Snow water equivalent (SWE) is a key variable for various hydrological applications. It is defined as the depth of water that would result upon complete melting of a mass of snow. However, until now, continuous measurements of the SWE are either scarce, expensive, labor-intense, or lack temporal or spatial resolution especially in mountainous and remote regions. We derive the SWE for dry-snow conditions using carrier phase measurements from the Global Navigation Satellite System (GNSS) receivers. Two static GNSS receivers are used, whereby one antenna is placed below the snow and the other antenna is placed above the snow. The carrier phase measurements of both receivers are combined in double differences (DDs) to eliminate clock offsets and phase biases and to mitigate atmospheric errors. Each DD carrier phase measurement depends on the relative position between both antennas, an integer ambiguity due to the periodic nature of the carrier phase signal, and the SWE projected into the direction of incidence. The relative positions of the antennas are determined under snow-free conditions with millimeter accuracy using real-time kinematic positioning. Subsequently, the SWE and carrier phase integer ambiguities are jointly estimated with an integer least-squares estimator. We tested our method at an Alpine test site in Switzerland during the dry-snow season 2015-2016. The SWE derived solely by the GNSS shows very high correlation with conventionally measured snow pillow (root mean square error: 11 mm) and manual snow pit data. This method can be applied to dense low-cost GNSS receiver networks to improve the spatial and temporal information on snow.

Snow water equivalent (SWE) can be measured using low-cost Global Navigation Satellite System (GNSS) sensors with one antenna placed below the snowpack and another one serving as a reference above the snow. The underlying GNSS signal-based algorithm for SWE determination for dry- and wet-snow conditions processes the carrier phases and signal strengths and additionally derives liquid water content (LWC) and snow depth (HS). So far, the algorithm was tested intensively for high-alpine conditions with distinct seasonal accumulation and ablation phases. In general, snow occurrence, snow amount, snow density and LWC can vary considerably with climatic conditions and elevation. Regarding alpine regions, lower elevations mean generally earlier and faster melting, more rain-on-snow events, and shallower snowpack. Therefore, we assessed the applicability of the GNSS-based SWE measurement at four stations along a steep elevation gradient (820, 1185, 1510 and 2540 m a.s.l.) in the eastern Swiss Alps during two winter seasons (2018–2020). Reference data of SWE, LWC and HS were collected manually and with additional automated sensors at all locations. The GNSS-derived SWE estimates agreed very well with manual reference measurements along the elevation gradient, and the accuracy (RMSE = 34 mm, RMSRE = 11 %) was similar under wet- and dry-snow conditions, although significant differences in snow density and meteorological conditions existed between the locations. The GNSS-derived SWE was more accurate than measured with other automated SWE sensors. However, with the current version of the GNSS algorithm, the determination of daily changes of SWE was found to be less suitable compared to manual measurements or pluviometer recordings and needs further refinement. The values of the GNSS-derived LWC were robust and within the precision of the manual and radar measurements. The additionally derived HS correlated well with the validation data. We conclude that SWE can reliably be determined using low-cost GNSS sensors under a broad range of climatic conditions, and LWC and HS are valuable add-ons.

The performance of bit-interleaved coded modulation with iterative decoding (BICM-ID) depends strongly on the applied mapping. We analyse the use of extended mapping schemes with more than one label per signal point: assuming a fix signal constellation and a constant number of information bits per symbol, the increase in label length results in an ambiguous mapping scheme but also provides additional parity bits which allow the use of a stronger channel code. We derive the optimum MAP detector and give some optimized mapping schemes for 16-QAM. Simulation results include an EXIT-chart analysis and show the considerable reduction of the asymptotic bit error probability. As a consequence of the more powerful mapping, we can obtain a very low bit error floor with extremely simple channel codes

Precise point positioning is analysed with new ionosphere-free mixed code-carrier combinations of satellite-satellite single difference (SD) measurements. The large wavelength of 3.215 m and the low noise level of 3.76 cm of an L1-E5 linear combination enable reliable fixing of ambiguities with a sequential bootstrapping and an integer decorrelation transformation. This linear combination suppresses the L1 code noise and multipath by 23.5 dB. The bias estimation accuracy is improved by an additional ionosphere-free L1-E5 linear combination of time-differenced measurements that is uncorrelated with respect to the first linear combination. The SD biases of the discrimination maximizing linear combination are determined at a single reference station with an accuracy between a few millimeters and 1 cm within 5 min. These biases refer to a geometry-preserving linear combination and are directly applicable at the mobile receiver. Moreover, the SD phase and code biases on L1 and E5 are determined separately by subdividing the Galileo E5 band into the E5a, E5b and E5c band whereas the latter one corresponds to the central lobe between E5a and E5b.