J. Appl. Geodesy, Vol. \volume? (2013), pp. 1–10
Copyright © 2013 De Gruyter. DOI 10.1515/jag-2013-0016
Using Geomagnetic Field for Indoor Positioning
Binghao Li,1,∗ Thomas Gallagher,1 Chris Rizos1 and Andrew G. Dempster2 1
2
School of Civil and Environmental Engineering, University of NSW, Sydney, Australia School of Electrical Engineering and Telecommunications, University of NSW, Sydney, Australia
Abstract. Geomagnetic field variation in support to indoor positioning and navigation has recently attracted considerable interest because of the advantage that technology based on the geomagnetic field has no infrastructure needs. Test using sensitive magnetometers has confirmed that it is possible to use geomagnetic field information for positioning purposes, however there are still issues to be addressed before it can be used in real applications. For example, are the low cost built-in magnetometers in mobile phones good enough for positioning purposes based on "fingerprinting" approaches? Is the geomagnetic field temporally stable for very long period of time? Tests have been carried out using several devices including smart phones. Because geomagnetic field positioning techniques alone may have difficulties, integration with other positioning methods is necessary. Wi-Fi is one of the obvious technology options. One approach is using Wi-Fi to first estimate approximate position, and then applying geomagnetic field information to refine position estimation. An experiment was carried out to test the proposed approach, and the error of fingerprintbased magnetic field positioning was analysed. Keywords. Geomagnetic field, Indoor positioning, Finger-
printing.
1
Introduction
Global Navigation Satellite System (GNSS) technology is the dominant outdoor positioning option. The applications of GNSS can be found across almost all of a nation’s economic, scientific and social activities. However, a GNSS fails to operate in "urban canyon" and indoor environments, where it is not possible to track sufficient satellite signals. Studies indicate that human beings "are basically an indoor species" [12], and about 90% of time a person is located Corresponding author: Binghao Li, School of Civil and Environmental Engineering, University of NSW, Sydney, Australia. E-mail:
[email protected]. Received: August 08, 2013. Accepted: September 24, 2013.
indoors [5]. Although many people spend most of their time in very familiar indoor environments, such as home, work, shops, cinemas, and restaurants, the amount of time that people are in unfamiliar indoor environments, such as shopping malls, airports, office buildings, etc., is significant compared with the time spent outdoors (only 2%). Compared with outdoor environments, indoor positioning is very challenging not only because of the complexity of the environments, the blockage of signals and severe multipath, but also because of the accuracy requirement(s). Many technologies have been developed, or are under development, including: infrared and acoustic-based indoor positioning systems have been deployed since the 1990s [18, 19]; cellular network (including assisted-GNSS and high sensitivity GNSS) can be used for emergency services [9, 21]; UWB (ultra-wide band) systems can provide accurate (decimetre-level) range measurements [14]; Optical systems utilise a vision sensor (camera) on its own or in combination with other sensor technology to determine position [10, 11, 16]); Pseudolites are GNSS-like systems, with the signal transmitters treated as "ground-based satellites". Considering the cost of deploying new positioning infrastructure, engineers and system developers prefer to use existing wireless (and other) infrastructure for indoor positioning. That is one of the main reasons that Wi-Fi positioning systems have become so widely used. Similar systems are based on FM radio, Bluetooth, and Zigbee signals. Recently use of the Earth’s magnetic field has attracted attention. An obvious advantage of using the magnetic field for positioning is that no infrastructure needs to be pre-deployed, nor does it use transmitted signals. The geomagnetic field is often used to determine the orientation (heading) of a device [13]. However, significant magnetic disturbances in indoor environments often adversely impact on the accuracy of orientation estimation. Calibration is normally necessary, however this is not an easy task [1]. On the other hand, the anomalies caused by magnetic disturbances could be used as "fingerprints". In 2000, [15] collected magnetically-derived heading information as a robot travelled along a hallway. Subsequently the robot measured the magnetic field features and matched them with the pre-stored data. If a match was found, the robot could determine its location. In [3] a magnetic sensor array was used to detect the indoor magnetic field intensity, and several metres positioning accuracy was reported. [7] investigated the feasibility of predicting the magnetic field indoors. In [6] geomagnetic field sensor and an inertial measurement unit were integrated to estimate the device’s location in an experiment, and slight worse than
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B. Li, T. Gallagher, C. Rizos and A. G. Dempster
one metre accuracy was achieved. Several basic issues of using the geomagnetic field for positioning such as the stability, uniqueness of the magnetic field and interference was discussed in [8]. Using magnetic field for Simultaneous Localization and Mapping (SLAM) has also been investigated [2, 17] To utilise the fingerprinting approach, a survey for the area of interest is required. Similar to Wi-Fi fingerprinting positioning systems, the survey of the spatial variability of the geomagnetic field is not a trivial task. Another challenge is that the magnetic field intensity data only consists of three components - intensities in the X, Y and Z directions. In many applications the intensities in the X and Y directions cannot be separated. Hence only two, and a maximum of three elements can be used to represent the fingerprint. This leads to ambiguities in the positioning phase. There is a high risk of locating the user in a very wrong position if there is no other information to assist [8]. There are still issues to be addressed for real applications. For instance, are the low cost built-in magnetometers in mobile phones good enough for positioning using the fingerprinting approach? Is the geomagnetic field stable over a long period of time? In this paper further tests using the latest smart phones are reported. However because using geomagnetic field information alone for positioning may have difficulties, integration with Wi-Fi is discussed. One approach is to use Wi-Fi to first estimate the approximate position, and then apply geomagnetic field techniques to refine the estimation. An experiment was carried out to test this proposed methodology. The rest of paper is organised as follows: basic concepts of the geomagnetic field are introduced in section 2, a discussion of the long term stability of the geomagnetic field is given in section 3; section 4 investigates the integration of Wi-Fi and geomagnetic field information for positioning; and section 5 presents the concluding remarks.
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Figure 1. The seven parameters of the Earth’s magnetic
field (in the southern hemisphere, Z is negative). and east (Y ) components of the H, and total intensity (F) (refer to Figure 1). A compass can be used to find magnetic north, which is different from "true north" or "geographic north". True or geographic north is defined by the point where the Earth’s rotational axis pierces the surface at the north pole and referenced by the meridian lines, while magnetic north refers to the geomagnetic pole position. Declination is used to describe the difference between these two north directions. The value of declination varies depending on the location of magnetic north on the surface of the Earth. Inclination is the angle between the horizontal plane and the total field vector, measured positive into the Earth. A common representation of the Earth’s magnetic field is in terms of X, Y and Z coordinates. It can also be represented by F, D and I. Significant variations of the geomagnetic field can be observed inside buildings. The major cause of these variations is the steel shells of most modern buildings. Pipes, wires, electric equipment, etc., also contribute to the variations.
Earth’s Geomagnetic Field
In this paper, the term "magnetic or geomagnetic field" refers to a magnetic B field which is more commonly used as it reveals the real cause of the magnetic field is moving electric charge. The most commonly used units of B are Tesla (T) or Gauss (G) (1T=10000G). µT (10−6 T) and nT (10−9 T). The Earth’s magnetic field is spatially characterised by direction and intensity. The geomagnetic field intensity ranges between approximately 23,000 and 66,000 nT [11]. The direction of the geomagnetic field is always towards "magnetic north". The horizontal components of the geomagnetic field are used to determine the compass direction. The Earth’s magnetic field is described by seven nonindependent parameters: declination (D), inclination (I), horizontal intensity (H), vertical intensity (Z), the north (X)
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Long Term Stability Of Geomagnetic Field
A basic requirement if geomagnetic field information were to be used for indoor positioning is that the measured magnetic field intensity should be stable over a relatively long period of time. An Xsens MTi device was used (refer to Figure 2, the device on the very left side) to collect 3D geomagnetic field measurements at several test environments. The MTi can provide 3D acceleration, 3D rate-of-turn and 3D geomagnetic field measurements [20]. The magnetic field output was normalised to the Earth’s field strength at a specific location, hence it is in arbitrary units. The output rate was selected as 25Hz. More than a year later similar tests were conducted in the same locations. Ideally, the same device should be used to collect the magnetic field data at the same
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Using Geomagnetic Field
Figure 2. Devices used in this study (from left to right: Xsens MTi, HMR2300, Samsung Nexus, Samsung Galaxy
Nexus S). locations. Unfortunately, the Xsens MTi device was faulty, and a HMR2300 sensor was used instead (see Figure 2). The HMR2300 is a high accuracy three-axis digital magnetometer, with magnetic field output in units of µT [4]. The data logged at the same test environment is shown in Figure 3. Although the units of magnetic intensity are different, the ratios of the intensity in the X, Y and Z directions are similar. If the intensities are normalised, the values in the X, Y and Z directions are 0.4861, -0.1484, 0.8612 for the Xsens MTi sensor, and 0.4420, -0.1536, 0.8838 for the HMR2300 sensor. The results are not exactly the same. One reason for these differences is that the positions of the two tests are not exactly the same. The exact centres of the sensor units to which the measurements are referred are not known. Previous investigations have shown that even a few centimetres of offset may cause a noticeable change of the geomagnetic field measurement [8]. Nevertheless the small differences in results of these two tests indicate that the geomagnetic field is quite stable over time. However, further investigation is needed using the same sensor (HMR2300).
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Measuring the Geomagnetic Field Using Different Devices
Different devices to measure the same geomagnetic field may result in different field values. The measurement differences must be taken into account for fingerprint-based positioning. Four devices, Xsens MTi, HMR2300, Samsung Nexus and Samsung Galaxy Nexus S smart phones, were used in these investigations. A device was placed on a trolley with the X axis pointing to true north. The height of the trol-
ley was about 1.05 m, which is approximately the height of a person holding a mobile device. The trolley was moved along a 36 m long corridor with a speed that was as constant as possible. At the start point and end point, a device logged static data for several seconds. Figure 4 compares the results. There are several interesting things to be noted. Firstly, the patterns in these plots are similar except for the last one (Samsung Nexus). Obviously, the closer these patterns, the better for positioning. The Samsung Nexus makes the poorest quality magnetic measurements. The intensities in the Y direction are totally wrong as the value should be negative in the Sydney area when the X axis points to true north (in the Sydney area, the declination is about 12 degrees). The reason for this fault is unknown. Secondly, measurements from the HMR2300 are smoother than those from the other devices. There are two possible reasons for this. One is the quality of the sensors, and the other is the sampling rate. The HMR2300 is a high quality magnetic sensor; whereas the built-in sensors in smartphones are comparatively low quality. The sampling rates of these four devices were 25 Hz, 1 Hz, 100 Hz and 100 Hz, for the Xsens MTi, HMR2300, Samsung Galaxy Nexus S and Samsung Nexus respectively. Thirdly, the similarity of the measurement patterns of the Xsens MTi and those of other devices confirms the assumption of long term stability of the geomagnetic field because the Xsens test was carried out more than a year before the other tests. Lastly, the measurements from the HMR2300 and the Samsung Galaxy Nexus S are not the same although they both output measurements in units of µT. These differences may introduce errors when the fingerprinting technique is used for positioning. One possible solution is data normalisation; however it may also decrease the positioning accuracy.
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B. Li, T. Gallagher, C. Rizos and A. G. Dempster
Figure 3. Static test results using Xsens MTi and HMR2300 at the same location at different times.
Figure 4. Comparison of the measured magnetic intensities using different mobile devices.
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Using Geomagnetic Field
Figure 5. Comparison of the normalised magnetic intensities collected using different mobile devices.
To further investigate the differences in measurements from different mobile devices, the magnetic intensities collected from all devices except the Samsung Nexus were normalised. Figure 5 compares the results. Clearly the three plots are very similar; especially the first two (Xsens MTi and HMR2300). Not only the patterns but also the values are very similar. However, some small differences can be identified, especially with respect to the last one (Samsung Galaxy Nexus S) compared with the other two devices. The quality of the sensors and the placement of the devices may be the primary reasons for the differences. For instance, the back side of the smart phone is not flat, hence it could not be placed as level as the other two devices.
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Using The Geomagnetic Field For Positioning
Location fingerprinting has two phases: training and positioning. During the training phase a fingerprint database is created. Locating a measurement device at one reference point (RP) location, the relevant physical quantity (such as signal strength of Wi-Fi access points, magnetic intensities, etc.) is measured. From such measurements the characteristic feature of that RP is determined, which is then recorded in the database. This process is repeated at another RP, and so on, until all RPs are visited. In the positioning phase the device makes a measurement at a location where the position is to be determined. The measurements are compared with the information in the database using an appropriate search algorithm. The likeliest position of the device can then be output. In general, the more elements that can be used, the better the performance of fingerprint-based positioning. An obvious problem of using geomagnetic field positioning is the small number of elements that can be used to create the fingerprint data at a RP - only intensities in the X, Y and Z directions. In addition, intensities in the X and Y directions cannot be separated if true north (or magnetic north) is not known, or the manner of measuring the magnetic field
Figure 6. Using gravity to derive the vertical and horizontal
components of the magnetic field intensity (red: sensorfixed coordinate system, black: earth-fixed coordinate system, a is the opposite direction of gravity; b is the magnetic intensity measurement). is not the same. Hence in many applications only two elements (the vertical component and horizontal component) can be used, with the help of the gravity sensor. Figure 6 and Equation (1) illustrate the way to compute the Z 0 and X 0 Y 0 components. The key is to calculate θ [8].
cos
π
ax bx + ay by + az bz q −θ = q 2 2 ax + a2y + a2z b2x + b2y + b2z
(1)
To evaluate the performance of using geomagnetic field information for positioning, a corridor in a fourth floor of a multi-level building was selected as a test bed. The corridor is about 36 m in length and 2m wide. It has been shown in past studies that the changes of the geomagnetic field across
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B. Li, T. Gallagher, C. Rizos and A. G. Dempster
Figure 7. Test bed, the 3 red lines are the paths of measurement for the database, the red stars (in total 9) and green
squares (in total 11) are test points. a small area are significant. Hence the database was created and Euclidean distance are L1 and L2 respectively. In this study, Manhattan distance was used. in the following manner: As discussed in past studies, because of the small num• The measurement device was placed on the top of a ber of elements, there is a risk that the output position of the trolley as described in previous section. mobile device could be a considerable way from the true • The trolley was moved from one end of the corridor to position. Hence it is necessary to narrow down the searchthe other along a straight line (the red lines in Figure 7) ing space to avoid very large errors. One way to limit the with constant speed. searching space is to use another positioning technology to first generate a coarse location, and to then apply the geo• The step above was repeated along two more parallel magnetic positioning approach to refine the position deterlines about 60 cm apart. mination. In this test a search radius was used to restrict Once the database was created, test points were randomly the searching area and the centre of the searching area was selected in the test area (the read stars and green squares in the ground truth of each test position. This method was Figure 7). only used to evaluate the positioning performance in a relative manner (comparing the positioning errors under different scenarios or using different configurations). It can5.1 Test using HMR2300 not be used in real applications as the true position is not In this test the HMR2300 was used as a reference device to known. For the first 9 test points, three or two elements create the database and was also used as the mobile device can be chosen for positioning calculations. However, for to make measurements at each test point. At the first 9 test the remaining 11 test points only two elements can be conpoints the attitude of the sensor was exactly the same as sidered as it was not possible to separate the intensities in that in the training phase. In this case, all three elements the X 0 and Y 0 directions. Table 1 summarises the results. (i.e. magnetic intensities in the X 0 Y 0 and Z 0 directions) It can be seen that the positioning error of the first 9 test can be used. For the remaining 11 test points, the attitude of points was less than that of the full set of 20 test points. the sensor was different from that in the training phase (the If three elements can be used, the positioning results are device was still placed on the trolley as level as possible so always better than those tests that use only two elements. It that the X 0 Y 0 component could be obtained without using is impressive that when three elements were used, the posithe gravity sensor). Hence only two elements can be used. tioning error can be as small as 0.6 m. In addition, when To find the best match in the database, the magnetic field the search area was the whole test bed, 1 m accuracy can intensity distances were calculated: still be achieved. When two elements were used, the results were significantly worse if there was no searching restric! q1 n tion. However, narrowing down the searching area can help X (2) increase the positioning accuracy significantly. The last Lq = |mi − Mi |q i=1 column of Table 1 lists the positioning errors if all intensity measurements were normalised. Normalisation could where m and M are the measured magnetic intensity (a vecbe useful when different mobile devices are used to cretor of n elements) at different locations. Manhattan distance
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Using Geomagnetic Field
3 elements
9 test points
2 elements
20 test points
2 elements only
Search radius (m) ∞ 10 5 3 2 ∞ 10 5 3 2 ∞ 10 5 3 2
Positioning error (m) Without Normalise B normalisation 1.0 9.1 1.0 2.7 1.0 2.2 0.6 0.8 0.6 0.8 6.6 14.0 1.0 5.3 1.0 3.0 0.9 1.1 0.7 0.8 6.9 18.6 2.2 5.1 1.4 2.4 1.1 1.4 0.9 1.0
Table 1. Static Test Results Using HMR2300.
ate the fingerprint database, or to make measurements for user positioning. Unfortunately if normalisation is implemented the positioning performance is much worse. Sometimes even randomly selecting a position within the searching area could be better than the computed result! 5.2
Test using Samsung Galaxy Nexus
Similar tests were carried out using a smart phone. As before, a database was first created. Since a gravity sensor was available in the smart phone, the creation of the database and the collection of geomagnetic field data during the positioning phase was more flexible, and an arbitrary device orientation could be used during the measuring process. A dynamic test was also conducted by collecting test data walking along the central line of the corridor. The sampling rate was 1 Hz. The results are summarised in Table 2. When two elements were used, the results are clearly worse than those of the first test. Since the orientation sensor can report the azimuth (angle between the magnetic north direction and the Y −axis), intensities in the X and Y directions could be reconstructed from the magnitude of the horizontal intensities. However, the reliability of this method is affected by abnormalities of the geomagnetic field, which are in fact relied upon for positioning. Unfortunately, the results using this method are worse than the one using two elements. For the dynamic test there was a decrease in accuracy. Again, normalisation of the magnetic intensity actually increases the error.
5.3
Wi-Fi plus Magnetic Field for Positioning
To utilise geomagnetic field information for positioning a restriction of the searching area is required, especially when only two elements of the magnetic intensity are available. An obvious option for this is to use Wi-Fi. In this test, a Wi-Fi database was created using 32 RPs along the central line of the test bed. At each RP, 10-20 scans were recorded. The 20 test points were the same as for the previous tests (refer to Figure 7). During the positioning phase, only 1 WiFi scan was recorded. Wi-Fi positioning gave an average positioning error of 1.8 m. The magnetic intensity database was created in previous test. When the search radius was set to 1.5 m use of the magnetic field can help refine the positioning to 1.4 m. Setting different values for the radius leads to different results. As there is no reliable way to estimate the Wi-Fi positioning error, the searching radius can only be chosen based on experience. There is still much research work that can be done. Integration of other sensors to improve the positioning accuracy before geomagnetic field positioning is applied is an attractive option.
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Analysis Of Errors
The fingerprinting approach is based on the assumption that the further the geometric distance, the larger the "vector distance" (in this case magnetic intensity distance). To investigate the relationship between these two distances a grid test was carried out. In this test, two grids - a large one (8 by
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B. Li, T. Gallagher, C. Rizos and A. G. Dempster
2 elements
3 elements (using orientation sensor)
Dynamic, 2 elements
Search radius (m) ∞ 10 5 3 2 ∞ 10 5 3 2 ∞ 10 5 3 2
Positioning error (m) Without normalisation 11 3.7 2.0 1.2 1.0 10.3 4.0 2.6 1.5 1.2 10.3 2.7 2.1 1.6 1.2
Normalise B 15.7 5.4 2.3 1.7 1.2 13.9 4.3 2.7 1.6 1.2 10.6 4.3 2.5 1.6 1.2
Table 2. . Test results using Samsung Galaxy Nexus.
Figure 8. Distribution of Manhattan distances between 64 test points versus the real distance between the test points in
the "big grid" test.
Figure 9. Distribution of Manhattan distances between 36 test points versus the real distance between the test points in
the "small grid" test.
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Using Geomagnetic Field
8) and a small one (6 by 6) - were selected. The spacing of the large grid was 30.5 cm while that of the small one was 5 cm. In fact the small grid is part of the large grid. Data were collected at each grid point for 30 s. In total there were 64 data sets for the large grid and 36 data sets for the small grid. By studying the Manhattan distance between the test points’ fingerprints and comparing them with the actual distance it can be seen that there is a definite trend. Figure 8 and Figure 9 show the relationship between the magnetic intensity distance and the real distance. In the left plot of Figure 8 (using three elements), several polynomial fits are also shown. A cubic fit to the data gives a root-mean-square (rms) error of 0.0717. The red circles are the mean values at each real distance. The curve of the mean values looks similar to the cubic fit. When the real distances of the test points are small (say less than 1 m), the relationship between the two distances is almost linear; then the curve becomes gradually flattens until it rises again. Since the number of samples is very small when the distance is larger than 250 cm, the rising of the curve is not reliable. When only two elements were used a similar plot was obtained, however the curve of the mean value is flatter. Hence using three elements can typically give better results. A similar phenomenon can be observed in the small grid test (refer to Figure 9). The plot of the small grid test is consistent with that of the big grid test when the real distance is small. This suggests that using fingerprint-based magnetic field positioning with a restricted searching area can help ensure an accurate result. On the other hand, increasing the searching area may introduce large positioning errors.
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Concluding Remarks
Using geomagnetic field variations for indoor positioning and navigation is a very interesting topic. It seems possible to apply a variation of the fingerprint-based approach. However, there are still many difficulties when it comes to using this technique in real world applications. For instance, the quality of the sensor, especially those found in smart phones, is an important issue. A low quality sensor would not aid positioning. Using geomagnetic field information alone for positioning is very challenging. One possible use scenario is when the paths are very narrow and a patternmatching method is used to determine the position of the mobile device with embedded magnetic field sensor. Otherwise integration with some other location-determination technology is an option, such as using Wi-Fi signals. However, Wi-Fi positioning accuracy may not good enough to utilise the magnetic field to refine the position results. Furthermore, generating the geomagnetic intensity database in a cost effective manner is far from an easy task. More investigations are needed.
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