RO-SLAM method. An interesting article about RO-
SLAM is described in (J.L. Blanco, 2008).
The beacons or landmarks, which are shown in
Figure 1, are the characteristics of the map that pro-
vide a quantifiable measure of what has been the
movement of the system. For this purpose, it is possi-
ble to use a wide variety of sensors: lasers, cameras,
sonar, wireless sensor networks, etc.
The difference between SLAM and RO-SLAM is
based on the fact that, RO-SLAM solves this problem
considering that the information received by the sys-
tem is only the distance to the beacons. That is, the
system knows that it has a beacon at a distance fixed
but the direction is unknown. SLAM also knows the
direction in which the beacon is located. The RO-
SLAM scenario allows the use of simplified sensors:
less sophisticated and therefore less expensive sen-
sors.
A frequent and cheap way to implement a distance
sensor is based in the use of wireless communications.
There are many manufacturers that provide this kind
of sensors. Therefore, to make a localization based
on the power level of the RF signals (Received Sig-
nal Strength Intensity, RSSI), the first step is to have
a quantitative correlation between distance and power
level of a radio link. This essential first step has re-
quired a big percentage of the time spent on the devel-
opment of the work described in this paper. The suc-
cess of the localization technique designed is based
on the accuracy of this step.
3 PANORAMIC OF RSSI VS
DISTANCE MODELS
This section collects a summary of the most impor-
tant models presented in the literature that relates the
strength of the radio signal received in a wireless de-
vice and emitted by a transmitter and the distance be-
tween them.
Currently, the RSSI propagation models in wire-
less sensor networks (WSN) include the model of free
space, the bidirectional ground reflectance model and
the log-normal shadow model or log distance path
loss model (J. Xu, 2010).
The free space loss (FSL) measures the spread of
the power in free space without obstacles. If the dis-
tance (d) is measured in meters and the frequency (f)
is measured in hertz, the formula of the FSL could be:
FSL(dB) = 20log
10
d + 20log
10
f − 187.5 (1)
In practice, the relationship between distance and re-
ceived signal power is more complex than the above
expression. Actually, the received power will be the
sum of a series of signals coming from different di-
rections, due to reflections objects and obstacles that
partially block the signal. Thus, the received power
resulting may be higher or lower than the output when
space free.
The ground bidirectional reflectance model is very
accurate when used in urban environment (J. Xu,
2010) but can not be applied to the context of this
work due to the heights of the antennas (below 50 me-
ters).
Furthermore, the log-normal shadow model is a
more general propagation. It is suitable for both in-
door and outdoor communications. The model pro-
vides a number of parameters that can be configured
according to different environments (J. Xu, 2010).
The model is usually expressed as the following equa-
tion:
L(dB) = P
o
+ 10nlog
10
(
d
d
o
) + X
σ
(2)
Where L is the loss of power on the path, n is the path
loss exponent, d is the distance between transmitter
and receiver, X
σ
is a Gaussian random variable with
standard deviation σ and P
o
is the received power ref-
erenced in the distance d
o
.
Over the years there have been a large number
of models to predict the path loss in typical wire-
less environments as large urban cells, small urban
cells, and more recently in buildings. These models
are mainly based on empirical measurements at dif-
ferent distances for a given range of frequencies and
in a particular geographical area or building. Exam-
ples of these models are the model Okumura, Hata
model or model of COST 231 (H. Rábanos, 2006).
All these models are complex for their application in
the present work, therefore the simplified model of
the log-normal shadow model is chosen for the exper-
imentation.
This simplification is specified by Chipcon in (A.
Faheem, 2010). Chipcon is a transceivers manufac-
turer of the TelosB motes. The RSSI is given by the
following expression:
RSSI(dBm) = −10nlog
10
d + A (3)
Where n is the propagation exponent, d is the distance
from the transmitter measured in meters and A is the
strength of the received signal at a distance of one me-
ter. In this approach to the problem, RSSI and A pa-
rameters are known. In this way, n (4) can be cleared
and estimated as an average with each pair of (RSSI,
distance) collected in the experiment to find a plau-
sible parameter value. Then, the distance (5) can be
cleared in order to calculate its estimated value ac-
cording every RSSI value. Finally, it is interesting to
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