Triangle Extension: Efficient Localizability Detection in Wireless Sensor Networks

Abstract

Determining whether nodes can be localized, called localizability detection, is essential for wireless sensor networks (WSNs). This step is required for localizing nodes, achieving low-cost deployments, and identifying prerequisites in location-based applications. Centralized graph algorithms are inapplicable to a resource-limited WSN because of their high computation and communication costs, whereas distributed approaches may miss a large number of theoretically localizable nodes in a resource-limited WSN. In this paper, we propose an efficient and effective distributed approach in order to address this problem. Furthermore, we prove the correctness of our algorithm and analyze the reasons our algorithm can find more localizable nodes while requiring fewer known location nodes than existing algorithms, under the same network configurations. The time complexity of our algorithm is linear with respect to the number of nodes in a network. We conduct both simulations and real-world WSN experiments to evaluate our algorithm under various network settings. The results show that our algorithm significantly outperforms the existing algorithms in terms of both the latency and the accuracy of localizability detection.

ProLo: Localization via Projection for Three-Dimensional Mobile Underwater Sensor Networks

“…The nodes then construct a 2D globally rigid graph on the beacon plane in a distributed manner using only the information of neighbors. Although it also uses TE, this globally rigid graph construction process is different from that in our previous scheme [16], in that an MUWSN is three-dimensional. To construct a globally rigid graph, the sensor nodes should first calculate the projections of the distances between themselves.…”

“…The reason is that the localizability of a node in a graph is closely related to the rigidity property of the graph, as having been proved in previous work [11,12,13,14]. Specifically, in double-struckE2, the global rigidity can be used to determine the node localizability in a graph [15,16]. Therefore, in this paper, we still employ the concept of global rigidity to ensure the node localizability, but the problem involves a graph in the three-dimensional space instead of a graph on a two-dimensional plane.…”

“…Our previous study [16] has shown that the nodes in a graph in double-struckE2 are localizable, if the graph satisfies the following three conditions: (1) It is globally rigid. (2) It contains at least three beacons that are non-collinear.…”

“…It is feasible to project the coordinate vectors of the underwater sensors onto the beacon plane and obtain a new two-dimensional graph. The global rigidity of the projected graph on the two-dimensional plane can be constructed using our previous triangle extension approach (TE) [16]. The simplified process of constructing a globally rigid graph for a MUWSN is presented as follows.…”

“…The construction of the globally rigid graph in localization is a one-time operation performed only at initialization. The complexity of constructing the globally rigid graph is O(n) using TE [16]. The complexity of the localization part is O(m2), where m is the number of direct communication neighbors.…”