The Expected Uncertainty of Range Free Localization Protocols in Sensor Networks

We consider three range-free localization protocols for sensor networks and analyze their accuracy in terms of the expected area of uncertainty of position per sensor. Assuming a small set of anchor nodes that know their position and broadcast it, we consider at first the simple Intersection protocol. In this protocol a sensor assumes its position is within the part of the plane that is covered by all the broadcasts it can receive. This protocol was also analyzed in [10], but our result contrast theirs. We then extend this protocol by assuming every sensor is preloaded with the entire arrangement of anchors before being deployed. We show that in this case the same expected uncertainty can be achieved with 1/2 the anchor nodes. Finally we propose an approximation for the arrangement based protocol which does not require any preliminary steps and prove that its accuracy converges to that of the arrangement protocol with high probability as the number of anchors increases.