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.

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.

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Abstract-Global Navigation Satellite Systems signals can be used in bi-static radar systems in order to get altimetric measurements. With a single classic GNSS ground-based receiver processing the combination of the signals coming directly and after one reflection to the receiving antennas, the Interference Pattern Technique allows the computation of the height of the reflecting surface. In this case, the observed parameter is the Signal to Noise Ratio of the received composite signal, which oscillates at a frequency proportional to this height. However, the signal recordings are generally very long since the accuracy of the SNR frequency estimation is proportional to the variation of the satellite elevation during the observation interval. In this article, we propose a calibration technique that allows reducing the observation duration while keeping a centimeter accuracy performance. The proposed technique is tested on both synthetic and real data.