Efficient and Accurate Localization in Multihop Networks Stefano Severi † , Giuseppe Abreu ⋆ , Giuseppe Destino ⋆ and Davide Dardari † † Dipartimento di Elettronica Informatica e Sistemistica, Universit` a degli Studi di Bologna Via Venezia 52, Cesena, Italy 47023 Email: {stefano.severi,ddardari}@ieee.org ⋆ Centre for Wireless Communications, University of Oulu, Finland P.O.Box 4500 FIN-90014 Email: {destino,giuseppe}@ee.oulu.fi Abstract—We present evidence that multihop node-to-anchor distance information is sufficient to allow accurate self- localization in multihop wireless networks (such as ad hoc and sensor networks, as well as future cellular systems based on LTE). To this purpose we have implemented two new distance- based source localization algorithms, which prove highly robust to inaccurate range information characterized by distance estimates exceeding the correct ones. Our contribution is a contrasting al- ternative to current distributed self-localization algorithms, which are founded on the idea of “diffusing” the known location of a few nodes (anchor) to the entire the network via a typically large number of message exchanges amongst neighbors, resulting in high communications costs, low robustness to mobility, and little (location) privacy to end users. To the best of our knowledge, this work is the first example that the aforementioned disadvantages are not an unavoidable price to be payed for accurate location information in multihop networks. I. I NTRODUCTION In typical distributed cooperative algorithms currently con- sidered for self localization in autonomic multihop network, nodes estimate their own location by collecting information on the location of and distances to neighboring nodes [1]– [3]. While such a message-passing concept is solidly founded on sequential Bayesian inference, a characteristic problem of those algorithms is that the communication cost or complexity – measured in terms of the number of message exchanges required for convergence [4] – grows geometrically with the number N of nodes in the network. In addition to the resulting low efficiency, when the number n A of nodes with known location (anchors) is small compared to the network size (n A ≪ N ), convergence time easily exceeds typical network coherence times causing the localization algorithm to diverge. Last but not least, an inherent disadvantage of such algorithms is that cooperation comes at the cost of non-anonymity, since nodes must disclose their location to neighbors. In this article we demonstrate – to our knowledge for the first time – that the aforementioned drawbacks are not a necessity of distributed cooperative localization algorithms in order to achieve good localization performances. The multihop localization is not a totally new idea. Savvides [5] exploits the location information over multiple hops to perform, in his Collaborative Multilateration a gradient descend optimization. This approach however has the initial requirement of a con- siderable number of nodes having knowledge of their aboslute position; otherwise, as shown in subsection II-B, it leads to poor localitazion performances. The DV-hops algorithm is a similar approach developed by Niculescu [6]. In this case first is computed the distance between any pair of nodes in terms of number of hops; then the average hop-length is derived and finally localitazion is performed via multilateration. Although is a very simply method, the performances can not be very accurate increasing the size of the network. In our work we describe a self-localization algorithm in which any node seeking to find its own location simply collects the multihop distances between itself and a sufficient number of surrounding anchors, which can be performed efficiently, e.g. via distributed tree-based discovery algorithms [4] or geo- graphic routing [7]. While the scheme is distributed (nodes find their own location) and cooperative (neighboring nodes must relay packets towards/from anchors), fundamental differences with respect to current distributed cooperative self-localization algorithms are: a) nodes do not repeatedly update/exchange location information with neighbors (with clear benefits for the security of the network [8]), but rather forward inquires on the location of anchors to the anchors themselves, via multihop routing; b) nodes need not disclose their location to neighbors, and instead simply add each estimated hop distance to the routes length, and c) the algorithm is not iterative, such that its “convergence” time equals the delay associated with the slowest route to the anchors. In section II the model used in simulations is introduced and it is demonstrated that in such scenario classic algorithms are not able to guarantee sufficient accuracy. Two more robust algorithms, one proposed for the first time within this article and the second only recently developed, are then described in section III. Performance comparison and comments are given in section IV while conclusions follow in section V. II. PRELIMINARIES A. Network scenarios and model A typical example of a multihop network is represented in fig. 1(a). Here, the network is understood as a set of N interconnected nodes randomly deployed. Only the location of a small fraction (n A ≪ N ) of nodes is known exactly a priori. These are referred to as anchors (marked by black dots) and A  [a 1 , ··· , a nA ] is the node coordinate matrix carrying the column vectors with their corresponding locations. The coordi- nate matrix of the remaining nodes, X  [x 0 , ··· , x N-nA-1 ] is unknown. The i-th node x i can however perform ranging measurements to any neighbor x j , obtaining a noisy estimate