In this paper we explore how to use the magnetic tracking technique for indoor navigation. The six degrees of freedom (6 DoF) magnetic tracking technology is selected because it is less influenced by the environment and has the highest accuracy among other techniques. A new method is proposed, called the alternating direct current (ADC) method, which permits one to get a double update rate, reduce the influence of Earth's magnetic field by a factor of 2 and reduce the power consumption by a factor of 3. The theoretical basis of the new magnetic tracking method is given, including a mathematical modeling of the local field, a mathematical model of the measurement of the positioning field by a 3-D transducer based on the Hall effect sensors, and the mathematical model for the estimation of the measurement errors. A new, net-like source of the positioning local magnetic field is proposed for indoor navigation with a scalable coverage area. A mathematical model of the distributed positioning field is given. The results of simulations are shown.

The task of an indoor navigation system is to determine the position of a user,
who is equipped with a small mobile receiver in closed spaces where the
GNSS (Global Navigation Satellite Systems; a satellite-based
navigation systems like GPS or GLONASS) signals are not directly available without
assistance (White, 2015; Chao, 2013; Fuller and Malkos, 2014). We
will consider here the most relevant application area of indoor navigation,
the “mass market”, where a static linear positioning error at a level of

The motivation of this work is determined by the following consideration. In
order to be competitive, the system should fulfill not only a linear
positioning but also the definition of the orientation of the mobile
receiver. The positioning error should be similar to the size of the
distinguishable objects but not worse than

In this work we will not consider dynamic positioning techniques, such as the
pedestrian navigation – which takes place while walking around an urban
environment (IPIN, 2015). Also the mechanical positioning technology (the
tactile system) is excluded from our consideration. Besides, we will not
consider the “high sensitive GNSS”, which due to strong signal
attenuation provides accuracy at a level of only

The main aim of this article is the investigation and analysis of the positioning capabilities of the new method that satisfies the above requirements for indoor navigation. The paper is organized as follows: first we evaluate the main parameters for the selected method of indoor navigation, such as the possible update rate and the specific power consumption. We also consider the influence of external factors such as the Earth's magnetic field and the surrounding medium. Further, the requirements for both mobile and fixed parts of the indoor navigation system will be examined. The investigation is completed with the mathematical and physical modeling of the movement of a user in the proposed system of indoor navigation with scalable coverage.

The technology of indoor navigation presented here is suitable for a modern smartphone that has a video, an audio, a magnetometer, and a radio channel. To illustrate the new technique, we will present here only the static positioning method, when the mobile receiver is motionless during the measurement. The extension to the dynamic positioning will be presented elsewhere.

Consider, what features are provided with current navigation technology, and whether they can be applied to modern user gadgets, i.e., smartphones?

The reference (IPIN, 2015; Mautz, 2012) contains an overview of the following well-known indoor navigation technologies. Optical systems for visible light contain both the cameras on the mobile object, and the markers on the environment. In the case of the invisible infrared light the systems contain the active LED-badges on the users, and fixed receivers. A passive system is applied to detect natural human radiation. Optical scanning systems exist such as “Kinect” (Microsoft, 2016), polar systems, or laser trackers, acoustic positioning systems (sound, ultrasound) use the triangulation method, and there are known the radio frequency (RF) technologies, such as WiFi systems, RFID (radio frequency identification), time-of-arrival ultra wideband (UWB), active beacons, ZigBee, Bluetooth, or GSM (global system for mobile communication) fingerprinting. The ultra hybrid systems are using inertial navigation and dead reckoning. A priori mapping of magnetic fingerprints is also applied for navigation.

The main drawback of the known technologies is the influence of the surrounding environment, like the reflection from the walls and furniture. Moreover, the multipath, the influence of moving people and opening doors and the limitation of positioning in one room due to the signal attenuation when passing obstacles with high density (walls, floors, ceilings) determine additional difficulties of known technologies. All the above methods have a need for direct visibility. Only linear coordinates are being calculated and the orientation cannot be determined. The optical methods need information about the distance in order to convert the image to coordinates. The triangulation systems have a large size. Most of the technologies can not be implemented on the basis of existing smartphones.

In review (IPIN, 2015; Mautz, 2012) it is shown that all abovementioned
technologies are very sensitive to the environment and require a free
line of sight. As a result, the accuracy of the positioning is poor, at
a level not better than

Table 1 shows that the magnetic systems have an accuracy of 3 orders of magnitude better than all other technologies. Furthermore, the six degrees of freedom (6 DoF) magnetic tracking technology is less influenced by the environment. This basic magnetic technology includes creating a local magnetic field with a known spatial distribution. The accurate measurement of the field components is provided with a small mobile receiver. Therefore, a comparison of the measured values with the calculated fields for the initially approximated coordinates is being carried out, and the iterative approaching of coordinates from initial approximation to actual values allows one to obtain the desired output data.

An evaluation of basic parameters of known technologies of indoor navigation, which are most suitable for modern smartphones.

To find the six coordinates, the system must provide at least six independent
measurements at each point of the positioning zone. That is why the classical
magnetic tracker includes three orthogonal windings (

The known active magnetic trackers are based on AC
(alternating current with sinusoidal shape – Fig. 1; Hansen, 1986) or DC (direct current with pulse
shape – Fig. 2; Blood, 1997;
Altman et al., 2009; Scully and Schneider, 2015) local magnetic field. In the first case (AC), all windings
of the source are working simultaneously (

Dimensionless charts of the excitation currents through the windings of the sinusoidal magnetic positioning systems.

Dimensionless charts of the excitation currents in pulse magnetic positioning systems.

In both cases at each point of the trajectory nine measurements are performed by three sensors from three windings. Then, at each point the system of nonlinear equations is solved using iterative approximation methods, based on the initial approximation of coordinates.

The achievable parameters of a modern 6 DoF magnetic DC tracker include the
operation distance – up to 1 or 3 m depending on the source size;
accuracy – about

The influence of motionless ferromagnetic elements is eliminated by the mapping (Jones, 2002) of the magnetic field over the coverage area. The mapping is carried out by a priori sequential measurement of induction vectors from each winding at each grid node, covering the whole of the positioning area. That is why the moving ferromagnetics should not be situated inside the zone of movement. Due to the measurements performed on the plateau of the pulse, the effect of electro conductive elements is determined by the ratio between magnetic field pulse duration and eddy current decay time constant, exited in these elements by a pulse magnetic field. For a DC tracker the contribution of EMF depends on the object velocity and for a stationary object is zero. The dielectric environment elements have no effect (unlike all the alternative methods of indoor navigation) on the positioning accuracy due to full transparency of the magnetic field.

There have been several trials to apply the active magnetic positioning to the indoor navigation task (Pirkl and Lukowicz, 2013). The author of this paper tried to apply a resonance kind of AC method for tracking humans. As a result the accuracy of linear positioning (ca. 60 cm) was demonstrated at the estimated distance no more than 1.5 m. Unfortunately there is no indication of how the authors are going to increase the coverage area above the standard 1 m. Moreover, the proposed inductive sensors are absent in the standard modern mobile communication devices. In addition, such sensors have low noise immunity, due to the large area of their measurement coils, and this trial does not successfully solve the indoor navigation problem. Therefore, we will further consider only the DC method. To evaluate the possibility of using magnetic tracking in indoor navigation, we will define the most visible disadvantages of magnetic technology.

The analysis shows that the main problems and drawbacks of known magnetic tracking for the indoor navigation are based on a limited tracking area. The positioning zone of 1 m is not enough for use in large halls of supermarkets and airports. The power consumption is also very significant – about 100 W over a sphere with a 4 m radius. It is important to take into account the need of the EMF and to provide the positioning of the moving object, not just the fixed objects. A limited update frequency has taken place – the magnetic fields switches up to 4 times faster than the output is updated, as shown on Fig. 2. This means that in order to further increase the output frequency, it is necessary to reduce the duration of the magnetic field pulses, which will increase the effect of eddy currents in the interior.

Schematically comparison of ADC and DC methods to organize the field of positioning.

That is why it can be seen that the existing magnetic tracking technology does not fully meet the requirements of the indoor navigation. Therefore, this paper describes the results of an investigation of the possibility to improve the magnetic trackers for indoor navigation. The refined requirements for the developed magnetic system of indoor navigation shall be based on increased accuracy of positioning, which must be at the level of the abovementioned possibilities of active magnetic tracking for a local, limited coverage area. The coverage area in this case must be unlimited or, at least, scalable – in order to have the ability to increase the area by adding hardware. The infrastructure required for the operation should be of a minimum. The external equipment of an indoor navigation system should not extend or restrict the free space of application halls. To extend the functionality, the output data should contain six coordinates instead of three like the other abovementioned technologies. For the convenience of the users update rate should be no worse than 1 Hz in the mode of indoor navigation. The way to increase the update rate must be determined to provide the tracking of movable objects. Regarding the number of users – it should have a dual mode – single, or multiple users. For example, in the sport application the single user mode is important to train of athletes. In hypermarkets and airports multiple users mode is more in demand. The system latency of output data is indifferent for the static measurements. The method must provide dynamic measurements in the long run more for sport applications. For a mass market and other similar applications, the use of static measurements seems reasonable.

As can be seen from this analysis – none of the above technologies, including known magnetic tracking, allows one to get closer to the requirements listed above. This proves the relevance of establishing of a system of indoor navigation based on magnetic tracking, with an extended coverage area, minimized power of consumption, and reduced influence of EMF.

Next, let us look at ways to address the abovementioned issues.

To satisfy the requirements, formulated above regarding accuracy, coverage area, infrastructure, number of coordinate, update rate, number of user and influence of EMF, a new method called the alternating direct current (ADC) method is proposed (Zhelamskij, 2011). The main idea of this new method is its special way of managing the local magnetic positioning field. Unlike the unipolar DC method, a new ADC method proposes bipolar current pulse to excite the same windings. Figure 3 shows the comparative chart of pulse currents in the source windings for a DC prototype (top graph, as the sum of the currents through all three windings for the same source like on Fig. 2), and for the new ADC method (three lower graphics, separately for each of windings). In both cases the graphics are presented for three orthogonal windings of local positioning systems (Hansen, 1986; Blood, 1997). Each winding contains about a hundred turns with full current around 700 amps. The source on a distance of 1 m has a shape of a cube with a side of 100 mm. The magnetic field pulses duration and amplitudes are equal for both methods for this figure. As above, the rise and fall of pulse current is much shorter than the pulse duration. It is seen in the top graph that for the DC method the current pulses are separated by a pause, as shown in detail on Fig. 2. In the new method the bipolar current pulses are continuously supplied, running consecutively one by one without pause. Let us consider now the main features of new method.

At the top of each bipolar impulse the positioning field vector is folded
with the EMF at a mobile receiver:

Using Eq. (1) the system of equations for the two time moments

The residual value of the EMF,

Hence, taking into account that

Additionally, as follows from Fig. 3, the condition

Three modes of ADC method operation.

Three possible modes of the ADC method operation are illustrated on Fig. 4.
From Eq. (5) the results show that if the amplitudes of the pulsed current are
really equal

A full parameter comparison of the DC and ADC methods is shown in the Table 2.
The update rate and the magnitude of measured induction are doubled in
accordance with Eq. (4). The module of the induction vector at a great distance
from the windings with current can be described by the following simplified
formula:

Due to the presented advantages, it is worth taking a look at a new way of organizing for the positioning field, because it better meets the conditions for indoor navigation for the update rate, power consumption, and the impact of EMF.

Comparison of parameters of the prototype and new method.

Now, having an improved method for magnetic tracking, one needs to understand how to use this proposal for addressing indoor navigation.

In addition to Zhelamskij (2014a, b), the theoretical basis of the new magnetic tracking method for the indoor navigation is given here in more detail, including a mathematical model of the positioning field, a mathematical model of the measurement of the positioning field with a 3-D Hall effect sensors, and a mathematical model of the measurement errors.

The expression for the projection of the induction vector, created at the
observation point with the coordinates of

Linear position and orientation of mobile receiver relative to the source in Cartesian coordinate system.

Furthermore, the positioning field is not only important for indoor navigation but also measuring technology, which is considered below.

Let us consider a 3-D magnetometer based on the Hall effect sensors, which is
available in modern smartphones, as a mobile receiver for the positioning field.
These magnetometers are intended for measurement of homogeneous Earth's
magnetic field only. However, the local positioning field is not uniform.
Therefore, the mathematical model is proposed to apply this magnetometer to
measure the inhomogeneous positioning field (Zhelamskij, 2014a). The
model is written as follows:

It can be seen from Eq. (8) that the total induction applied to the
sensor:

As a result, the mathematical model for the systematic positioning error of
the field measurement is given by

The specificity of the positioning field measurements results from Eq. (9),
where the full error depends not only on the magnitude, but also on the
distance (

The presented mathematical model of measurements of positioning field allows for starting the creation of an indoor navigation theory. This theory must explore the impact of the properties of the receiver and analog–digital converters into positioning accuracy. The influence of distance and the errors of mathematical description of the positioning field should also be explained. The investigation of this model made it possible to formulate the requirements for mobile receiver for the different task's condition. The first consideration of the metrological conditions of indoor navigation, based on the proposed model of measurement, are fulfilled in Zhelamskij (2015), where the models and tools for both measurement and reproducing inhomogeneous positioning magnetic fields are offered.

Now let us try to link the proposed mathematical models into a common indoor navigation system based on magnetic tracking.

A new, net-like source of the positioning local magnetic field is proposed in Zhelamskij (2014a) for the indoor navigation with a scalable coverage area. The fragment of the distributed source is shown on Fig. 6. The power supply is not shown here and will be considered elsewhere. The windings, marked with the same numbers, are working simultaneously in bipolar pulse mode. The user with a moveable smartphone receiver is designated by the star.

A mathematical model of the distributed positioning field for the windings
of the group “1” will be written as follows:

Based on the above considerations a formula is proposed that links the
mutual removal of windings

This means that in this case, the main contribution to the measured value of
the induction vector module at any point of positioning area is created by
the winding nearest to the user. The influence of other windings is thus
negligible. In this case the expression in Eq. (11) coincides with the
expression in Eq. (7) within one square of the grid:

Cofactor

A location of windings in the nodes of the net – like the distributed source of positioning field.

The windings of the distributed source have a flat shape and can be located in the interior elements – in walls, ceilings, or basically under the floor. The numerical simulation shown (Zhelamskij, 2015) that both orientation of source windings are available as horizontal and vertical. The former can be situated in the floor or the ceiling of the room. The vertical oriented windings can be located behind the walls, not occupying the free space of room. Simultaneously it was considered that the flat winding round shape, rectangular, or freeform agreed with the building designs of the room. The mathematical models of magnetic field are given in Zhelamskij (2015) for all the mentioned shape of windings and their orientations.

The operation of distributed source has a number of features, which are discussed below.

An additional tracking task for a distributed magnetic field is how one synchronizes the user mobile receiver with the operation sequence of a distributed source. A method of binding the receiver's mobile software to the sequence of switching groups of the distributed source windings (sync in time) is proposed for autonomous user, who has no connection with the source. The point of synchronization is the introduction of additional breaks into a sequence of the bipolar pulses, as shown in Fig. 7.

The pause is introduced periodically, such as once over 30 s, for
example. The duration of the pause must be enough for the recognition by the
autonomous mobile receiver, for example

The synchronization pause to start the calculation procedure at autonomous receiver.

It can be seen that the pause confidently allows for detecting when the
distributed source starts at moment “

It is equally important to understand the start of positioning; i.e., in which square of the distributed source a user is situated when the smartphone could be switched on at anytime.

The initial binding of mobile receiver in the coordinate system of the distributed source is a one-time procedure, which is carried out everywhere over the coverage zone at any time at the user's request to initialize the positioning calculation. A method for the initial capture of coordinates is proposed here, based on an additional excitation of reference sinusoidal oscillations over the individual frequencies in the distributed windings.

We assign each winding its own frequency, value of which is defined by the
expression:

It is supposed further that each winding creates a magnetic field at the
assigned frequency all the time, excepting the bipolar positioning field
duration, as shown in Fig. 8. In this case, the mobile receiver will see
the following signal:

Dimensionless free oscillations of current in the winding after completion of bipolar pulse.

It is obvious that to identify the square in the net it is enough to define its two peaks, located diagonally, as shown in Fig. 9 by circles.

Therefore, having a priori the binding frequency to the windings of the distributed source, it is possible to define a square grid in which the mobile receiver is placed, and to start the positioning. Thus, the proposed method of initial capture of the mobile receiver coordinates allows to eliminate the disambiguate solutions of the linear positioning, associated with the periodic nature of the distributed fields.

The location of winding with oscillating circuits to be used for an initial capture to start a positioning.

The new method has to be robust to changing environmental conditions.

There is no influence of non-metallic interior elements (walls, ceilings,
floors) on the positioning accuracy as the magnetic permeability of these
materials is equal to one (

In some cases, the stationary ferromagnetic iron may be situated within the
zone of positioning, such as ferromagnetic racks or building structures. The
influence of the iron can be reduced by the mapping of the positioning field
gridded with steps agreed with the linear positioning error. In this case,
for the distributed source in Fig. 6, the grid of mapping can be about 0.3 m. Full vector of position field at an arbitrary point

Next we ask the question – what will be happen if the vehicle like tram or bus
will pass near the positioning zone? The answer is – nothing will happen.
First, in accordance with Eq. (6) the field falls as the cube of the distance.
That is, at the distance (3–4) m from the source the induction of
residual field is < 10

The first numerical estimations were conducted for the hall of the
hypermarket, where it is necessary to provide steady positioning of
arbitrarily moving users. For this case the initial parameters of the
distributed source of the positioning field are shown in Table 3. The
windings with square shape are arranged under the non–magnetic floor in
the same plane. The height of the movable receiver is limited by the growth
of humans and does not exceed

Main parameters of distributed source.

As specified above in Table 3, we get periodic distributed source fields, as
shown in Fig. 10 for one group of windings “1”, activated simultaneously
at the same time. The number of such windings in the group “1” is equal to

Periodic positioning field of distributed source.

Calculation was carried out for the height

The numerical simulation of the linear movement was simulated on the
fragment of distributed source as shown on Fig. 11. In this case, one can
record the coordinates of the six windings:

Due to the obvious symmetry of the position field, shown in Fig. 10, a
mobile receiver can not distinguish its position relative to the symmetry
line shown in Fig. 10, for example in the field of winding

The object flow through the periodic elements of the distributed source.

The linear coordinates of the mobile object

The functional CF is subject to minimization, compiled from the discrepancies
of the six couple of measured and calculated modules of the induction
vectors from different windings, as follows:

A cycle of windings excitation to be applied to the Fig. 11 fragment of
distributed source will be described with the following sequence (

The exception of symmetry solution relative on line

The same assessment is applied to find the direction of the induction
vector, created by the windings

In result, if

A similar procedure is being applied when the user is approaching the
borders (

The results of the numerical simulation of the movement are given in Zhelamskij (2014a), where the possibility of unrestricted movement is shown within the zone, covered by the distributed source, despite the symmetry and periodicity of the positioning field.

Based on the conditions of the task, six coordinates of the mobile object should be obtained during the positioning. Such an opportunity should be provided.

In addition to the linear positioning description (Zhelamskij, 2014b),
the orientation angles of a mobile object in the case of a distributed
source at given linear coordinates are found from the system of nonlinear
equations of the following type

A decision of system (Eq. 21) is based on a minimization of the following
functionality:

For linear coordinates, obtained from the solution of system (Eq. 18), the
steepest descent method is applied to minimize the functional (Eq. 22), with the
iterative step selection by the method of dichotomy. For the angular
coordinates it is described with the following iterative formula:

The dependence of functional CF (in logarithmic scale) vs. number of
iterations “

The initial position in the study of the ranges of magnetic tracking operation with concentrated source. On the left – a local source with orthogonal coils with common center, to the right – the movable receiver on the base.

The movable object orientation angles [

The orientation of destination point is [

The orientation of initial approach.

As seen in Fig. 12 that the number of iterations “

At this initial stage, the handmade prototype to check the functioning of
the main elements of the positioning system was set up as shown in Fig. 13.
The prototype consist of – local source of position field (to the left),
the movable receiver (to the right), and the computer (not shown). The windings
in the source have a rectangular shape as described above for distributed
source. The windings are arranged orthogonally to each other and have a common
center. Dimensions of maximum winding are 0.28

The composition of the mobile receiver includes three orthogonal Hall sensor,
analog preamplifiers, which are the source of excitation current for sensors. The size of
the sensors sensitive area is 100

The calculation the receiver coordinates is performed by iterative formulas (19, 23).
These investigations have shown that the range of the orientation
angles of movable object is

The magnetometers of the modern smartphones, designed to measure the EMF,
are built mostly on the Hall effect sensors. The magnetometer AK8975 (Asahi
Kasei Corp.) (Asahi – Kasei, 2016), with a size of about 3

In this case, the measuring time is

A variable orientation of the smartphone

In Table 5 we present the results of the numerical simulation for the error components of the measurement, which are mostly caused with the mobile receiver properties (Asahi – Kasei, 2016). In addition, as shown below in Sect. 8.4, measurement errors are also determined by the nature of the positioning field. The simulation was made in accordance with the mathematical model of Eq. (8) for the positioning field measurement. The calculations were performed for two distances between the winding and receiver, and for a constant temperature of the environment.

Content of error of magnetic induction field measurement.

The noise of the receiver is neglected

For a distributed source, as described in Sect. 7.1, one should evaluated
the possible duration of the initial procedure to bind an autonomous
receiver in the source coordinate system. As can be seen from Fig. 8, the
break between bipolar pulses of the current in each winding, intended for
initial binding, contains

Identification frequencies [Hz] at multi-level distributed source.

The simulation showed that the duration of the initial capture of the
coordinates is defined with only a time of the calculations of the signals
spectrum in accordance with Eqs. (15, 16), which are observable at the
point where the receiver situates. So, the initial capture may be performed
during a single period of distributed fields source switching

For the same source from Sect. 6.1, the estimation of the power is produced, which is consumed by a distributed source, normalized to the area of the positioning zone.

The investigations have also shown that there are two possible options: single user mode positioning and an unlimited number of users. For a single user only the closest windings are switching on. Otherwise all windings of the distributed source are used in the unlimited number of users mode. For both modes the specific power consumption was found in comparison with WiFi, the most widespread alternative technology.

In the first case, for single user, taking into account the results from the
Table 2 for mode

Building regulations give the amount of energy at the level of 60 W m

Finally, the above considerations lets one determine the possible accuracy of
positioning. For the stationary receiver the measurement error is the sum of
the following components:

The random error of measurement can be neglected

The next step in advancing the project of active magnetic positioning for indoor navigation should consist of preparing and conducting a full-scale physical experiment, which must demonstrate to potential customers the basic properties of the proposed method. The minimum equipment must comply with Fig. 11.

A further increase in the number of windings allows one to extend the field of application of the experimental results obtained. As part of the planned experiment it the transition to autonomous receiver – a smartphone will be made. Before that, the first experimental studies should be conducted on a special receiver similar to the one shown in Fig. 13. The importance to promote of the project is the metrological support of both generation and measurement of positioning field. Initial ideas concerning this issue are formulated and presented in Zhelamskij (2015). As result of this further work the proposed technique will be fully experimentally validated.

The known methods of indoor navigation have limited accuracy no better than

The method provides a scalable coverage zone due to the synchronized building of elements of the positioning field distributed source. The original way to sync and initial binding (capture) was proposed for autonomous mobile receiver operation.

Thus, assessments show that it is possible to measure the positioning field by using the magnetometer of the modern smartphone, intended to measure the Earth's magnetic field. To do this, a mathematical model is proposed, which takes into account a special source of errors such as the spatial diversity of the receiver sensors. To improve the accuracy of position measurement it may be necessary to individually calibrate the smartphone's magnetometer.

The estimations were made about the values of the power consumption for the
distributed source, accuracy of positioning, and update rate of output data.
The power usage for the distributed magnetic tracking is minimal among all
other known technologies and can be reduced down to 1 W m

The sustainability of the new method to the interior is provided by the
following circumstances. The ratio between the magnetic pulse duration (

A comparison of results with other technologies shows that only magnetic tracking provides six coordinates instead three for other technologies. The accuracy of magnetic tracking in indoor navigation is expected as the percentage of the meter that is unachievable for other technologies. The scalable coverage can be provided with the proposed improvement of magnetic tracking opens the way to unlimited zone of positioning, such as the smartphone's network, which is able to cover the entire world.

Great thanks Natalia Popova for her faithful support in writing this work. Also, the author is deeply grateful to old Swiss friend and colleague Alexander Anghel from PSI for assistance in accurate scientific translation of articles into English. Edited by: I. Bársony Reviewed by: three anonymous referees