## 1 Introduction  
Due to environmental concerns and to the limited lifetime of energy resources, an intensive research activity is being carried out in energy-efficient protocols and algorithms for wireless networks, trying to reduce the energy consumption of the different network activities. One of the activities that should be optimized is the localization of the nodes, as many applications rely on the knowledge of the position of the user or the surrounding objects to provide useful information and services. Furthermore, knowing the position of the nodes can be used to optimize other network aspects, such as routing [1,2] or in-network data compression [3,4], leading to energy savings. The localization of the nodes in wireless networks is usually based on radio frequency techniques [5], which consist in measuring certain parameters of the radio signal that one node receives from other nodes, for example, the angle of arrival (AOA), the time of arrival (TOA) or the received signal strength (RSS). From these measurements, the position of the wireless nodes can be inferred using a triangulation algorithm [6] or by comparing the measurement with others previously saved in a database [7,8]. The research in localization for wireless sensor and ad hoc networks is very active, and a number of works have considered the energy consumption as a factor in the design of localization techniques and algorithms. This is a critical issue, since wireless devices have limited energy resources (batteries), which should be efficiently managed in order to extend the life of the network as much as possible [9]. Consequently, practical and effective solutions are needed to perform the localization in an energy-efficient way. Approaches that include the use of dedicated hardware specially designed for this purpose [10] cannot be used with commercial off-the-shelf systems. On the other hand, given that the radio system is the most energy demanding part of a wireless node [11,12], whereas the other elements (processor, memory, _etc._) consume significantly less energy, solutions that focus on reducing the computational complexity of the localization algorithms [13,14] will not contribute to significantly reduce the global energy consumption. Therefore, to effectively reduce the amount of energy that is consumed during the localization, the aim should be put on reducing the amount of time that the nodes are communicating. In other words, the transmitted/received signals that are used to measure the parameter in which the localization is based (e.g., RSS, TOA) should be kept to the minimum. However, energy consumption cannot be considered independently. The accuracy of the localization should be also taken into account, as in general, we could probably allow higher energy consumption if more accurate localization result is needed. In contrast to other works that focus on this trade-off by modifying the frequency of the localization to trade higher energy consumption for better localization accuracy (in terms of update rate) [15, 16, 17, 18], we propose to trade the accuracy of the RSS or TOA measurements for energy consumption. Our approach can be applied regardless of the localization update frequency, thus it complements the existing work and further reduces the energy consumption. In particular, we propose and evaluate a strategy that minimizes the total consumed energy during the localization process, while ensuring a certain desired accuracy in distance estimations. Although we illustrate the results of the analysis for a particular channel and communications model, the method is directly extensible to other models. Our work includes an exhaustive analysis based on simulations, which shows that not only the energy consumption is reduced with respect to other techniques (leading to energy savings of around 50% in some cases), but also that the accuracy of the localization is improved and assured to maintain a desired value.