unknowns (where n must be > p + 1).
The possible order p of the polynomial
function depends on the number of
available signal strength observations n
and the desired level of approximation.
From previously conducted tests (see
Retscher and Fu, 2007a) it could be
seen that the mean of the residuals is
larger using the logarithmic model than
for the simple polynomial fit for the
signal strength to distance conversion
in trilateration. For this reason, the
simple polynomial model provides
a more accurate fit to the distance
data as the logarithmic model.
If several RFID tags are located in thesurrounding environment the current
position of the RFID reader can be
obtained using trilateration. Then the
deduced distances to at least three
RFID tags are needed to calculate a 2-D
position fix with intersection and an
unknown scale factor which takes the
difference between the deduced ranges
to the RFID tags and the reference point
system into account. If more than three
distances are available, the position fix
can be calculated using a least squares
adjustment (see Retscher and Fu, 2008).
Field test setups and results
For testing our approach the path from a
public transport stop (i.e., underground
station
‘Karlsplatz’) to an
University building
was selected (see
Figure 1). Three
RFID tags were
installed at the
entrance of the
underground
station ‘Karlsplatz’
(indoor area).
Along a road
between the
underground
station and the
university building
(‘TU Vienna’ in
Figure 1; outdoor area) seven tags were
installed on buildings
along the way.
Additionally, three
tags were installed
at the building’s
entrance (indoor area).
Each circle indicates
a different cell.
In the experiment
cell-based positioning
has been applied in
outdoor areas as an
alternative to GPS
positioning. As the
accuracy of cell-based
positioning generally
depends on the size
of the distinguishable
cells, the achievable positioning
accuracies might not be sufficient for
indoor areas.
Ranges from the
RFID tags location
have been achieved
up to around 20 m.
In the indoor area
mostly higher
positioning
accuracies are
required. Therefore
several RFID
tags have been
installed in the
transition zones
between outdoor
to indoor to be
able to locate the
user with a higher precision.
For a conversion of the measured
signal strength into a range a so called
calibration was carried out in the
indoor environments in order to get the
coefficients of the polynomial model
described in equation (5). Figure 2
shows the installation of the tags in the
entrance of the underground station
‘Karlsplatz’ as an example. For the
conversion of the signal strength into a
range a calibration along three baselines
from the RFID tags has been performed
to obtain calibration parameters of a
characteristic curve for each line.
Figure 3 shows the polynomial model
approximation with an order of p = 3
and their resulting coefficients for one
of the three baselines in the underground
station ‘Karlsplatz’. For each baseline different coefficients are obtained,
because the signal strengths of different
tags were influenced differently by
the objects in their surroundings. The
mean values of the residuals of all the
polynomial approximations are nearly
zero and their standard deviations
are also almost zero. This means that
a good approximation with the used
polynomial model is achieved. The trend
of the polynomial fit is very similar. The
measurements have been performed at
night with no people walking around.
Two sorts of test were carried out in
total. In the first test the signal strength
measurements were performed static
over a time span of around one minute on
the same points used in the calibration,
since we know the true location of
these points. In the second test the user
was walking continuously inside the
test area either from the entrance to the
center of the test area or vice versa.
The positioning results of the static test
for the entrance of the underground station
‘Karlsplatz’ are shown in Figure 4. Table
1 shows the deviations in the X- and
Y-coordinates (dX and dY) from their true
location and the radial deviation dr for all
test points. In average the radial deviation
is only 0.32 m with a standard deviation of
± 0.40 m. The maximum deviation of one
point was 0.34 m in the X-coordinates and
-1.44 m in the Y-coordinates. This pointcan be considered
as an outlier as the
deviations of the
other points are
much smaller.w
In the second
kinematic test the
reader was carried
from the middle
of the entrance of
the underground
station ‘Karlsplatz’
to the middle of
tag 50 and 51
(from right to left
in Figure 2) over a
distance of around
14 m. Unlike the measurements in the
first test, in this test every point was
measured only for a few seconds. Figures
5 shows the positioning results. It can be
seen that the trend of the trajectory can
be correctly determined. The positioning
accuracy was in the range of ± 2 to 3 m.
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