## 1 Introduction
### Related Work  
Passive self-localization systems rely on a signal that is sent by beacons, which are installed prior to operations and whose positions are known to the mobile robots. The robot position is obtained in relation to the beacons by either determining the range to the beacons (spherical positioning) or by determining the difference between the ranges (hyperbolic positioning). Acoustic localization is one possible approach for confined underwater environments. However, in contrast to open waters such as oceans or lakes, multi-path propagation, reflections and reverberation of one to two seconds provide serious challenges for acoustic approaches. Moreover, \(\mu\)AUVs often do not possess the possibility for clock synchronization, which helps to accurately determine the time of flight of acoustic signals. An acoustic spherical positioning system with channel switching that does not require clock synchronization is suggested in [10]. The authors present simulations whereby the degrading effects are not included because they are in general difficult to simulate. In [11], an acoustic hyperbolic localization approach for confined environments is presented. Cyclically-transmitted signals render clock synchronization unnecessary. Experimental results show sub-decimeter localization accuracy, but vulnerability to reflections and reverberation. An acoustic model for \(\mu\)AUVs that allows packet-based ranging and active localization is presented in [12; 13]. The hardware is suitable for medium-sized (15 m to 100 m length scales) underwater environments.  
Recently, a series of papers [3; 4; 5; 6; 7] by groups from the Pohang University of Science and Technology (POSTECH) and the Seoul National University of Science and Technology (SEOULTECH) introduced a novel approach for determining ranges underwater by using spherical localization based on the attenuation of EM carrier waves. Furthermore, the authors show the feasibility of the system for accurate localization in confined underwater environments. In [3] the authors derive the relationship between range and EM wave attenuation from the Maxwell equations and the Friis transmission formula. This relationship is used in [4] to demonstrate self-localization in the horizontal plane based on the attenuation of EM carrier waves. Further analysis of the system in freshwater and seawater is provided in [4]. Thorough analyses for the issues occurring, when the system is deployed in three-dimensional space, are provided in [6; 7]. The results are used to show the feasibility of self-localization in three-dimensional space. The benefits of the EM approach are that multi-path propagation, reflections and reverberation are much weaker for EM waves than for acoustic waves in water because of the high attenuation rate in liquids. The localization accuracies that are reported in [3; 4; 5; 6; 7] are within millimeter range at a 1000-Hz update rate. A key step in the signal processing chain is the computation of a power density spectrum of an ultra-high frequency (UHF) signal. All results reported in [3; 4; 5; 6; 7] use a full-fledged spectrum analyzer for computing the power density spectrum. Such a spectrum analyzer is not deployable in \(\mu\)AUVs, because it is too large, too heavy and too costly. An embedded system that allows the installation on-board \(\mu\)AUVs will necessarily have a degraded performance in terms of localization accuracy and update rate. However, even accuracies of a centimeter magnitude at an update rate of 10 Hz would still fulfill most localization specifications for confined underwater environments, if the approach can be embedded within \(\mu\)AUVs. It would be a significant improvement over the state of the art, which would render \(\mu\)AUV operations in confined underwater environments possible.