5. Beacon Positioning and Operations

We address the problem of placing a minimal number of beacons in a complex terrain in such a way that any arbitrary stationary or mobile node can locate itself within specified error and time limits. The starting point for our approach is the data-driven distance measurement, environment, and localization error models. These models are used to create the OFs for the three phases of our approach: (1) beacon placement, (2) beacon grouping for simultaneous activation, and (3) beacon scheduling. We prove that each of these three tasks is NP-complete and create heuristics and (integer) linear programming algorithms. In the first phase, we construct nonparametric statistical localization error models that capture the joint conditional probability of expected location error based on two properties: number of distance measurements and the third largest angle of all neighbors. The beacons are placed so that the location errors are minimized for a representative set of nodes. In the last two phases, we address the problem of which beacons, when, and how to broadcast acoustic signals, so that maximum number of unknown-location nodes can calculate their distance measurements as frequently as possible. We analyze the scalability of our approach and its dependency on parameters such as network connectivity and size and beacon density. Location discovery has received a great deal of research attention in wireless ad hoc community because of its role as an essential enabler required by other tasks such as routing and data fusion. A number of exceptionally creative and effective LD approaches have been demonstrated. A closely related problem is building and operating permanent or ad hoc Location Discovery Infrastructure (LDI), where the goal is to place a small number of beacons in such a way that any other node at an arbitrary location can accurately calculate its location. Surprisingly, this problem received rather little attention regardless of its apparent usefulness and technically challenging structure. The problem is challenging because it consists of three-layered NP-complete sub-problems and the statistical uncertainty of the distance measurements.