Communications and Network, 2013, 5, 37-42
doi:10.4236/cn.2013.52B007 Published Online May 2013 (http://www.scirp.org/journal/cn)
RSSI-based Algorithm for Indoor Localization
Xiuyan Zhu, Yuan Feng*
College of Information Science and Engineering, Ocean University of China, Qingdao, China
Received 2013
ABSTRACT
Wireless node localization is one of the key technologies for wireless sensor networks. Outdoor localization can use
GPS, AGPS (Assisted Global Positioning System) [6], but in buildings like supermarkets and underground parking, the
accuracy of GPS and even AGPS will be greatly reduced. Since Indoor localization requests higher accuracy, using
GPS or AGPS for indoor localization is not feasible in the current view. RSSI-based trilateral localization algorithm,
due to its low cost, no additional hardware support, and easy-understanding, it becomes the mainstream localization
algorithm in wireless sensor networks. With the development of wireless sensor networks and smart devices, the num-
ber of WIFI access point in these buildings is increasing, as long as a mobile smart device can detect three or three more
known WIFI hotspots’ positions, it would be relatively easy to realize self-localization (Usually WIFI access points
locations are fixed). The key problem is that the RSSI value is relatively vulnerable to the influence of the physical en-
vironment, causing large calculation error in RSSI-based localization algorithm. The paper proposes an improved
RSSI-based algorithm, the experimental results show that compared with original RSSI-based localization algorithms
the algorithm improves the localization accuracy and reduces the deviation.
Keywords: Indoor Localization Algorithm; RSSI-based; WIFI Access Point; Smart Phones
1. Introduction
More than 80% information is related to spatial location,
and modern people spend about 80% - 90% time of their
whole life indoors. Now along with the popularization of
information and communication technology, people’s
demands for indoor location information are growing. In
some public places, such as shopping malls, airports,
exhibition halls, office buildings, warehouses, under-
ground parking, prisons, military training bases, people
need precise location information. Precise indoor loca-
tion information can be used to achieve efficient man-
agement of the available space and inventory substances;
can help police, firefighters, soldiers, medical staff to
complete specific tasks; smart spaces and pervasive
computing are also inseparable from the location-based
services. So currently, indoor localization is a hot re-
search with broad application prospects [9].
Compared with outdoor localization, the difficulty of
indoor localization lies in that indoor maps pay more
attention to small areas, large-scale, high precision and
subtly display of the internal elements [7].
Along with the rapid development of wireless net-
works and smart phones, the number of WIFI access
points increase dramatically and most WIFI access
points’ locations are fixed. This phenomenon suggests a
new direction for indoor localization research in wireless
sensor network.
Existing wireless localization algorithms require either
special hardware support or complex computing, which
consuming valuable battery resources greatly, especially
comes to smart phones or sensors. The contribution of
this paper is that it proposed a new algorithm，which
increase the indoor localization accuracy without any
additional hardware support or increasing the computa-
tional complexity.
2. Related Work
2.1. Indoor Localization Technologies
There are many wireless localization technologies and
solutions. The commonly used localization techniques
include infrared, ultrasonic, radio frequency signal, Blue-
tooth, and Ultra-Wideband, WIFI, etc.[8], but they are
not suitable for indoor localization. Infrared is only suit-
able for short-distance transmission, and could easily be
influenced by fluorescent lamp or the light in the room,
there are limitations on the localization accuracy; ultra-
sonic, Bluetooth and Ultra-Wideband require special
equipment, the cost is too high, hence they are not widely
used; RF signal does not have communication capability,
and is not easy to be integrated into other systems.
At present, more and more indoor WIFI access points
*Corresponding author.

X. Y. ZHU, Y. Feng
38
are open and free. The most widely used localization
technology is using WIFI.
2.2. Localization Algorithms
Wireless localization algorithms can be roughly divided
into two categories[2], Range-based and Range-free lo-
calization algorithms.
Range-based localization algorithms mainly include
RSSI-based trilateral localization algorithm, arrival angle
algorithm (AOA), arrival time algorithm (TOA) and time
difference of arrival (TDOA) algorithm. TOA requires
precise clock synchronization; TDOA node is equipped
with ultrasonic transmitters and receivers; AOA needs
antenna array or microphone arrays. These three algo-
rithms’ localization accuracy is high, however with high
hardware requirements.
Range-free localization algorithm mainly includes
centroid algorithm, DV-hop algorithm, MDS-MAP algo-
rithm and convex programming. Range-free algorithms
mainly use the geometric relationship between neighbor-
ing nodes to estimate localization. They have low hard-
ware requirements, but the localization accuracy is too
low for indoor environment.
Because of its simple, easy-understanding and low
cost, RSSI-based trilateral localization algorithm has a
wide range of applications.
3. Trilateral Localization Algorithm
3.1. Wireless Signal Propagation Loss Models
In this paper we use the mainstream logarithmic distance
path loss model, i.e., log model. The propagation model
points out that whether in indoor or outdoor channel, the
average received signal power decreases with the loga-
rithm of distance. This model has been widely used. For
any T-R distance, the path loss is expressed as:
 
0
1, 2,...,
i
id
LdPi
d




η

n
(1)
or


010
0
10log(1, 2,...,)
i
d
PL dBPL din
d


 


(2)
In the above formula, 0 represents near earth refer-
ence distance,
d


0
PL d is the signal strength at distance
0 and d

is the signal attenuation factor and its value
is between 2 to 6 in different environments.
3.2. Trilateral Localization
Assume there are n anchor nodes, and the location of the
unknown node is (, )
x
y, '
i is the estimated distance
between the unknown node and the anchor node
dith
(, )
ii
x
y obtained by using the log-model and repre-
sents the real distance. Then
i
d
'22
00
()( )(1,2,...
ii i
dxxyyi )n (3)
The difference between the real distance and the esti-
mated distance is expressed as '
iii
dd  . Because of
inevitable error, i

cannot be zero, the solution of ac-
quiring the best estimated location is to use the least
squares algorithm to make 2
1
n
i
i



minimum.
From (3) we can get n formulas as follows:

2222 2
0000
22
(1,2,...)
iiii i
x
ydxxyyx y
in
 
 (4)
Use the prior n-1 formulas minus the formula
respectively; we can get n-1 new formulas:
nth
222 22
00
2( ) 2( )
innin
in i
i
n
yx ydd
xx xyyy
x 

2
0
(5)
Let ;
222 22 2
11 1
222222
22 2
222222
11 1
nn n
nnn
nnnnnn
B
xyxydd
xyxydd
xyxydd
 











0
X
x
y



;




11
22
11
22(
22(
22(
nn
nn
nnnn
A
xx yy
xx yy
)
)
)
x
xyy











,
then we obtain the following equation:
A
Xb (6)
Usually i in b is unknown, but i composed of
can be estimated by the model mentioned before, so
d' d
'
b
2
1
n
i
i
min



means '
2
AXmi bn, then the resolution of
'
X is as follows:
'1
()
TT
XA '
A
bA   (7)
The more beacon nodes there are, the higher localiza-
tion accuracy we get, but the greater the cost. In real
cases, three anchor nodes are enough to locate an un-
known node, so we take n = 3. Figure 1 shows the trilat-
eral localization algorithm.
4. The Improved Algorithm
In this paper, a new algorithm is proposed through com-
bining the original RSSI-based localization algorithm
and signal propagation characteristics mentioned in
[1].The experimental results confirmed that the proposed
algorithm does improve the localization accuracy.

X. Y. ZHU, Y. Feng
39
4.1. Algorithm Idea
In the original RSSI-based localization algorithm, when
measuring the actual RSSI values of the beacon nodes,
the error caused by the obstacles (i.e., when the device
holder’s back towards the WIFI node, the device holder
is the obstacle) or the antenna direction will be persis-
tently substituted into the formula involved in the opera-
tion, the error becomes greater with the accumulation.
This is one of the main reasons of the big error in
RSSI-based localization.
[1] proposes that when a device holder stands with his
back towards the WIFI access point, a sharp decline of
the WIFI signal appears due to the blocking of body. In
the paper, mobile device owners do 6
s
 uniform mo-
tion while collecting data once per second and one revo-
lution takes one minute. But in reality, this cannot be
done in all circumstances. So we use built-in gyro sensor
in smart phones to collect intensity value of the gyro-
scope while collecting WIFI signal. The rotated angle
can be obtained by calculating the gyro sensor values, so
that even if our rotation is non-uniform motion, the RSSI
value and the rotated angle can be recorded within a
shorter time. The observed signal strength profiles with
user rotation are shown in Figures 2-4:
0
1
2
3
02
3
1
(a) (b)
Figure 1. Trilateration. (a) Measuring distance to 3 anchor
nodes; (b) Ranging circles.
Figure 2. Data from different phones.
Figure 3. Data from different genders.
Figure 4. Data from different WIFI Aps.

X. Y. ZHU, Y. Feng
40
Figure 2 shows that the signal profile displays a clear
low signal artifact when a user holds different phones. In
Figure 3, we repeat the above experiments using differ-
ent persons, with varying heights and weights. The same
artifact consistently appears. In Figure 4, with different
APs, the low signal artifact still comes across clearly in
measurement results. This demonstrates that the low sig-
nal effect appears stably when the device holder’s back
faces the WIFI AP, the RSSI values will decline. Using
gyroscope saves time, breaks the restrictions of the uni-
form motion, maintains the accuracy simultaneously (the
average error is 5°to 15°).
In most cases, when the device holder faces the WIFI
access point, the WIFI signal attenuation is minimal. If
we can find the direction of facing the WIFI access point
and use the RSSI value on this direction as the trilateral
localization input, then the accuracy of the subsequent
calculations to obtain the position will increase. [1,4,5]
have proposed algorithms of looking for WIFI direction.
[1] uses sliding window on the RSSI data, while [4] and
[5] use RSSI gradient map. Finding WIFI access points
make people get faster data transmission rate by shorten-
ing the distance to WIFI point, it can also be applied to
rescue tasks. Here we combine it with original trilateral
localization algorithm to get higher localization accuracy.
It is a simple calculation algorithm without requiring any
additional hardware support. Because gradient algorithm
is more complex than the sliding window algorithm and
for mobile devices the battery resource is limited, we
decide to use the former.
Let the mobile device holder spins around to collect
tetrad

123
j
jjj
A
ngles RSSIRSSIRSSI of one circle.
j
A
ngles thj stands for therotation angle and

1, 2, 3;1, 2,...
ij
RSSI ijn
represents the RSSI value of the WIFI
access point. Use the sliding window to process the col-
lected data to obtain the facing angle
thjthi

. In order not to
increase the complexity of the algorithm, we take the
average of the RSSI values in the interval






 
as the input of the trilateral local-
ization algorithm.
1
1
n
ii
j
ij
AveRSSI RSSI
n
Angles






 

 (8)
The angle error calculated is between .
(5~ 15)


To reduce the error as much as possible, we take β =
15.
Using formula (8) we can obtain
i
A
veRSSI . Respec-
tively, substitute the three values into the log model and
get the distances of the mobile phone to the three WIFI
APs. Then use the least square algorithm mentioned in
section 3 to get the phone’s position. The experimental
results prove that this algorithm can obtain higher accu-
racy and less error than the original trilateral localization
algorithm without any additional hardware support.
4.2. Experimental Environment Parameter
Fitting
The signal propagation is susceptible to the influence of
environmental factors, such that under different circum-
stances, the degree of signal attenuation differs [3]. We
reduce the location deviation caused by environmental
factors by fitting out the initial model parameters com-
plied with the current environment.
In the experiment, we took (m/km) and col-
lected 20 groups of
01d


;1, 2,...20 ij
RSSIij 
(1, 2
1, 2,...10
,...10)
at
10 different distances i
di

from three routers
respectively. ij represents the RSSI value
at the
RSSI thi
th
i

location, and

i
d PL
i
d stands for average signal strength at distance .

20
1
(1, 2,10;1, 2,20)
iij
j
PL dRSSI
ij


 
 (9)

PL d

Let 0 X




;
10 1
10 2
10 10
110log()
110log()
110log()
d
d
Z
d










And



1
2
10
PL d
PL d
Y
PL d










)
, then we can obtain the matrix
equation (10) as follows:
0
Z (1YXd

 (10)
The problem of finding the initial value


0
PL d and
attenuation factor

that applies to the current envi-
ronment turns into computing the value of X that satisfy
the formula (11), to minimize that the sum of the squares
of the difference between the calculated function curve
and the observed value, we get the following expressed
as:
 



1
1
22
0
0
10 10
2
110 log()
110log()
,
110 log()
PL d
d
min dPL d
PL d
PL d
dPL d
min ZX Y
X













 
 



 

 
(11)

X. Y. ZHU, Y. Feng 41
The solution to the formula (11) is1 ()
TT
X
AA Ab

.
Put X into equation (2) to gain the model that adjusts to
the current environment.
Using the above algorithm, the initial parameters for
the experimental environment we get is shown in the
following Table 1.
5. Algorithm Evaluation
5.1. Establish the Coordinate System
The size of the laboratory is about . Figure 5
shows the layout of the laboratory. There are three wire-
less routings deployed at three non-linear different places.
Take the east as the positive direction of the x-axis, and
the west-north of the laboratory as the origin.
2
8*7 m()
5.2. Experiment Results
In Table 2, AFT which represents our algorithm, means
AP Faced Trilateral. It shows the statistics positioning
result of traditional trilateral and AFT, including the av-
erage positioning deviations and positioning deviations
under the best and the worst circumstances.
Figure 6 shows the comparison of the positions calcu-
lated by using the proposed algorithm and the original
algorithm respectively. It can be seen that the computed
positions of the improved algorithm are distributed in a
circle with a radius of 1m, (3.6, -3.3) as the origin, and
the computed locations of the original algorithm are
more dispersed.
Figure 7 shows the error comparison that obtained in
the 20 tests between the two algorithms. It can be seen
that in the vast majority of cases, the improved algorithm
gained the higher accuracy than the original algorithm,
and only in a particular case, the presence of the multi-
path effects in signal propagation, making the algorithm
failed.
Table 1. The fitting arguments for the attenuation model.
Environment


0
PL d

LAB 44 3.6
Figure 5. Experiment environment topology.
Table 2. Positioning statistics.
Algorithms AFT Trilateral
Minimum deviation 0.2358 0.3528
Maximum deviation 1.5769 2.9730
Average deviation 0.8562 1.4235
Variance 0.2374 0.7808
Figure 6. The location of the unknow n node c omputed by these two algorithms.
Figure 7. Comparison of the computed deviation of the these two algorithms.

X. Y. ZHU, Y. Feng
42
6. Conclusions
Although the experiment results show that the proposed
algorithm in this paper raised the localization accuracy
without increasing the complexity and cost, but the algo-
rithm is still defective. First of all, people can only local-
ize themselves where at least there are three WIFI access
points around; second, the frequency of mining data can
only adopt the minimum value between the gyroscope
sampling rate and WIFI scan rate to ensure not collect
useless data. Gyroscope is a short-time precision instru-
ment, so the gyro accuracy cannot be fully utilized and
cannot get more intensive WIFI access points’ data. It
will be the further research direction, and if these two
problems can be solved, the indoor localization accuracy
can be further improved.
7. Acknowledgements
This research is partially supported by National Natural
Science Foundation of China under Grant No. 60933011
and 61003238.
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