Image Processing Reference
In-Depth Information
(a) Phase 1
(b) Phase 2
(c) Phase 3
FIGURE .
Phases of DLS algorithm. (From Reichenbach, F., Resource aware algorithms for exact localization in
wireless sensor networks, PhD thesis, University of Rostock, Rostock, Germany, December . With permission.)
relations between two communicating nodes can be transfered into a system of equations. Radial
relations are given by an ideal circular transmission range. For example, if two nodes with
r
m
establish a symmetric link, then both nodes are in range between and m. By adjustable
transmission ranges more constraints can be considered.
If angles are provided, angular relations can be found. In [DPG], optical techniques for angle
measurements are suggested. Regardless, which relation was used, all relations are sent to a central
node with sufficient resources. his high powered node estimates the node's position in a central con-
vex optimization process and send every position back to the specific node. his convex optimization
is very efficient and therefore very precise for large sensor networks with a high node density.
=
6.3.7 Iterative Methods
6.3.7.1 Sweeps
In [GBY
+
], Goldenberg et al. present an approach with so-called “Sweeps.” his algorithm is pro-
cessed iteratively, whereby sensor nodes calculate all their possible positions on basis of a trilateration.
As many positions as beacon triples exist are possible to determine. he “Sweeps” algorithm differs
in () nodes with exact one position estimate, () nodes with more than one position estimate, and
() nodes without a position. he third case occurs if less then three beacons are in range of a node.
Sweeps is arranged in different phases. First, only beacons provide a position to sensor nodes. Next,
in phase , sensor nodes collect information of neighboring sensor nodes and calculate all possible
trilaterations, respectively all estimated positions. At the end, one position can be determined.
6.3.7.2 Ad Hoc Positioning System
In the “ad hoc positioning system” initially beacons flood their positions into the network [NN,
NN]. On every sensor node, first minimum three distances are determined by a DV-hop tech-
nique (Section .), which are bases for a trilateration process. In [SRL], a refinement phase is
appendedtothealgorithm,inwhichinitialpositionestimatesaresendtoneighbors.hisinformation
is included in a second estimation that results in better precision.
6.3.7.3 Assumption-Based Coordinates
The “assumption-based coordinates” (ABC) algorithm starts the localization process with an initial
sensor node
S
, whose position is placed in the origin of a relative coordinate system
S
[SRB,
SRL]. In a next step, two neighboring nodes of
S
determine their distances to
S
,whichare
d
as
well as
d
and the distance between each other
d
. his allows estimating a first position relative to
(
;
)
