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Fig. 1. An underwater positioning system (left), a desktop experiment (middle), and a GPS error budget from Wikipedia (right). Abstract-It is well known that the ordinary Global PositioningSystem (GPS) fails to provide location and time information under water. The reason is that the electromagnetic signals from the orbiting satellites are heavily damped in water and hence can not be detected by the receiver in most cases of interest. Acoustic waves are the canonical alternative, and there exist a variety of acoustically based systems.It is important to estimate the accuracy of position estimates and if possible correct for the errors. This is done systematically in the GPS case by the concept of Dilution Of Precision (DOP), and is also the natural approach underwater. The main issue presented below is a discussion and analysis of the concept of DOP in the context of Underwater Positioning Systems (UPS). This includes statistical models that differ from the one canonically used. Some of the sources of errors in the UPS case differs substantially from the GPS case. It is in particular demonstrated that the maximum likelihood estimator is biased. Alternative estimators, including an unbiased estimator and an optimal estimator, are discussed.The results are also briefly discussed in the context of an actual model experiment with ultrasound in air. A side effect of this is the demonstration of certain issues which have been ignored in the previous general discussion. The experiment also indicates that the results are relevant in other contexts. Other important classes of examples are given by Real Time Locating Systems as defined by the standard ISO/IEC 24730, and by Wireless Personal Area Networks as described in the IEEE 802.15 standard. These other contexts also provide most useful sources for research publications with results of relevance for UPS, and more generally for underwater communication systems.

During the development of an intelligent hearing protection and communication system the attenuation of two different earplugs were measured. Both earplugs were measured separately and in combination with earmuffs. Foam earplugs and custom-moulded silicone earplugs were both used. The hearing protection system in question is able to measure the ear canal with respect to leaks. If a leak is detected, the system will warn the user.The measurements show that the foam plug gives higher attenuation than the silicone plug at all frequencies, but particularly at frequencies below 2 kHz. It has a steadily increasing attenuation from 30 dB -43 dB over the frequency range 125 Hz -8 kHz. The silicone plug attenuates around 26 dB, from 125 Hz -1 kHz. Above this range, the attenuation increases to approximately 40 dB. With extra earmuffs added, the attenuation is 40 dB or better at all frequencies except 125 Hz, and the two plugs offer nearly identical protection.The results show that the mean and standard deviation of the attenuation for the foam earplug is as good as for an optimally fitted earplug. In the case of the silicone earplug, the mean attenuation is comparable to a typical custom earplug, but the standard deviation is better than comparable earplug. This finding is a result of the leakage control acting as a 'supervisor' in the fitting of the earplugs.

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