Algorithm for Nodes Localization in Wireless Ad-Hoc Networks Based on Cost Function

A new distributed algorithm is described in this paper for localizing sensor network nodes in Wireless Sensor Networks (WSN). The algorithm shares a common three-phase structure: (1) determine node-beacon distances, (2) build a cost function for every sensor node, and (3) compute the coordinate of the node. The coordinates of the sensor nodes are computed using either the Davidson-Fletcher-Powell QuasiNewton algorithm or the Direct Method. The algorithm is based on the capacity of the nodes to calculate the Time-of-Arrival (ToA) and Angle-of-Arrival (AoA) with their neighbors. The accuracy of the measurements rely on the use of Ultra Wide Band (UWB) technology. It has been shown that the properties of the UWB signal allow more accurate ToA measurements. In order to simulate the range measurement noise in ToA and AoA measurements, two independent random variables are introduced with two different variances (σT oA ,σAoA) for the ToA and AoA measurements. An extensive set of simulations is performed to assess the accuracy and performance of the algorithm. Also, we demonstrate its ability to localize the nodes in a large WSN.