Reliable and accurate positioning underwater has been the goal of many research activities in the last years. In this paper, we present our design of a self-maintainable underwater navigation system, which provides a simple, low-cost, and flexible solution. In our concept, a set of buoys is equipped with Global Navigation Satellite System (GNSS) receivers as well as underwater pseudolite signal transmitters. Therefore, the buoys are able estimate their position and transmit this information underwater through a pseudolite signal. We particularly designed this signal for underwater ranging for both fresh and salt water. Any suitable underwater receiver is then able to do ranging via these pseudolite signals. In this paper, we theoretically analyze and test our concept using several buoy distributions and diving depths. The optimal arrangement of buoys is determined in terms of accuracy and availability depending on the number of available buoys and targeted water depth for an efficient operation. For example, at a targeted depth of 30 m in fresh water, a maximum horizontal position root-mean-square (RMS) error of less than 3 m can be achieved with a set of five buoys providing a service radius of up to 72 m.

Railway transportation systems have high accuracy and high integrity demands for safe localization. In the future, railway signaling is expected to rely on onboard sensors like Global Navigation Satellite Systems (GNSSs) in order to reduce installation and maintenance costs. GNSS position determination can, however, be highly degraded because of the presence of multipath on the train and railway environment. This paper tackles the characterization of multipath in code measurements caused exclusively by the antenna installation and derives a conservative error model of the antenna-installation-induced multipath and noise. First, we isolate multipath and noise from other GNSS errors using the Code-Minus-Carrier method. Second, an overbounding error model is derived. The limitation of modeling with restricted set of real data typically found in practice is discussed and we review methods that ensure the independence of samples. A new approach that creates separate data sets is ultimately proposed to derive an overbounding sigma. The presented methodology is supported by real measurements collected in an open-sky railway scenario. The derived models can be used as a reference nominal error models to build the null hypothesis of fault detection algorithms that detects the presence of excessive multipath in dynamic scenarios or as a part of a total error budget consideration.