values. For power level 2, the algorithm assumes the
tolerance ρ (Sec. 2.2) of 8 units on either side which
means that the tracking point is turned into a segment
(range) from 54 to 70. This ranking gets us nowhere,
because all the ranks become zero in this metric.
For power level 3, we again see a single RSS entry
for the same Peg 13. The case is similar to the previ-
ous level (not surprisingly, all locations have samples
with entries for Peg 13 and power level 3) and, fol-
lowing the iteration, the ranks still remain at all ze-
ros. For iteration 4, there are two entries: 73 and 83,
for Pegs 12 and 13, respectively. The coordinates are
listed in the increasing order of Peg numbers, so their
interpretation as dimensions is unambiguous.
Still, all locations include entries for the two Pegs
(so they all still remain in the game) with the list of
points:
1 < 70 67> < 69 67> <81 65> <77 66> <77 88>
2 < 68 72> < 70 79>
3 < 68 74> < 98 101>
4 < 70 81> < 78 91>
5 < 78 80> < 98 109> <70 84> <69 76> <70 89>
6 < 70 81> < 76 70> <91 98> <78 85> <80 91>
7 <119 130> <108 120> <70 76> <84 103> <75 78>
8 < 76 81>
9 < 68 59> < 73 92>
10 < 73 69> < 81 81>
11 < 86 93> < 77 90> <81 85> <67 81>
This time the points are two-dimensional, so the hulls
amount to polygons. The tolerance ρ for power level
4 is 7, so we are looking at distances between the seg-
ment (73 + t,83+ t), −7 ≤ t ≤ 7 and the polygons
built of the above sets of points. This brings in the
non-trivial ranks: 5→1.0, 6→1.0, 11→1.0, 7→1.01,
4→1.6, 1→1.7, 9→2.4, 3→3.5, 8→3.74, 2→6.48,
10→7.48.
Power level 5 is the first non-degenerate case with
all three coordinates present. The Pegs with the three
largest RSS readings are 7, 12, 13 and the tracking
point is (83, 85, 96). This time, the list of locations
with samples matching all three Pegs at power level
5 consists of 5, 6, 7, 8, 9, 10, 11, so these are the
locations carried over to the next iteration, their new
ranks being: 7→1.11, 11→1.71, 5→1.73, 8→4.72,
10→8.48, 6→10.27, 9→14.28. This set remains un-
changed through the remaining two iterations, how-
ever, their ranks change with the final values (af-
ter iteration 7) being: 5→5.81, 11→8.0, 7→10.1,
10→10.02, 8→12.97, 6→33.04, 9→33.06. These
(badness) values are transformed into the follow-
ing (goodness) percentages: 5→19, 11→17, 10→16,
7→15, 8→14, 6→8, 9→8. The estimation does not
look extremely reliable, but the top candidate has
been guessed correctly.
A meaningful, quantified expression of the results
from our experiments is difficult, mostly because the
location tracking problem has been defined in qual-
itative terms: to have a satisfactory solution sepa-
rating named locations (potentially of various sizes
and shapes), with honest acceptance of failures in
those cases where the environment is predictably un-
friendly. This is in some contrast to our previous
work (Haque et al., 2009) where the problem was de-
fined as estimating Cartesian coordinates of points in
2-space (so one could say by how far one missed the
target). In the present case, the success rate depends
on where the Tag is positioned within a givenlocation,
and it isn’t easy to express numerically how much
more important (or relevant) some of those spots are
than the others. For example, location 7 in our test
setup is poorly covered by Pegs, so estimates taken
from the bottom half of that location tend to be mostly
useless, being confused with locations 11, 5, and 10.
This is hardly unexpected. On the other hand, 95% of
attempts from location 6 succeed perfectly, with the
rate approaching 100% in the NE section, with only
slight deterioration as one gets closer to the bound-
aries. Notably, even location 2, which has no specific
Peg, is correctly identified (87% success rate in the
central area), although the results tend to be worse as
we move closer to the neighboring locations. This
is because the distribution of nearby Pegs provides
enough diversity and balance in their RSS readings to
transform those readings into meaningful (and mostly
correct) location ranks. As the success rates depend
on the position within the monitored locations, they
have to be weighted by the distribution of Tags in a
practical deployment (how likely the tracked person
or object is to be positioned close to the central area,
as opposed to its boundary) to be meaningful. Such
weights can be arrived at by inspecting room (apart-
ment) layouts, i.e., the arrangement of furniture, or
even suggesting layouts that will increase the likeli-
hood of successful positioning. Owing to the some-
what accidental distribution of Pegs in our test net-
work (not quite inspired by the location tracking prob-
lem) one can be sure that a better crafted design will
result in more reliable estimates.
4 CONCLUSIONS
We have presented a practical location tracking algo-
rithm to accompany a WSN deployable in an institu-
tion where people or objects need to be tracked with
the accuracy of rooms or apartments. The known
problem of poor representation of locations by RSS
readings is addressed in our solution in two ways.
First, by diversifying the transmit power levels of
packets in location bursts we attempt to emulate pas-