a few nT in
total intensity and about 0.1 degree in declination and
inclination are reported for a carbon fiber vessel [2]).
However, when using steel vessels with a strong
associated magnetic signal such calibration techniques
break down and yield much higher errors [3]. One can
mitigate some effects by sophisticated calibration
algorithms such as Tolles-Lawson which holds if the
permanent, induced and eddy current terms can be
approximated linearly [4]. Continuous calibration
routines can be carried out throughout the voyage to
reduce the calibration error.
Since seawater is a weak electrical conductor,
motional induction of sea water moving in the earth
magnetic field causes magnetic signals. These can be
tidal effects or ocean swells. Tidal effects play a role in
Europe in areas such as the Northern Sea. Due to their
periodic nature these effects can be modeled in a
similar way to daily variations of the earth’s magnetic
field. Ocean swells have been studied since 1965 [5]. As
both experimentally and theoretically shown, the
period of the ocean swell and of the magnetic field is
the same. In case of [6] the ocean swell has a period of
about 13s with a sharp spectral peak and a magnetic
signal of about 1.6 nT for every meter of wave motion.
Such sharp spectral peaks can be filtered in marine
magnetic measurements. The swell signal decays
exponentially with height which means that if the
magnetometers are mounted on board big ships the
effects of ocean swell are typically negligible.
944
5 OVERVIEW OVER DIFFERENT
MAGNETOMETERS
5.1 Definition of sensitivity and accuracy
Concerning magnetometer technology parameters
such as the necessary accuracy and sensitivity, power
requirements, additional requirements (e.g.
cryogenics), dimensions of the setup and operating
frequencies, bandwidth and drift need to be considered
for the use case. The dynamic range of the
magnetometers needs to be sufficient to measure the
earth’s magnetic field which ranges between
approximately 22 and 67 μT. In this review we are
focusing on the necessary accuracy for positioning in
the civil maritime sector.
Sensitivity and accuracy are two important
properties of magnetometer sensors. Sensitivity, i.e. the
larger value of either sensor noise or sensor resolution,
is typically given in units of nT/sqrt(Hertz) RMS. This
means that a measurement rate of one microsecond
decreases the sensitivity by a factor of one thousand.
As a rule, higher frequency variations of the earth
magnetic field tend to have lower amplitudes [2]. From
a navigation standpoint this is beneficial, as the larger
temporal variations will vary more slowly with time. If
the sampling frequency is at least twice the highest
frequency (Nyquist frequence), information about such
high-frequency signals can be analyzed and bandpass
filters applied to suppress the errors.
The accuracy, i.e. the precision with which the total
magnetic field can be measured, is a tricky specification
to describe in the context of measuring the earth’s
magnetic anomaly field. The actual instruments have a
certain absolute accuracy, but they measure the total
field, including the vessel’s magnetic field, which can
never be totally removed. The actual sensor’s absolute
accuracy may be well under 1nT for e.g. an optically
pumped magnetometer, but if the vessel’s field cannot
be removed to that extent, it will be the vessel
compensation system which is driving the accuracy of
the sensor with respect to measuring the earth’s
magnetic field.
5.2 Scalar magnetometers
Scalar magnetometers have been used since the sixties
in aerial surveys and are well-proven instruments.
Optical pumping alkali vapor magnetometers with
high sampling rate and high sensitivity are generally
used aboard airframes whereas proton precession
magnetometers (including Overhauser) are favoured
at sea. There are several types of nuclear resonance
magnetometers including proton-precession, optically
pumped magnetometers and Overhauser
magnetometers. Proton precision and Overhauser
magnetometers are a mature technology while there
has been a lot of development for optically pumped [8]
magnetometers concerning miniaturisation and the
need of cryogenic cooling. Optically pumped
magnetometers still have a small dynamic range, so
that they can be deployed in the earth’s magnetic field,
but they cannot be objected to too high magnetic fields.
The nuclear resonance magnetometers are small,
lightweight, stand-alone instruments which can
digitally provide an extremely sensitive (typically
smaller than 0.04nT/sqrt(Hz)) and accurate (smaller
than 3nT) magnetic field measurement [8]. A good way
to measure the sensor accuracy is to watch how a
gradient measurement drifts in a constant field.
Because the gradient measurement is subtracting out
the common field between each instrument, any drift
is likely due to inaccuracies. Novel magnetometers
such as optomechanical magnetometers [10] [11]
promise sensitivities ranging from several nT/sqrt(Hz)
down to tens of pT/sqrt(Hz). However, these platforms
are novel and will need some further research and
engineering before allowing to use them in operation.
5.3 Gradient magnetometers
Gradient magnetometers have been deployed since the
eighties. They are typically towed behind a ship with a
distance between the two sensors of a few 100m.
Summing up the differences between the field values
of the two sensors along the line reconstructs the
spatial variations that are due to the main field of the
Earth and the crustal magnetic sources. It also allows
the recognition and removal of time varying field
variations. The effect of vessel on the earth’s magnetic
field is negligible at long tow distances. Some papers
[2] report towing distances of more than 700 m, where
the ship’s magnetic field is well below one nT and can
be assumed constant along a line with constant course.
However, a very long cable is required to maintain the
distance between the ship and the magnetometer
which could lead to potential positional inaccuracies.
Because gradiometers are towed behind the ship
and therefore do not get additional errors due to the
magnetic field of the vessel, they provide the most
accurate data of gradients and are very well suited for
map building of magnetic anomaly fields as well as
measuring the gradients of the earth magnetic fields for
navigation purposes.
5.4 Vector magnetometers
Vector magnetometers can be an important tool at the
poles and equatorial regions where the vector
components of the earth magnetic field differ greatly.
Here scalar magnetometers reach their limits. While in
the pole region the horizontal component of the
magnetic field is large, and the total magnetic field is
low, close to the equator the vertical component of the
magnetic field is about doubled to the total field. Here
vector magnetometer can be used to model the
anomalies by fitting the enhanced vertical component
together with the magnetic field [2].
When considering vector magnetometers, the roll
and pitch of vessels needs to be considered to
transform the strap-down vector magnetometer data
into a world reference frame. Attitude sensors typically
do not have the necessary resolution. To allow for a
resolution of 1 nT in the earth magnetic field, which is
on average about 50 000 nT strong, an attitude accuracy
of atan(1/50 000)=30.6 arcsec or 0.001 degree is
necessary. Such requirement is almost impossible. If
the attitude sensor and the magnetometer were 10 cm
away from each other, the relative orientation between
attitude sensor and magnetometer would be below one
micrometre. Values around 0.01 degree orientation
error are reachable with modern attitude sensors and
result in a systematic error of the magnetic field of
945
about 15 nT. However, there exist algorithmic methods
to correct for the attitude in operation and can provide
data with the necessary accuracy [23].
The existing vector magnetometers have quite
different specifications: e.g. SQUID magnetometers
[10] [11] [12] have (size, weight and power)
requirements which are difficult to achieve in the
maritime environment, but which have been
implemented [2] despite these difficulties. Novel
quantum sensors based on the Zeeman effect such as
nitrogen-vacancy centers (NV) in diamond [17] [18]
[19] have low power, size and weight requirements.
These magnetometers have a high accuracy [2] and do
not need to be calibrated. Due to their novelty these
magnetometers have not been used in magnetic field
surveys often.
Nowadays flux-gate sensors are most often used.
They measure the relative magnetic field with respect
to some uncalibrated baseline. The most accurate
fluxgate magnetometers [15] are accurate to within
about +/- 100nT.
Due to all the above difficulties (attitude accuracy,
accuracy of the vector magnetometers), no high-
resolution magnetic vector maps exist. This lack of
high-resolution vector data stands in stark contrast to
the widespread availability of scalar magnetic data.
Thus, for navigational purposes vector maps need to be
created. These can be measured with a lot of effort or
analytically derived from the scalar maps using the
declination and inclination angle that is known from
the IGRF and World Magnetic Map (WMM) data [33].
It is yet to be proven if such maps are a good
approximation to reality. As stated in [5] the position
accuracy between using vector magnetometers plus
INS or using scalar magnetometers plus INS is
expected to be quite small for commercial scale INS,
but becomes more significant when using more precise
INS.
5.5 Tensor gradiometers
Tensor gradiometers which are setup by using two
vector magnetometers with a certain towing distance,
measure the gradients of vector components. Like
scalar gradiometers they are relatively immune to
noise sources from the vessel and temporal variations.
The spatial gradients form a tensor with nine
components. In a conductive medium, such as
seawater, conduction currents are present, and the curl
of the magnetic field is non-zero. The gradient tensor is
asymmetric with eight independent components [6].
However, since vector magnetometers are in an
insulating instrument capsule one can assume that the
magnetic gradient tensor in the cavity is symmetric and
traceless.
Tensor gradiometers have a high sensitivity and are
in use for the detection of magnetic underwater objects.
Concerning positioning with the help of tensor
gradiometers there is clearly no map of magnetic field
tensors available, and it might be difficult to construct
one with the help of existing data. Therefore,
positioning with tensor gradiometers remains an open
topic for future research.
5.6 Advantages and Disadvantages of the different
magnetometer types
The advantages and disadvantages of the different
magnetometer types and implementations are
summarised in Table 2. Concerning the sensitivity of
magnetometers and the irreducible noise and errors
from temporal variations, the effects of the vessel and
the effects of seawater, it seems that towed
gradiometers are the best choice for the measurement
of the earth’s magnetic field anomalies in the maritime
environment despite the positioning inaccuracies that
occur with this setup but which are well below the
targeted positioning accuracy of a few hundred meters.
Table 2. High-level overview over the advantages and
disadvantages of different magnetometer types and
implementations
Magnetometer
Type
Main
Implementations
Advantages
Disadvantages
Scalar
Proton precession
including
Overhauser and
optically pumped
High accuracy,
most maps are
built from scalar
measurements,
well-proven
Drift of
magnetometers
over time
Gradient
At least 2 scalar
magnetometers
which are towed
in line
Cancels out
temporal
variations of
earth’s magnetic
field and
reduced effect of
vessel due to
towing
Deployment in
tow fish requires
more effort and
adds to
positioning
inaccuracies
Vector
Fluxgate, SQUID,
nitrogen-vacancy
centers (NV) in
diamond
SQUID and
diamond high
accuracy, more
information,
positioning at
poles and near
equator possible
No vector maps,
issues with the
attitude, flux
gate only with
relative
measurement
Tensor
At least 2 vector
magnetometers
which are towed
in a line
Gives more
information of
the magnetic
field tensor
Difficult to
setup, tow fish
adds to
positioning
inaccuracies
Existing magnetometer platforms (such as fluxgate,
proton precision, Overhauser, SQUID) have proven
utility and will continue to be used in the future [6].
However, they have limitations. E.g. fluxgates suffer
from drifting scale factors and voltage offsets with both
time and temperature requiring periodic recalibration.
Proton-precision magnetometers have an excellent
sensitivity, accuracy and dynamic range, but they have
considerable mass and power requirements as well as
a large size. SQUID (Superconducting Quantum
Interference Device) require a cryonic environment.
There is currently a surge of novel magnetometer
platforms that use optical readout, including optically
pumped magnetometers, magnetometers based on
quantum defects in diamond and optomechanical
magnetometers. These novel magnetometers offer a
combination of field sensitivity, size, weight, and
power consumption that allows them to reach
performance regimes that are inaccessible with existing
techniques. While each of these kinds of magnetometer
have quite different characteristics, in general, a key
attraction has been that they offer exquisite sensitivity.
In recent years, they have also experienced rapid
miniaturization and reduction in power consumption
which is likely to continue. Therefore, these novel types
946
of magnetometers become more important in future for
maritime operations.
6 CONCLUSIONS
Concerning map-based positioning methods, using the
earth’s magnetic anomaly field is a good approach
either stand-alone or complementing other positioning
methods in case of GNSS free navigation. The gradient
of the magnetic field is high enough to allow for
navigation accuracies in the order of a few hundred
meters. Adequate magnetometers are needed both to
generate maps with a higher resolution and to navigate
with the help of more accurate maps. To estimate the
necessary sensitivity and accuracy of the
magnetometers, temporal variations, tidal effects and
effects of the vessel on the earth’s magnetic field need
to be considered as the main error source. These error
sources limit the desired accuracy and sensitivity to
1nT for the magnetometers. Several magnetometer
technologies exist which deliver either scalar or vector
information of the magnetic field with a sensitivity and
a dynamic range compatible with the earth’s magnetic
field. These can be combined to deliver gradient or
tensor information. Scalar magnetometers (such as
proton precession or optically pumped magnetometer)
have a high accuracy and are well proven. They can be
combined as gradient magnetometers (i.e. at least two
scalar magnetometers towed in a line) allow to cancel
out temporal variations of the earth’s magnetic field.
Vector magnetometers (fluxgate, SQUID, novel sensors
such as diamond sensors) have very different
challenges. While fluxgates have low accuracy,
SQUIDs are difficult to setup and there is not much
data available for diamond sensors. However, SQUID
and diamond sensors have a high accuracy and vector
magnetometers allow positioning close to the poles.
Tensor magnetometers (i.e. at least two vector
magnetometers towed in a line) give a lot of
information about the magnetic field tensor for which
no maps exist yet but are difficult to set up and
therefore more apt for specific surveys rather than
general positioning. We recommend using gradient
information by setting up magnetometers in a tow fish
to reduce the effect of the vessel on the accuracy of the
magnetometers and to cancel out most of the temporal
variations.
ACKNOWLEDGEMENTS
The results presented in this paper partly rely on data
collected at magnetic observatories. We thank the national
institutes that support them and INTERMAGNET for
promoting high standards of magnetic observatory practice
(www.intermagnet.org).
REFERENCES
[1] F. Jie, „Kalman Filter underwater passive geomagnetic
navigation technology research considering the impact of
diurnal variation,“ Image and Signal Processing CISP,
IEEE, 2009.
[2] Y. Liu, M. Wu, H. Xiaoping und H. Xie, „Geomagnetism
aided inertial navigation system,“ Systems Control in
Aerospace and Astronautics, IEEE, 2008.
[3] M. Liu, „Research on particle filter based geomagnetic
aided intertial navigation algorithm,“ 3rd Symposium on
Systems and Control in Aeronautics and Astronautics
(ISSCAA), 2010.
[4] I. Nygren, „Robust and efficient terrain navigation of
underwater vehicles,“ Position, Location and Navigation
Symposium, IEEE, pp. 1390-1395, 2008.
[5] L. Ming-Ming, H. Lu, H. Yin und X. Luang, „Novel
algorithm for geomagnetic navigation,“ Journal of
Central South University of Technology, Bde. %1 von
%2791-799, p. 18, 2011.
[6] A. Larey, E. Aknin und I. Klein, „Multiple Inertial
Measurement Units An Empirical Study,“ IEEE Access,
Bd. 8, pp. 75656-75665, 2020.
[7] P. Alken, E. Thebault und C. Beggan et al., „International
Geomagnetic Reference Field: the thirteenth generation,“
Earth Planets Space, Nr. 73,49, 2021.
[8] B. Meyer, R. Saltus und A. Chulliat, „EMAG2v3: Earth
Magnetic Anomaly Grid (2-arc-minute resolution),
Version 3,“ NOAA National Centers for Environmental
Information, 2017.
[9] R. Frese, W. Hinze und L. Braile, „Spherical earth gravity
and magnetic anomaly analysis by equivalent point
source inversion,“ Earth and Planetary Science Letters,
Bd. 53, Nr. 1, pp. 69-83, 1981.
[10] W. Hinze, R. Frese und A. Saad, Gravity and Magnetic
Exploration, Cambridge University Press, 2013.
[11] N. Wahlström, M. Kok, T. Schön und F. Gustafsson,
„Modeling magnetic fields using Gaussian processes,“
IEEE International Conference on Acoustics, Speech and
Signal Processing, pp. 3522-3526, 2013.
[12] A. Canciani, „Absolute Positioning Using the Earth's
Magnetic Anomaly Field,“ Theses and Dissertations, Bd.
251, 2016.
[13] C. Reeves, „Aeromagnetic surveys; principles, practice
and interpretation.,“ Geosoft, 2005.
[14] J. Bartels, N. Heck und H. Johnston, „The three-hour-
range index measuring geomagnetic activity,“ Journal of
Geophysical Research, Bd. 44, Nr. 4, p. 411–454, 1939.
[15] V. Lesur, T. Clark, C. Turbitt und S. Flower, „A technique
for estimating the absolute vector geomagnetic field from
a marine vessel,“ Journal of Geophysics and Engineering,
Bd. 1, Nr. 2, pp. 109-115, 2004.
[16] V. Lesur und C. Turbitt, „Marine Vector Magnetometer
on RRS Discovery,“ British Geological Survey,
Nottingham, UK, 2004.
[17] A. Gnadt, A. Wollaber und A. Nielsen, „Derivation and
Extensions of the Tolles-Lawson Model for Aeromagnetic
Compensation,“ arXiv:2212.09899 , 2022.
[18] J. Weaver, „Magnetic variations associated with ocean
waves and swell,“ Journal of Geophysical Research, Bd.
70, Nr. 8, pp. 1921-1929, 1965.
[19] F. Lilley, A. Hitchman, P. Milligan und T. Pedersen,
„Sea-surface observations of the magnetic signals of
ocean swells,“ Geophysical Journal International, Bd. 159,
Nr. 2, pp. 565-572, 2004.
[20] C. Constable und S. Constable, „A grand spectrum of the
geomagnetic field,“ Physics of the Earth and Planetary
Interiors, Bd. 344, 2023.
[21] J. Kitching, „Chip-scale atomic devices,“ Appl. Phys.
Rev., Bd. 5, 2018.
[22] M. Hamoudi, Y. Quesnel, J. Dyment und V. Lesur,
„Aeromagnetic and Marine Measurements,“ in
Geomagnetic Observations and Models. IAGA Special
Sopron Book Series, vol. 5, Springer, 2011, pp. 57-103.
[23] B. Li, H. Greenall, S. Forstner, E. Sheridan, H.
Rubinsztein-Dunlop und W. Bowen, „Ultrabroadband
and sensitive cavity optomechanical magnetometry,“
Photonics Research, Bd. 7, pp. 1064-1071, 2020.
[24] B. Li, D. Bulla, V. Prakash, S. Forstner, A. Dehghan-
Manshadi, H. Rubinsztein-Dunlop, S. Forster und W.
Bowen, „Invited Article: Scalable high-sensitivity
optomechanical magnetometers on a chip,“ APL
Photonics, Bd. 3, Nr. 12, 2018.
947
[25] M. Engels, U. Barckhausen und J. Gee, „A new towed
marine vector magnetometer: methods and results from a
Central Pacific cruise,“ Geophysical Journal
International, Bd. 172, Nr. 1, 2008.
[26] A. Canciani und C. Brennan, „An Analysis of the Benefits
and Difficulties of Aerial Magnetic Vector Navigation,“
IEEE Transactions on Aerospace and Electronic Systems,
Bd. 56, pp. 4161-4176, 2020.
[27] D. Drung, C. Abmann, J. Beyer, A. Kirste, M. Peters und
F. Ruede, „Highly Sensitive and Easy-to-Use SQUID
Sensors,“ IEEE Transactions on Applied
Superconductivity, Bd. 17, Nr. 2, pp. 699-704.
[28] J. Kirtley, M. Ketchen, K. Stawiasz, J. Sun, W. Gallagher,
S. Blanton und S. Wind, „ High ‐ resolution scanning
SQUID microscope,“ Appl. Phys. Lett., Bd. 66, pp. 1138-
1140, 1995.
[29] H. Hao, H. Wang, L. Chen, J. Wu, L. Qiu und L. Rong,
„Initial Results from SQUID Sensor: Analysis and
Modeling for the ELF/VLF Atmospheric Noise,“ Sensors,
Bd. 17, Nr. 2, 2017.
[30] A. Chwala, M. Schmelz, V. Zakosarenko, M. Schiffler, M.
Schneider, M. Thürk, S. Bräuer, F. Bauer, M. Schulz, A.
Krüger and R. Stolz, "Underwater operation of a full
tensor SQUID gradiometer system," Superconductor
Science and Technology, vol. 32, no. 2.
[31] I. Fescenko, A. Jarmola, I. Savukov, P. Kehayias, J. Smits,
J. Damron, N. Ristoff, N. Mosavian und V. Acosta,
„Diamond magnetometer enhanced by ferrite flux
concentrators,“ Phys. Rev. Research, Bd. 2, 2020.
[32] J. Webb, J. Clement, L. Troise, S. Ahmadi, G. Johansen,
A. Huck und U. Andersen, „Nanotesla sensitivity
magnetic field sensing using a compact diamond
nitrogen-vacancy magnetometer,“ Appl. Phys. Lett., Bd.
114, 2019.
[33] T. Wolf, P. Neumann, K. Nakamura, H. Sumiya, T.
Ohshima, J. Isoya und J. Wrachtrup, „Subpicotesla
Diamond Magnetometry,“ Phys. Rev. X , Bd. 5, 2015.
[34] J. Schloss, J. Barry, M. Turner und R. Walsworth,
„Simultaneous Broadband Vector Magnetometry Using
Solid-State Spins,“ Phys. Rev. Applied, Bd. 10, 2018.
[35] C. Lu, J. Huang, P. Chiu, S. Chiu und J. Jeng, „High-
Sensitivity Low-Noise Miniature Fluxgate
Magnetometers Using a Flip Chip Conceptual Design,“
Sensors, Bd. 14, Nr. 8, pp. 13815-13829, 2014.
[36] A. Chulliat, W. Brown, P. Alken, C. Beggan, M. Nair, G.
Cox, A. Woods, S. Macmillan, B. Meyer und M. Paniccia,
„The US/UK World Magnetic Model for 2020-2025,“
British Geological Survey, p. 121, 2020.
[37] A. Canciani und C. Brennan, „An Analysis of the Benefits
and Difficulties of Aerial Magnetic Vector Navigation,“
IEEE Transactions on Aerospace and Electronic Systems,
Bd. 56, Nr. 6, pp. 4161-4176, 2020.
[38] J. Young und D. Clark, „Magnetic tensor gradiometry in
the marine environment,“ International Conference on
Electromagnetics in Advanced Applications, 2010.
[39] J. Bennett, B. Vyhnalek, H. Greenall, E. Bridge, F.
Gotardo, S. Forstner, G. Harris, F. Miranda und P.
Warwick, „Precision Magnetometers for Aerospace
Applications: A Review,“ Sensors, Bd. 21, Nr. 16, 2021.