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This article is dedicated to the design of a linear-circular regression technique and to its application to ground-based GNSS-Reflectometry (GNSS-R) altimetry. The altimetric estimation is based on the observation of the phase delay between a GNSS signal sensed directly and after a reflection off of the Earth's surface. This delay evolves linearly with the sine of the emitting satellite elevation, with a slope proportional to the height between the reflecting surface and the receiving antenna. However, GNSS-R phase delay observations are angular and affected by a noise assumed to follow the von Mises distribution. In order to estimate the phase delay slope, a linear-circular regression estimator is thus defined in the maximum likelihood sense. The proposed estimator is able to fuse phase observations obtained from several satellite signals. Moreover, unlike the usual unwrapping approach, the proposed estimator allows the sea-surface height to be estimated from datasets with large data gaps. The proposed regression technique and altimeter performances are studied theoretically, with further assessment on both synthetic and real data. [ABSTRACT FROM AUTHOR]

This article presents a new estimator of the pseudorange between a global navigation satellite systems (GNSS) satellite and a stand-alone receiver, and its application to GNSS-reflectometry (GNSS-R) altimetry. In our approach, we use as independent observations the difference between the code delay provided by successive acquisitions of the GNSS signal and the code delay truncated using the phase and Doppler information. We show that the mean value of these observations is an estimate of the first pseudorange of the observed time series. The ability of the proposed estimator to provide the centimeter accuracy is theoretically evaluated. In ground-based altimetry applications using GNSS signals, the direct pseudorange and the pseudorange associated to the reflected signal can be assumed to have the same dynamic evolution. Based on this assumption, the proposed estimate uses as observations the difference between the code delays obtained by successive acquisitions of both signals, without using phase measurement. The assessment of the method for ground-based GNSS-R is realized with real data. [ABSTRACT FROM PUBLISHER]

It is well known that reflected signals from Global Navigation Satellite Systems (GNSS) can be used for altimetry applications, such as monitoring of water levels and determining snow height. Due to the interference of these reflected signals and the motion of satellites in space, the signal-to-noise ratio (SNR) measured at the receiver slowly oscillates. The oscillation rate is proportional to the change in the propagation path difference between the direct and reflected signals, which depends on the satellite elevation angle. Assuming a known receiver position, it is possible to compute the distance between the antenna and the surface of reflection from the measured oscillation rate. This technique is usually known as the interference pattern technique (IPT). In this paper, we propose to normalize the measurements in order to derive an alternative model of the SNR variations. From this model, we define a maximum likelihood estimate of the antenna height that reduces the estimation time to a fraction of one period of the SNR variation. We also derive the Cramér-Rao lower bound for the IPT and use it to assess the sensitivity of different parameters to the estimation of the antenna height. Finally, we propose an experimental framework, and we use it to assess our approach with real GPS L1 C/A signals. [ABSTRACT FROM AUTHOR]