Image Processing Reference
In-Depth Information
S
,whichis
S
(
d
;
)
. Assuming that the square root of
y
is positive, the second node's position is
;
√
d
d
+
d
+
d
given to
S
S
.heresultingsystemofequationscanbeeasilysolved.All
remaining sensor nodes determine their own position estimate iteratively by trilateration until the
wholenetworkiscovered.Iflaterabsolutecoordinatesareknown,thentheserelativecoordinatescan
be transformed in an absolute coordinate system, which requires additional computation overhead.
Similar algorithms are suggested in [CHH,PBDT].
(
−
(
x
))
d
6.3.8 Pattern Matching Techniques
The propagation character of electromagnetic waves in a static environment with constant beacon
positions is subject to a specific signature. hisefect is basis for pattern matching techniques, whereas
signal characteristics are measured at many points in the room. This data is stored in a so-called
signal map. Signal maps, for example, consist of many RSSI at different coordinates. Every sensor
node initially saves one signal map, which is after deployment basis for a comparison algorithm.
In detail, sensor nodes measure RSSI at the location, where they were deployed. Then, measured
valuesarecomparedwithvaluesinthesignalmap,whereasthebestandthusmostprobablematch
gives a position estimate. his method is also known as “pattern recognition” or “fingerprinting” and
developed by Bahl and Padmanabhan [BP].
6.4 Conclusions
Due to the strong limitations in sensor networks (e.g., very small form factor, limited capacity of
energy), an efficient localization method requires small communication overhead and energy-aware
algorithms to meet the conditions. In practice, a precise localization is impeded additionally by faulty
input values caused by measurements of the environment. Supplementally, underlying ideal models
lead in reality to distorted data as can be seen by the distance estimation based on circular signal
attenuation.
The localization error generally fluctuates depending on the specifics of the selected localization
algorithm. But, the precision of the localization is significantly affected by the calibration of the sys-
tem,e.g.,theadjustedtransmissionpowerofthetransceiverortheratiobetweenbeaconsandsensor
nodes.
Faulty or heavily unsteady input data lead inevitably to an increasing localization error. Espe-
cially, classical localization algorithms (trilateration, triangulation) or pattern matching are very
vulnerable whereas proximity-based algorithms react more stably. In contrast, iterative methods
and optimization methods behave more robust in systems with a high node density or with lots of
measured data. Due to the redundant data, sensor nodes estimate positions optimally by using more
information than needed. However, the resource requirements increase noticably in these networks.
Thus, choosing a localization algorithm usually depends on a lot of constraints imposed by the
specific application.
References
[BCKM] Bill, R., Cap, C., Kofahl, M., and Mundt, T.: Indoor and outdoor positioning in mobile
environments, a review and some investigations on WLAN positioning.
Geographic Infor-
mation Sciences
(), -.
[BHE]
Bulusu, N., Heidemann, J., and Estrin, D.: Adaptive beacon placement. In:
st
International Conference on Distributed Computing Systems
, , IEEE Computer Society,
Washington, DC, pp. -.
