Traditional network localization algorithms contain ranging and localization steps, which have systematic disadvantages. We propose an algorithm dubbed direct particle filter based distributed network localization (DiPNet). A node's location is directly estimated from the received signals, incorporating location uncertainty of neighboring nodes. The propagation effects on DiPNet become insignificant for dense networks, due to the massive-link collective physical layer processing. DiPNet achieves a near-optimal performance with low complexity, which is particularly attractive for realtime dense-network localization.
In this paper, we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly
We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero.