In fingerprinting techniques using a magnetic field signal, since the moving direction of the current user may be different from the moving direction of the person who creates the magnetic field map at the collection time, the sampled magnetic vector may have different values from the vector values recorded in the field map. This may substantially lower the positioning accuracy. In this paper we propose a vector calibration algorithm which can adjust the sampled magnetic vector values to the vector direction of the magnetic field map by using the parametric equation of a circle. This can minimize the inaccuracy caused by the direction mismatch. To implement this, we just need to compute the relative azimuth from the moving direction of the current user to the moving direction during the magnetic field map collection. To evaluate our vector calibration algorithm, we first collected a magnetic field map in our test-bed. Then, a user walked through a random path and we adjust the sampled vector values to match the recorded magnetic field direction in the map. As a result, we can decrease the difference between the sampled magnetic vector and the magnetic field map values from 17.34 μT to 2.98 μT in x dimension, and from 13.12 μT to 1.98 μT in y dimension on average. This translates to 85% reduction in the map mismatch compared to the numbers without calibration. In addition, we also demonstrate the effectiveness of the calibration by applying the algorithm to our LSTM-based indoor positioning system (IPS).
The magnetic field is the attractive signal for indoor localization. The magnetic signal
has two distinct advantages over RF signals. First, it does not require extra signal
generation infrastructure such as beacons or APs since they are everywhere by nature.
Therefore, you do not have to worry about the maintenance of functionality or
discharge. Second, the magnetic signals are quite stable over time unlike RF or acoustic
signals in indoor environment [
However, magnetic sensors have the disadvantage that their vector values differ depending on the direction. It causes a mismatch with the magnetic field map. To avoid this problem, many researches usually use only the magnitude of the vector, which remains constant for rotation. However, using only the magnitude reduces the uniqueness of the fingerprint. In the fingerprinting technique, the more values used as the fingerprint, the higher the uniqueness of the fingerprinting. The uniqueness of the fingerprint is an important factor affecting both the localization accuracy and the speed of initial positioning.
In this paper, we propose a magnetic vector calibration algorithm that can compensate the change of a user's moving direction and adjust the sampled vector sequence to the original direction recorded in the magnetic map. Since we calibrate the vector sequences dynamically all the time relative to the original direction in the magnetic map, the calibrated vector sequences can still match the numbers stored in the magnetic map, minimizing the difference between the sampled vector sequences and the original sequences in the map for the same path. Due to the uniqueness of vector fingerprint compared to the magnitude fingerprint, we can achieve higher positioning accuracy as well as faster initial positioning.
To do the calibration, we should be able to compute the relative azimuth from the moving direction of the current user to the moving direction during the magnetic field map collection. For this, we use a gyroscope in a smartphone. Since the gyroscope measures the angular velocity, we can calculate the rotation angle of the smartphone, that is, the walking direction of the user. And we measure the azimuth from the magnetic north with a compass sensor. Then by applying the parametric equation of a circle, we can adjust the sampled magnetic vector values to the moving direction of the field map collector. As a result, although the user walked in a random direction in real-time test, we could reduce the mismatch with the magnetic map to about 85%.
We also test the impact of our magnetic vector calibration, by applying it to our
LSTM-based IPS [
The remainder of this paper is organized as follows. Section II discusses the related works. Section III presents the detailed vector calibration algorithm. Section IV shows the experimentation results of a real-time test with and without our proposed calibration algorithm. Finally, Section V concludes the paper. 2
In the magnetic signal-based fingerprinting, the three-dimensional magnetic vector signal is used as the fingerprint for each position. While the magnetic signal generally points to true north in outdoor environment, the magnetic field is further distorted in indoor environment by the structure of the building such as concrete walls, iron doors and elevators, which leads to a more unique signal value for each position.
In the magnetic field-based fingerprinting techniques, two types of magnetic signal values can be used: a magnetic vector or the magnitude of the magnetic vector.
Magnetic vector as a fingerprint: The 3-axis magnetic sensor reads a magnetic
vector in the three-dimensional space relative to the smartphone orientation. The vector
value differs depending on the orientation of the sensor, so it is quite difficult to use as
a fingerprint. During the positioning phase, a user may sample magnetic vectors in a
direction different from the field map. This can cause a mismatch for the mapping,
which leads to inaccurate localization. To avoid this problem, Chung et al. [
Magnitude of a magnetic vector as a fingerprint: The magnitude of the magnetic
vector is widely used in many magnetic field based IPSs [
In our work we use a magnetic vector as a fingerprint, which can maintain the uniqueness of the fingerprint, while we collect the magnetic field map only in one direction to minimize the manpower and collection time. In addition, with the dynamic vector calibration algorithm proposed in this paper we can minimize the map matching mismatches even if a user may change his or her direction anytime. 3
If you hold a smartphone horizontally and rotate 360 degrees collecting the magnetic field vector in x and y dimension, the graph showing the magnetic vector draws a circle as illustrated in Figure 1. 4 tor draws a circle. is an angle rotated counterclockwise from the magnetic north.
In an indoor environment, the magnetic north may change depending on the location because of magnetic field distortion. For example, Figure 2 shows both the magnetic north direction and the moving direction of the administrator at each location. The red arrows point to the direction of the moving direction of the administrator during the field map collection while the black arrows point to magnetic north. Since the magnetic vector is sensitive to the moving direction, i.e. the sensor orientation, the measurement for the field map collection should be performed in one direction only. the map collector and the magnetic vector, i.e. magnetic north be α. Since we assume that a user holds a smartphone horizontally, we can express the magnetic vector as the Equation (1) and Equation (2) by using the parametric equation of a circle. Since we only consider holing a smartphone horizontally in this paper, has the same value in any direction. So, in (1), r, the radius of the circle, can be expressed by Equation (2), where is the magnitude of the magnetic vector.
= (−
( )) =
( ) = √ 2
+ = √ 2 −
When a user walks in some direction during positioning phase, let the value of the magnetic vector sampled by the user be ( , , ) at the same position.
Since we assume that the user holds the smartphone horizontally, the value of the magnetic vector in z dimension is invariant to rotation in the horizontal plane. So, has the same value as
(3). Our goal is to calibrate ( , ) with respect to ( , ). . Therefore, the radius r can also be obtained by Equation = √ 2 +
2 = √ 2 − 2 During the positioning phase, if you know α, ( by (1) since we can compute radius r by using Equation (3). Since the radius is invariant to rotation in the horizontal plane, they can be measured regardless of the user’s moving direction. However, since α is changing depending on its position all the time, it cannot be computed by magnetic north.
To address this issue, we use a gyroscope and a compass sensor in a smartphone. The gyroscope can calculate the relative rotation angle, and the compass sensor can measure the azimuth from the magnetic north. When the map collection direction is zero degrees, the gyroscope calculates the current rotation angle, which we call the positioning relative angle. Also, whenever the user walks, the compass sensor calculate the azimuth from the magnetic north at each location, which we call the positioning azimuth. Then, the smartphone can calculate α by equation (4).
α = ℎ −
Originally, for relative angle measurements, the user must know the direction of the magnetic field map collection. But if we use true north, the user do not need to. When collecting the magnetic field map, record the relative azimuth from the true north to the database. Then, by measuring the relative azimuth from the true north during positioning phase, the relative rotation angle from the direction of the magnetic field map collection can be calculated dynamically.
Now that we have obtained α by (3), we can calculate ( , ). In other words, we can compute the magnetic vector values of the map in any direction in realtime. 4
As we discuss in Section 2, we collect magnetic vectors only in one direction when collecting the field map. Figure 3 visualizes the magnetic field map for our test-bed by showing the vectors only in x dimension. When a user walks along the test path, the smartphone was kept horizontal as in the map collection, but the user may make any horizontal movement freely, i.e. random yaw rotation. The magnetic vector values may change with the yaw rotation, but our goal is to adjust these values as closely as the magnetic field values stored in the field map.
(3) (4)
Figure 4 compares the same sequences for the same test path in dimensions x and y of the vector space. Unlike the case of magnitude, without calibration the mismatch between the map and the measured samples is quite large. The difference is as high as 65μT. Figure 5 compares only the differences between the map and measured samples in magnitude and vector space in dimensions x and y with and without calibration. The average difference in the magnitude is about 1.929μT while the average differences of the vector in dimensions x and y are 17.34 μT and 13.12 μT respectively. These huge differences will lead to inaccurate localization in a magnetic field based IPS. However, after applying our calibration, we could reduce these differences to 2.985μT on average in x dimension and to 1.981μT on average in y dimension. This suggests that we can effectively minimize sequence mismatches even with the magnetic vector with the proposed calibration algorithm.
Our LSTM-based IPS using the magnetic field has demonstrated outstanding
localization performance in large scale indoor environment [
From the magnetic field map shown in Figure 3 we generate 300,000 data sets, each
of which consists of 100 steps of a random pedestrian walk path assuming the random
waypoint model [
After training, the LSTM model has an average positioning error of 0.43 meters for the test set. However, in a real time test with a smartphone, the average positioning error rises to 16.97 meters assuming that we use magnetic vectors without calibration as input to the LSTM model. Figure 6 shows the predicted path result of LSTM model with and without calibration compared to the actual test path. However, with calibration we could reduce this average positioning error back to 0.73 meters. The predicted path with vector calibration is illustrated by the red line in Figure 6. 5
In this paper we propose a magnetic vector calibration algorithm for indoor localization. Since the magnetic vector values change depending on the sensor direction, i.e. the moving direction of a user, it has been seldom used for indoor localization. To enable the magnetic vector based localization, we need to compute the relative angle of rotation from the direction of the user movement to the direction of the field map collector. This is because we can compute the magnetic vectors if we know only the azimuth from the magnetic north when the administrator collected the magnetic map.
To evaluate our vector calibration, we performed a random walk test to measure the
differences in vector values between the map and the actual test. Without calibration,
the average difference between the vector samples and the magnetic field map data was
17.34μT in the x dimension, and 13.12 μT in the y dimension. After we applied the
calibration, we reduced these differences to 2.985μT in the x dimension, and 1.981μT
in the y dimension. To demonstrate the effect of our calibration algorithm in a magnetic
field based IPS, we applied the calibration algorithm to our LSTM-based IPS [
Acknowledgments. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF2017R1A2B2009641) and by the MSIT (Ministry of Science and ICT), Korea, under the ITRC (Information Technology Research Center) support program (IITP-20192015-0-00363) supervised by the IITP (Institute for Information & communications Technology Promotion). 6