Complexity and Error Propagation of Localization Using Interferometric Ranging

An interferometric ranging technique has been recently proposed as a possible way to localize ad hoc and sensor networks. Compared to the more common techniques such as received signal strength, time of arrival, and angle of arrival ranging, interferometric ranging has the advantage that the measurement could be highly precise. However, localization using interferometric ranging is difficult as it requires a large number of measurement readings. In this paper, we provide a formal proof of this difficulty in terms of algorithmic complexity. Furthermore, we propose an iterative algorithm that calculates node locations from a set of seeding anchors, gradually building a more global localization solution. Compared to previous localization algorithms, which treat localization as a global optimization problem, the iterative algorithm is a distributed algorithm that is simple to implement in larger networks. More importantly, the iterative algorithm allows us to study the error propagation behavior of localization using interferometric ranging. Using simulations, we validate the performance of the iterative algorithm in terms of localization error and coverage.