A beacon selection algorithm for bounded error location estimation in ad hoc networks

We consider the class of ad hoc networks, where a small percentage of the nodes are assumed to know their locations a priori and are denoted as reference nodes. Starting frorn the reference nodes, location information of other nodes are estimated in a hop by hop fashion. Beacon nodes are defined to be nodes that already have a location information (including the reference nodes). Using a two-dimensional cartesian coordinate system, we show that given a maximum of +/-epsilon error in the location of each of the beacon nodes and a maximum error of 6 in each of the measured ranges along either axes, the location of a node can be computed within an error bound of +/-[3 epsilon(1 + root 2-) + 2 delta] to +/- (3 epsilon + 2 delta) along one axis and within +/-[2 delta(1 + root 2) + 3 epsilon] to (3 epsilon + 2 delta) along its orthogonal axis, by using the beacon selection algorithm proposed in this paper