Date Added: Feb 2011
Collinear or near collinear placement of some sensors in a wireless sensor network causes the location estimates of nearby sensors to be sensitive to erroneous distance measurements which leads to large location estimation errors. These errors and the possible propagation of these errors to the entire network or a large portion of it, thereby causing larger estimation errors for some sensors' locations, is a major problem in localization. This phenomenon is well described in rigid graph theory, using the notion of "Flip ambiguity". This paper considers arbitrary sensor neighborhoods of two dimensional sensor networks and formulates an analytical expression for the probability of occurrence of the flip ambiguity.