Rank based fingerprinting algorithm for indoor positioning

Abstract

A novel Received Signal Strength (RSS) rank based fingerprinting algorithm for indoor positioning is presented. Because RSS rank is invariant to bias and scaling, the algorithm provides the same accuracy for any receiver device, without the need for RSS calibration. Similarity measures to compare ranked vectors are introduced and their impact on positioning accuracy is investigated in experiments. Experimental results shown that proposed algorithm can achieve better accuracy than commonly used NN and WKNN fingerprinting algorithms.

Full text

2011 International Conference on Indoor Positioning and Indoor Navigation (IPIN), 21-23 September 2011, Guimarães, Portugal
Rank Based Fingerprinting Algorithm for Indoor
Positioning
J. Machaj*, R. Piché** and P. Brida*
* University of Zilina, Department of Telecommunications and Multimedia, Zilina, Slovakia. Email:
Machaj@fel.uniza.sk, Brida@fel.uniza.sk
** Tampere University of Technology, Tampere, Finland. Email: Robert.Piche@tut.fi
Abstract—A novel Received Signal Strength (RSS) rank
based fingerprinting algorithm for indoor positioning is
presented. Because RSS rank is invariant to bias and
scaling, the algorithm provides the same accuracy for any
receiver device, without the need for RSS calibration.
Similarity measures to compare ranked vectors are
introduced and their impact on positioning accuracy is
investigated in experiments. Experimental results shown
that the algorithm can achieve better accuracy than some
commonly used fingerprinting algorithms.
Keywords—Indoor positioning; Fingerprinting; Localization
I. INTRODUCTION
The basic requirement for Location Based Services
(LBS) [1] is knowledge of the mobile device position.
This can be achieved in many different ways. Global
Navigation Satellite Systems (GNSS), like GPS (Global
Positioning System) or GLONASS (Global Navigation
Satellite System), are widely used, and these systems
work very well for outdoors, especially in areas with a
clear view to the satellites. In dense urban environments
GNSS can suffer from high signal attenuations and
reflections, which can seriously degrade position estimate
accuracy. In indoor environment the situation is even
worse, as GNSS signals are mostly too weak to be
received at all.
These drawbacks of GNSS have motivated the
development of positioning algorithms that use signals
from existing radio networks. These algorithms use
different properties of radio signals. Most common in
indoor environment are measurements of RSS (Received
Signal Strength) and ToA (Time of Arrival). The work
presented in this paper deals with RSS measurements,
which have the advantage that they are available on
almost every device.
Indoor positioning systems can be based on different
wireless technologies, for example Bluetooth [2], UWB
(Ultra Wide Band) [3] and WiFi (IEEE 802.11) [4-8]. This
work deals with WiFi signals, because WiFi is the most
common technology and it is supported by a wide range of
devices.
Most indoor positioning systems based on WiFi use
some kind of fingerprinting algorithm. In fingerprinting
algorithms, measured RSS values stored in a database
(known as a radio map) are compared to RSS values
measured by the mobile device. A basic difficulty here is
that because of hardware and software differences
between different devices (even devices of the same make
and model), the RSS reported by the mobile device may
differ from the RSS in the database, and this can degrade
the positioning accuracy [9].
One approach to dealing with this issue is to calibrate
the RSS scale and bias for the device, for example using a
self-calibration learning algorithm as proposed in [4].
In this paper we propose a novel fingerprint positioning
algorithm that uses only the rankings of the RSS values.
Because rank information is invariant to any monotonic
increasing transformation (bias and scale), the algorithm's
performance should be unaffected by the calibration of the
mobile device.
The rest of the paper is organized as follows. In the next
section related work in indoor positioning algorithms is
introduced. Section III describes the proposed rank based
algorithm. Similarity measures used in the algorithm are
described in Section IV. Results of tests in a real
environment are given in Section V and Section VI
concludes the paper.
II. RELATED WORK
A. Rank based localization
Rank based localization in wireless networks was
introduced by Yedavalli et al. in [10]. Their Ecolocation
algorithm uses a set of constraints to estimate the position
of a mobile device. Measured RSS values from the APs
(Access Points) that are within range are sorted and
compared with constraints. Position is estimated as the
centroid of points with the highest number of satisfied
constraints.
An improved version of the Ecolocation algorithm was
introduced in [11]. Bisector lines were introduced as lines
connecting points with the same RSS values from two
different APs. Position is estimated as a weighted mean of
positions with the highest number of satisfied constraints.
Another modification of the algorithm [12] uses the
centroids of nearest three regions with the highest number
of satisfied constraints estimated by the previous
algorithm.
A drawback of these methods is their use of bisector
lines, because signal propagation in indoor environment,
where there are many obstacles, is not accurate and equal
values of RSS from two APs are not in a straight line.
B. Fingerprinting localization
In fingerprinting localization, the position of a mobile
device is estimated by comparison of measured RSS
values and RSS values stored in a radio map database.

2011 International Conference on Indoor Positioning and Indoor Navigation (IPIN), 21-23 September 2011, Guimarães, Portugal
Fingerprinting algorithms have two phases – an offline
learning phase and an online operating phase.
In the offline phase, the radio map database is created.
The localization area is divided into small cells [6], and
each cell is represented by a reference point. RSS values
from all APs within range are measured and stored in the
radio map, which is a collection of data vectors that can be
described as:
MjP jNj j,...,2,1),,...,( 1



, (1)
where Nj is the number of APs heard at the j-th reference
point, M is the number of reference points,

i are RSS
values, and parameter vector

j contains additional
information that can be used in the localization phase.
In the online phase the mobile device measures RSS
values from all APs within range. These values are
compared to data stored in the radio map database.
Algorithms used for comparison between RSS data from
the two phases and estimation of position of mobile device
can be divided into two main frameworks – deterministic
and probabilistic.
In the probabilistic (or statistical) framework the mobile
device’s position is modeled as a random vector [13]. The
location candidate

is chosen if its posterior probability is
the highest. The decision rule uses Bayes' theorem:
)(
)()(
)( SP
PSP
SP ii
i


, (2)
where posteriori probability P(

i|S) is a function of
likelihood P(S|

i), prior probability P(

i) and observed
evidence )()()( ii
i
PSPSP


, vector S represents the
observed RSS values during online phase and

i stands for
i-th location candidate.
The deterministic framework is based on optimizing the
similarity between the measurement and the fingerprints.
The position estimate is computed using the weighted
average:





M
i
i
M
i
ii
ω
ω
x
1
1
ˆ

, (3)
where ωi is a non-negative weighting factor. Weights can
be calculated as the reciprocal of the distance between
RSS vectors from online and offline phase. Usually the
Euclidian distance is used but different distance metrics
are also possible [14].
The estimator (3) which keeps the K largest weights and
sets the others to zero is called the WKNN (Weighted K-
Nearest Neighbor) method [7]. WKNN with all weights

i = 1 is called the KNN (K-Nearest Neighbor) method.
The simplest method, where K = 1, is called the NN
(Nearest Neighbor) method. In [6] it was found that
WKNN and KNN methods perform better than the NN
method, particularly when values of parameter K
are 3 or 4.
III. RANK BASED FINGERPRINTING
The main difference between conventional
fingerprinting algorithms and the proposed Rank Based
Fingerprinting (RBF) localization algorithm is the way in
which measured data in offline and online phases are
compared and used to estimate position. In classical
fingerprinting algorithms, vectors of RSS values measured
in online and offline phase are directly compared to each
other.
In the proposed algorithm (Fig. 1) the RSS values
measured in the online phase from different APs are first
sorted from strongest to weakest. Then ranks (1, 2, 3, …)
are assigned to APs based on their position in the sorted
vector. The sorted vector of APs detected in the online
phase is then compared to vectors stored in the radio map.
Rank vectors are created for vectors stored in the database.
Ranks are assigned based on the MAC (Media Access
Control) address of AP and the rank of the AP in online
phase. In case that one (or more) of the APs from the
online phase is not found in the database, the rank vector
created from the radio map is padded with 0, to achieve
the same length as the rank vector from the online phase.
Radio map
RSS Data
MAC address
Sort and comparison
Rank Vector
Rank vector
comparison
Estimate
position
Figure 1. Block diagram of proposed RBF algorithm
These rank vectors are then compared to the online
phase vector using one of the similarity measures
introduced in the next section. The K reference points with
smallest difference are used to calculate the estimated
position using the weighted average formula (3).
x
ˆ
IV. SIMILARITY MEASURES
In this section similarity measures used to compare
ranking vectors in RBF algorithm are introduced. In all
cases the online and offline RSS vectors are assumed to
have the same length.
A. Spearman distance
Spearman distance [15] is the square of Euclidean
distance between two rank vectors:
, (4)




n
k
kkS yxD
1
2

where xk is the rank of k-th element in vector X, yk is the
rank of k-th element in vector Y and n is the number of
elements in vectors X and Y.

2011 International Conference on Indoor Positioning and Indoor Navigation (IPIN), 21-23 September 2011, Guimarães, Portugal
B. Spearman’s footrule
Spearman’s footrule distance measures total element-
wise displacement between two permutations [16]. It is
similar to the Manhattan distance for quantitative
variables. Spearman’s footrule distance can be computed
as:



n
k
kkF yxD
1. (5)
C. Jaccard coefficient
The Jaccard coefficient is used to measure the similarity
of two sets of data. It is defined as the size (cardinality) of
the intersection of the data sets divided by the size of the
data sets [17]. It is a special case of the normalized
Hamming distance and can be computed using:

n
yx
C
n
k
kk
J



1. (6)
D. Hamming distance
Hamming distance is the number of disagreements
between two vectors. Hamming distance can also be used
for ordinal variables to measure disorder of elements in
two vectors [18]. In the RBF algorithm a weighted
Hamming distance was used to compute distance between
two rank vectors:
, (7)




n
k
kkkH yxD
1


where ωk denotes the weight assigned to the k-th element
of the rank vector.
E. Canberra distance
The Canberra distance is the sum of fraction differences
between two vectors. Each fraction difference is a value
between 0 and 1 [19]. If one of coordinates is zero, the
term become unity regardless the other values, thus the
distance will not be affected. A weighted version of
Canberra distance was used in the RBF algorithm:
k
n
kkk
kk
Cyx
yx
D







1. (8)
V. EXPERIMENTAL RESULTS
The experiment was carried out in Tietotalo building at
Tampere University of Technology. The area was covered
with 96 reference points. The average number of heard
APs per fingerprint was 29 and altogether 206 APs were
detected during data collection.
Measurements in the offline phase of the fingerprinting
algorithm were done with Nokia N900 mobile phone and
the data collecting software was implemented with Qt
Developer. The area where the test was performed, with
the positions of reference points, is shown in Fig. 2.
Figure 2. Localization area
Experimental measurements in the online phase were
done a month later with the same mobile phone Nokia
N900 and then a couple of weeks later with an Asus N63
laptop using WirelessMon software. Measured RSS data
were used to estimate the position of the mobile device
using fingerprinting algorithms. Measurements were done
at 43 points. Track of mobile devices in online phase is
shown on Fig. 2 as a black line.
In this scenario differences in localization accuracy are
caused by the change of device used in the online phase
and also by changes in environment. Results achieved in
this scenario using proposed RBF algorithm with different
similarity measures are shown in Fig. 3.
Nokia N900 Asus N63
0
5
10
15
20
25
Error [m]
Spearman distance
Spearman's footrule
Hamming distance
Jaccard coefficient
Canberra distance
Figure 3. Bars show mean error achieved using RBF and error bars
show the 5% and 95% quantiles Asterix show median error.
From results shown in Fig. 3 it can be seen that
Spearman’s footrule performs best in this real world
scenario. When Spearman’s footrule was used, median
error does not change, and mean error decreased by 1.5
meter when different devices were used in online and
offline phases. It is interesting to see that Asus does better
than Nokia, even though the Nokia was used to create the
radio map. This may be caused by changes of the
environment and also by hardware and software
equipment of used devices.
When best similarity measure in RBF algorithm was
found, performance of this algorithm can be compared to
NN and WKNN algorithms. For this comparison the same
data were used; in these algorithms the distance between
RSS vectors and weights were calculated using Euclidean
distance.
From results shown on Fig. 4 it can be seen that mean
error of proposed RBF algorithm outperforms commonly

2011 International Conference on Indoor Positioning and Indoor Navigation (IPIN), 21-23 September 2011, Guimarães, Portugal
used NN and WKNN algorithms. It is clear that position
error is less affected by change of the mobile device and
environment. From these results RBF algorithm seems to
be a great improvement, compared to NN and WKNN
algorithms.
[3] L. Zheng, W. Dehaene, G. Gielen, “A 3-Tier UWB-based indoor
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Nokia N900 Asus N63
0
10
20
30
40
Error [m]
RBF
WKNN
NN
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Figure 4. Comparison of RBF with NN and WKNN
Compared to WKNN, the mean error (bars on Fig. 4.)
of RBF algorithm is 50% lower when the same device was
used and 65% lower in case the devices in online and
offline phases were different. Note that RBF performs
better than NN and WKNN with every implemented
similarity measure.
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VI. CONCLUSION AND FUTURE WORK
We have described a novel RBF algorithm for indoor
localization. The main advantage of this algorithm is that
its performance is about the same for any receiver,
without the need of calibration of RSS values.
Experimental results show that proposed algorithm
achieves better accuracy than algorithms NN and WKNN.
The impact of different similarity measures used in
RBF algorithm was also investigated. Spearman’s footrule
seems to perform best among all implemented measures in
a real indoor environment. RBF in combination with any
of the described similarity measures performs better than
NN and WKNN algorithms.
In future more experimental tests will be done, and the
impact of AP placement and the number of APs on
localization accuracy will be investigated. The impact of
density of reference points used in offline phase of
algorithm to accuracy of proposed algorithm will be
another part of future research. Other similarity measures,
such as in Webber et al. [20], will also be studied.
[12] Z. Liu; J. Chen, “A New Sequence-Based Iterative Localization in
Wireless Sensor Networks,” International Conference on
Information Engineering and Computer Science ICIECS 2009.,
pp.1-4, Dec. 2009
[13] Tsung-Nan Lin; Po-Chiang Lin, “Performance comparison of
indoor positioning techniques based on location fingerprinting in
wireless networks,” International Conference Wireless Networks,
Communications and Mobile Computing 2005, Volume 2, pp.
1569- 1574, 2005
[14] J. Machaj, P. Brida, “Performance Comparison of Similarity
Measurements for Database Correlation Localization Method,”
3rd Asian conference on intelligent information and database
systems ACIIDS 2011, April 2011 – “in press”
[15] I. Contreras, “Emphasizing the rank positions in a distance-based
aggregation procedure,” Decision Support Systems, Volume 51,
Issue 1, pp. 240-245 April 2011
[16] R. Kumar, S. Vassilvitskii, “Generalized distances between
rankings, Proceedings of the 19th international conference on
World wide web,” April 2010
[17] J. Bank, B. Cole, “Calculating the Jaccard Similarity Coefficient
with Map Reduce for Entity Pairs in Wikipedia,”, Wikipedia
Similarity Team, December 2008
ACKNOWLEDGMENT
This work was partially supported by the Slovak
Research and Development Agency under contract No.
LPP-0126-09 and by the Slovak VEGA grant agency,
Project No. 1/0392/10. We thank Laura Wirola, née
Koski, and Toni Fadjukoff for assistance in the data
collection.
[18] A. Tarsitano, “Comparing the effectiveness of rank correlation
statistics,” Working Papers, Università della Calabria,
Dipartimento di Economia e Statistica, 2009.
[19] S.-H. Cha, “Comprehensive survey on distance/similarity
measures between probability density functions,” International
Journal of Mathematical Models and Methods in Applied Science,
vol. 1, no. 4, 2007
[20] W. Webber, A. Moffat, J. Zobel, “A similarity measure for
indefinite rankings,” ACM Transactions on Information Systems,
Volume 28, Issue 4, 38 pages, November 2010
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