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.

This article is dedicated to the study of airborne GNSS-R signal processing techniques for water body detection and edge localization using a low-altitude airborne carrier with high rate reflectivity measurements. A GNSS-R setup on-board a carrier with reduced size and weight was developed for this application. We develop a radar technique for automatic GNSS signal segmentation in order to differentiate in-land water body surfaces based on the reflectivity measurements associated to different areas of reflection. Such measurements are derived from the GNSS signal amplitudes. We adapt a transitional model to characterize the changes in the measurements of the reflected GNSS signals from one area to another. We propose an on-line/off-line change detection algorithm for GNSS signal segmentation. A real flight experimentation took place in the context of this work obtaining reflections from different surfaces and landforms. We show, using the airborne GNSS measurements obtained, that the proposed radar technique detects in-land water body surfaces along the flight trajectory with high temporal (50 Hz ) and spatial resolution (order of 10 to 100 m${}^2$). We also show that we can localize the edges of the detected water body surfaces at meter accuracy.

Lock-in amplification (LIA) is an effective approach for recovery of weak signal buried in noise. Determination of the input signal amplitude in a classical dual-phase LIA is based on incoherent detection which leads to a biased estimation at low signal-to-noise ratio. This article presents, for the first time to our knowledge, a new architecture of LIA involving phase estimation with a linear-circular regression for coherent detection. The proposed phase delay estimate, between the input signal and a reference, is defined as the maximum-likelihood of a set of observations distributed according to a von Mises distribution. In our implementation this maximum is obtained with a Newton Raphson algorithm. We show that the proposed LIA architecture provides an unbiased estimate of the input signal amplitude. Theoretical simulations with synthetic data demonstrate that the classical LIA estimates are biased for SNR of the input signal lower than −20 dB, while the proposed LIA is able to accurately recover the weak signal amplitude. The novel approach is applied to an optical sensor for accurate measurement of NO ${}_2$ concentrations at the sub-ppbv level in the atmosphere. Side-by-side intercomparison measurements with a commercial LIA (SR830, Stanford Research Inc., Sunnyvale, CA, USA ) demonstrate that the proposed LIA has an identical performance in terms of measurement accuracy and precision but with simplified hardware architecture.

High-precision GNSS (global navigation satellite e system) measurements can be used for remote sensing and nowadays play a significant role in atmospheric sounding (station data, radio occultation observations) and sea surface altimetry based on reflectometry. A limiting factor of high-precision reflectometry is the loss of coherent phase information due to sea-state-induced surface roughness. This work studies airborne reflectometry observations recorded over coastal waters to examine the sea-state influence on Doppler distribution and the coherent residual phase retrieval. From coherent observations, the possibility of zenith total delay inversion is also investigated, considering the hydrostatic mapping factor from the Vienna mapping function and an exponential vertical decay factor depending on height receiver changes. The experiment consists of multiple flights performed along the coast between the cities of Calais and Boulogne-sur-Mer, France, in July 2019. Reflected signals acquired in a right-handed circular polarization are processed through a model-aided software receiver and passed through a retracking module to obtain the Doppler and phase-corrected signal. Results from grazing angle observations (elevation < 15°) show a high sensitivity of Doppler spread with respect to sea state with correlations of 0.75 and 0.88 with significant wave height and wind speed, respectively. An empirical Doppler spread threshold of 0.5 Hz is established for coherent reflections supported by the residual phase observations obtained. Phase coherence occurs in 15% of the observations; however, the estimated zenith total delay for the best event corresponds to 2.44 m, which differs from the typical zenith total delay (2.3 m) of 5%.

This article studies the use of airborne Global Navigation Satellite System Reflectometry (GNSS-R) techniques for remote sensing applications at regional scale. The objective is to classify the reflectivity of airborne GNSS signals in order to differentiate various reflective surfaces along the satellite traces. For this purpose, we propose a segmentation algorithm based on an online change point detector and an off-line change point localization estimate. Given the presence of speckle noise in GNSS signals, a homomorphic log-transformation is applied to mitigate this noise. In this context, the Cumulative Sum (CUSUM) change point detector and the Maximum Likelihood change point localization are designed for a Log-Gamma distribution. We show that the proposed radar segmentation system is able to automatically detect different land-forms along real flight experiments that took place in the Northern Region of France. Automatic classification using K-means clustering is applied to the segmented signals allowing to distinguish different segments of the signal.