Sensor Fusion for Position Estimation in Networked Systems 251 0 Sensor Fusion for Position Estimation in Networked Systems Giuseppe C. Calafiore, Luca Carlone and Mingzhu Wei Politecnico di Torino Italy 1. Introduction Recent advances in wireless communication have enabled the diffusion of networked systems whose capability of acquiring information and acting on wide areas, in a decentralized and autonomous way, represents an attractive peculiarity for many military and civil applications. Sensor networks are probably the best known example of such systems: cost reduction in pro- ducing smart sensors has allowed the deployment of constellations of low-cost low-power interconnected nodes, able to sense the environment, perform simple computation and com- municate within a given range (Akyildiz et al., 2002). Another example is mobile robotics, whose development has further stressed the importance of distributed control and coopera- tive task management in formations of agents (Siciliano & Khatib, 2008). A non-exhaustive list of emerging applications of networked systems encompasses target tracking, environmental monitoring, smart buildings surveillance and supervision, water quality and bush fire sur- veying (Martinez & Bullo, 2006). The intrinsically distributed nature of measurements acquired by the nodes requires the sys- tem to perform a fusion of sensor perceptions in order to obtain relevant information from the environment in which the system is deployed. This is the case of environmental monitoring, in which the nodes may measure the trend of variables of interest over a geographic region, in order to give a coherent overview on the scenario of observation. As in this last example, most of the mentioned fields of application require that each node has precise knowledge of its ge- ometric position for correctly performing information fusion, since actions and observations are location-dependent. Other cases in which it is necessary to associate a position to each node are formation control, which is based on the knowledge of agent positions, and location aware routing, which benefits from the position information for optimizing the flow of data through the network, to mention but a few. In this chapter we discuss the problem of network localization, that is the estimation of node positions from internodal measurements, focusing on the case of pairwise distance measure- ments. In Section 2 the estimation problem is first introduced, reporting the related literature on the topic. In Section 2.1 we consider the case of localization from range-only measure- ments, whereas in Section 3 we formalize the estimation problem at hand. Five approaches for solving network localization are extensively discussed in Section 4, where we report the theoretical basis of each technique, the corresponding convergence properties and numeri- cal experiments in realistic simulation setups. The first three localization methods, namely a gradient-based method,a Gauss-Newton approach and a trust region method are local, since 11