A distributive algorithm for WLAN localization

In this paper we propose a novel distributive algorithm for WLAN localization in which some nodes know their positions and others determine their position by measuring distances to these known nodes and neighboring nodes. Localization is a process by which physical positions of the nodes are determined. Localization where positions are reconstructed given measured distances is a non-convex optimization problem. Recently various researchers have analyzed the use of a convex semidefinite programming (SDP) for localization problems by applying some relaxations to an original problem. Although an original problem relaxed to convex SDP form can usually produce highly accurate results there are two problems associated with relaxed SDP optimization i.e. if a network is not universally rigid then a high rank solution with large estimation errors could be generated. Secondly SDP based optimizations are computationally demanding. Here we have proposed a novel algorithm that circumvents both problems. Number of nodes within a WLAN environment could vary from no-node to hundreds. For this dynamic environment each node must be able to measure distances between at least three known nodes for a 2-D localization, with this condition resultant trilateral network will always be universally rigid. Furthermore to reduce computational complexity for a network containing hundreds of nodes a network is subdivided into smaller subnets based on geographical positions and mobility. A subnet containing mobile nodes is more frequently updated for position estimations compared to subnets containing stationary nodes. This reduces computation complexity as only nodes classified as mobile are frequently localized compared to nodes classified as stationary. This novel distributive algorithm is adaptable to the diverse node distributions and there mobility levels within the WLAN environments and results in an accurate computationally efficient heuristic for localization. Finally by considering an ex- - ample the performance of the proposed algorithm is evaluated.