Digital Signal Processing Reference
In-Depth Information
Fig. 4.4
Left
: Average squared error of the moving least squares approximation (with fixed sup-
port radius
h
) for increasing noise power illustrated for order
n
0
,
1
,
2. At low noise levels,
quadratic MLS is superior, while with increasing noise levels, linear and then constant MLS have
better performance.
Right
: Average squared error of the moving least squares approximation (with
fixed noise power of 4) for varying kernel widths shown for order
n
=
0
,
1
,
2. Clearly, an optimal
communication range
h
can be found for each approximation order
=
4 was observed.
At this noise level, quadratic MLS with kernel width or communication range of
95 m proved to be the best (cf. Fig.
4.4
) and these settings are further used for the
simulation results provided in the following sections.
For the real-world RSSI measurements a noise power of
σ
N
=
4.3.3 Distance-to-Contour Flooding
ˆ
A node is now classified as interior with respect to the threshold contour if
RSSI
i
≥
RSSI
contour
. By determining the distance of each node to the closest interior nodes,
it is possible to establish an estimate of the shortest distance to the contour. From
this distance one can then iteratively approximate the transmit power, as will be
explained in Sect.
4.3.4
.
A fast marching algorithm will be used which bears similarities to Dijkstra's
shortest path algorithm. However, instead of computing a multihop distance, a
straight line distance will be computed to the contour, which is possible when GPS
coordinates are available. First, the centralized algorithm based on a priority queue
is discussed. Next, an approach is presented to make it fully distributed.
4.3.3.1 Centralized Distance-to-Contour Computation
During the execution of the algorithm each node
N
i
stores its distance
d
i
to the
closest interior node, or footpoint
f
i
, inside the contour. The algorithm starts by
setting
d
i
←
0 and
f
i
←
x
i
for all interior nodes. The distance for all other nodes is
set to infinity (
d
i
←∞
0 are added to a priority queue, which
is sorted in increasing distance to contour order.
). The nodes with
d
i
=
