Multihop versus Message-Passing: a Complexity and Accuracy Comparison for Distributed Localization 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 47521 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—In this paper we present the multihop-approach as a complexity and energy-efficient alternative to the classical message-passing scheme in distributed localization for wireless sensor networks (WSNs). While it is the approach currently most often considered for cooperative localization, message-passing localization algorithms (MPLAs) rely on the “diffusion” of the known location of a few nodes (anchors) to the entire network via a typically large number of message exchanges amongst neigh- bors, resulting in high communications costs, low robustness to mobility, little location privacy to end users and slow convergence. In contrast, in multihop localization algorithms (MHLAs) each node is localized based on the multihop distances between itself and anchors, such that substantially lower communication costs, intrinsic privacy and faster location-acquisition are inherently achieved. Based on the fact that the Cramer-Rao lower bounds (CRLBs) of MHLAs and MPLAs are comparable in most cases of interest, we demonstrated via simulations that from a complexity and energy-efficiency point of view, MHLAs with higher signal- to-noise ratio (SNR) but “near-zero” communication costs are a valid alternative to MPLAs. I. I NTRODUCTION Distributed localization is a well-known framework that nowadays, due to its intrinsic characteristics, is gaining more and more attention. In particular distributed algorithms can be employed on large-scale and ad-hoc sensor networks, and in the same time they have self-organizing capabilities without requiring a global-infrastructure, thus resulting appealing for many contexts [1]. The majority of algorithms currently considered for dis- tributed localization can be classified according to two main approaches: message-passing localization algorithms (MPLAs) and multihop localization algorithms (MHLAs). In the first, dominating approach, nodes estimate their own location by exchanging information on the location of, and distances to, neighboring nodes [2], [3]. For these reasons we will refer to this approach also as “Network-Wide”, as in fig. 1(a), since the localization process, even to obtain the position of a single node whose position is unknown (depicted as white square and in the following referred to as target) involves all the nodes in the network. On the other hand, MHLAs can be described as “Target-Specific” approaches, since the localization process (a) Network-Wide approach. (b) Target-Specific approach. Fig. 1. Different approaches for distributed localization. can involve only a single target (see fig. 1(b)) estimating the distances between itself and a set of nodes whose position is known a-priori (depicted by black circles and in the following referred to as anchors). Although such message-passing localization algorithms (MPLAs) are very performing in term of localization accuracy, a characteristic problem of MPLAs is that the communication cost or complexity – measured in terms of the number of message exchanges required for convergence – grows geomet- rically with the number N of nodes in the network.