wireless ad hoc networking

262 Wireless Ad Hoc Networking
9.2.2.2 Smallest Polygon
The idea of smallest polygon 10 is similar to NNSS-AVG. The difference
between the NNSS-AVG and the smallest polygon is that the NNSS-AVG
focuses on the signal domain, but the smallest polygon focuses on the
space domain. After estimating some candidate locations via certain methods
(like the smallest Euclidean distance), the NNSS-AVG makes various
polygons from the candidate locations and then selects a smallest polygon
and obtains the location of the MU from the centroid of the smallest
polygon. Figure 9.6 assumes that the candidate locations A, B, C, and D are
selected by the similar RSS (i.e., smaller Euclidean distance), and the candidate
locations form the variant triangles, △ABC, △ABD, △BCD, and △ACD.
The smallest polygon method selects the triangle △BCD with the smallest
area and estimates the centroid of △BCD to be the location of the MU.
In addition, the approximate point-in-triangulation (APIT) 11 is a localization
algorithm applied in wireless sensor network. Figure 9.7 illustrates
how the APIT algorithm locates a node through various triangles that are
formed by the anchors. These anchors are a small part of sensing nodes
A
D
C
B
Figure 9.6 The candidate locations A, B, C, and D form variant triangles. △BCD
is the smallest area and the centroid of △BCD is the estimated location.
Figure 9.7
An overview of APIT algorithm.