Characterizing Ionospheric Effects on GNSS Reflectometry at Grazing Angles from Space

Coherent observations in GNSS reflectometry are prominent in regions with smooth reflecting surfaces and at grazing elevation angles. However, within these lower elevation ranges, GNSS signals traverse a more extensive atmospheric path, and increased ionospheric effects (e.g., delay biases) are expected. These biases can be mitigated by employing dual-frequency receivers or models tailored for single-frequency receivers. In preparation for the single-frequency GNSS-R ESA “PRETTY” mission, this study aims to characterize ionospheric effects under variable parameter conditions: elevation angles in the grazing range (5° to 30°), latitude-dependent regions (north, tropic, south) and diurnal changes (day and nighttime). The investigation employs simulations using orbit data from Spire Global Inc.’s Lemur-2 CubeSat constellation at the solar minimum (F10.7 index at 75) in March 2021. Changes towards higher solar activity are accounted for with an additional scenario (F10.7 index at 180) in March 2023. The electron density associated with each reflection event is determined using the Neustrelitz Electron Density Model (NEDM2020) and the NeQuick 2 model. The results from periods of low solar activity reveal fluctuations of up to approximately 300 TECUs in slant total electron content, 19 m in relative ionospheric delay for the GPS L1 frequency, 2 Hz in Doppler shifts, and variations in the peak electron density height ranging from 215 to 330 km. Sea surface height uncertainty associated with ionospheric model-based corrections in group delay altimetric inversion can reach a standard deviation at the meter level

Atmospheric effects resolved in airborne GNSS reflectometry by data fusion processing

The advent of the Global Satellite Navigation Systems (GNSS) allowed the emergence of multiple satellite, airborne and terrestrial systems for remote sensing and Earth observation that make use of GNSS signals for navigation and positioning. However, GNSS signals can be also used as a remote sensing technique to obtain characteristics of the Earth's surface once they get reflected. This technique is nowadays called GNSS Reflectometry (GNSS-R) and offers different applications such as sea state, soil moisture, and sea ice concentration. GNSS reflectometry relies on bistatic radar configuration. Therefore, it is necessary to integrate multiple data sources to produce more accurate, useful, and consistent information from the transmitter-surface-receiver interaction. In this study, we fuse GNSS and ancillary data to resolve the tropospheric residual from the signal path change over the observed period. The experiment consisted of four flights performed with a gyrocopter in July 2019 along the coast between Calais and Boulogne-Sur-Mer, France. The processing comprises the integration of aircraft trajectory, broadcasted GNSS satellites orbits, and geoid model for direct and reflected signal path difference modeling. The latter is used for GNSS-R data processing by means of a model-aided software receiver. The resulting reflected signal is passed through a retracking module to obtain the corrected phase residual observable comparable with the tropospheric residual retrieved from ray-tracing modeling. Initial results have shown promising performance at calm sea and grazing angles. Satellites with low elevations (E < 10°) reveal coherent observations that allow resolving atmospheric effects from GNSS-R airborne data

Atmospheric effects resolved in coherent airborne GNSS reflectometry

The advent of the Global Satellite Navigation Systems (GNSS) allowed the emergence of multiple satellites, airborne and terrestrial systems for remote sensing, and Earth observation. GNSS signals, designed for positioning and navigation, can be used to obtain characteristics of the Earth's surface once they get reflected. Recent studies have made use of GNSS Reflectometry as a tool for atmospheric sounding with promising results, broadening the spectrum for the use of the reflected GNSS signals. This study examines the occurrence of high-precision phase delay information for airborne reflectometry under the condition of various sea states in coastal waters. We fuse GNSS and ancillary data to resolve the tropospheric residual from the signal path change over the observed period. The experiment consisted of four flights performed with a gyrocopter in July 2019 along the coast between Calais and Boulogne-Sur-Mer, France. The processing comprises the integration of aircraft trajectory, GNSS satellites orbits, and geoid model for direct and reflected signal path difference modeling. Path predictions are used for GNSS-R data processing by means of a model-aided software receiver. The resulting reflected signal is passed through a retracking module to obtain the corrected Doppler shift and residual phase observable comparable with the tropospheric residual retrieved from ray-tracing modeling assuming a standard atmosphere. Initial results have shown promising performance at calm sea and grazing angles. Satellites with low elevations (E < 10°) reveal coherent observations that allow resolving tropospheric effects from GNSS-R airborne data

Sea state-dependent Doppler spread as a limit of coherent GNSS reflectometry from an airborne platform

Sea level rise and sea state variability due to climate change and global warming are major research topics in the scientific community. Ocean weather conditions considerably impact coastal areas, and wind speed (WS) and significant wave height (SWH) are usable parameters to monitor the sea state threats on the coasts. GNSS reflectometry (GNSS-R) has shown considerable promise as a remote sensing technique for ocean parameters estimation. Multiple studies have been conducted successfully in the recent two decades by using GNSS-R ground-based, airborne and spaceborne data to retrieve geophysical properties of the ocean surface. The focus of this study is to investigate the Doppler shift of the reflected signal as observable to estimate the Doppler spread (DS) and determine its correlation with sea state changes employing GNSS-R airborne data in coastal areas. An additional aim is to study the possibility of using the Doppler spread as a metric for coherent GNSS reflectometry for applications such as precise altimetry and precise total electron content (TEC) estimates. An experiment was conducted from the 12th to the 19th of July 2019 along Opal Coast, between the cities of Calais and Boulogne-sur-Mer, France. The experiment consisted of multiple flights at an altitude of ~780m (a.m.s.l), and the direct and reflected signals were received by dual-polarized (Right-Handed and Left-Handed Circular Polarizations) antenna mounted on a gyrocopter. A software receiver is used to process the direct and reflected signals from the right-hand channel. The resulting in-phase (I) and quadrature (Q) components (at 50 Hz rate) of the reflected signals are analyzed in the spectral domain every ten seconds to obtain the relative Doppler shift and power estimates. The coherence is established by analyzing the phase observations obtained from I and Q. The sensitivity of the reflected signal parameters and the sea state is determined by the correlation between the Doppler Spread with wind speed and significant wave height. The latter two were obtained from the atmospheric, land and oceanic climate model, ERA5, provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). Initial results have shown promising performance at a calm sea (WS: 2.9 m/s and SWH: 0.26 m) and grazing angles. Satellites with low elevations (E 30°). The DS increases up to 2.1 Hz and the correlation decrease to 0.55 and 0.42 respectively. Coherence conditions are still under study; however, preliminary phase analysis reveals coherent observations at events with elevations below 15° and sea state with a significant wave height of 0.26 m

Sea state dependent Doppler spread as a limit of coherent GNSS reflectometry from an airborne platform

Sea level rise and sea state variability due to climate change and global warming are major research topics in the scientific community. Wind speed (WS) and significant wave height (SWH) are usable parameters to monitor sea state threats and the impact of ocean weather conditions in coastal areas. GNSS reflectometry (GNSS-R) has shown considerable promise as a remote sensing technique for ocean parameter estimation. Multiple studies have been successfully conducted in the recent two decades by using GNSS-R ground-based, airborne and spaceborne data to retrieve geophysical properties of the sea surface. The focus of this study is to investigate the Doppler shift of the reflected signal as observable to estimate the Doppler spread (DS) and determine its correlation with sea state changes, making use of GNSS-R airborne data in coastal areas. An additional aim is to study the possibility of using the Doppler spread as a metric for coherent GNSS reflectometry for applications such as precise altimetry and precise total electron content (TEC) estimates. An experiment was conducted from the 12th to the 19th of July 2019 along Opal Coast, between the cities of Calais and Boulogne-sur-Mer, France. The experiment consisted of multiple flights at an altitude of ~780m (a.m.s.l). The direct and reflected signals were received by dual-polarized (Right-Handed and Left-Handed Circular Polarizations) antenna mounted on a gyrocopter. A software receiver is used to process the direct and reflected signals from the right-hand channel. The resulting in-phase (I) and quadrature (Q) components (at 50 Hz rate) of the reflected signals are analyzed in the spectral domain every ten seconds to obtain the relative Doppler shift and power estimates. The coherence is established by analyzing the phase observations obtained from I and Q. The sensitivity of the reflected signal estimates and the sea state is determined by the correlation between the Doppler Spread with wind speed and significant wave height. The latter two were obtained from the atmospheric, land and oceanic climate model, ERA5, provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). Initial results have shown promising performance at a calm sea (WS: 2.9 m/s and SWH: 0.26 m) and grazing angles. Satellites with low elevations (E 30°). The DS increases up to 2.1 Hz and the correlation decrease to 0.55 and 0.42 respectively. Coherence conditions are still under study; however, preliminary phase analysis reveals coherent observations at events with elevations below 15° and sea state with a significant wave height of 0.26 m

Airborne Coherent GNSS Reflectometry and Zenith Total Delay Estimation over Coastal Waters

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%

Calibration of the GNSS Signal Amplitudes in the Interference Pattern Technique for Altimetry

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

Normalized GNSS Interference Pattern Technique

It is well known that water level and snow height can be monitored with the ground reflectometry GNSS-R approach [1, 2]. In this approach the antenna situated on a mast, receives a direct GNSS signal coming from the satellite and a nadir signal reflected by the observed surface. Assuming that the antenna position is known we can compute the position of the surface of reflection. For water level monitoring and snow determination, this approach provides precise localization and dating of the measures that allows to process spatio-temporal comparison of water level and snow cover, respectively. These parameters are very important for flood monitoring, avalanche prevention, as well as for hydroelectic companies. Furthermore the approach is noninvasive and can be easily implemented on a portable instrument and embedded in a vehicle with a mast. The Interference Pattern Technique considers the behavior of the SNR of the received GNSS signal as a function of the satellite elevation [1]. The received signal is indeed the integration by the antenna of the direct and nadir reflected GNSS signals. Due to their different phase variations, the SNR oscillates at a rate proportional to the height between the antenna and the surface of specular reflection. Unfortunately the measurement is typically very long because it needs to process the SNR for high satellite elevation variations. We indeed need to observe a sufficient number of SNR oscillations to estimate the frequency and derive the surface height. In order to reduce the estimation time to a fraction of one period of the SNR variation, we propose to normalize the measures. The normalization consists in varying the antenna height of a value dh in order to read the minimum and maximum value of SNR for a given satellite elevation, and then in processing with these values the SNR measured for different satellite elevations. We show in this paper that the normalization allows to compute the cosine of the phase delay between the direct and reflected signals and to estimate the signal frequency on a fraction of a period. We also derive the minimum antenna variation range dh as a function of the satellite elevation. We deduce from this function the minimum time of observation as a function of the satellite elevation rate. We derive the exact evolution of the SNR as a function of the signals parameters (Doppler frequency, code delay, CN0) of the visible satellites [3]. The proposed method is assessed on real and synthetic signals

Circular signals processing applied to altimetry using the phase of GNSS signals

Lorsqu'une grandeur est observée par une série temporelle de mesures périodiques, telles que des mesures d'angles, les outils statistiques du domaine linéaire ne sont plus adaptés à l'estimation des paramètres statistiques de cette série. Nous proposons des filtres et un opérateur de fusion adaptés aux grandeurs aléatoires circulaires. Ils sont développés dans un cadre bayésien avec la distribution circulaire normale de von Mises. De plus, on propose un estimateur circulaire GLR (Global Likehood Ratio) de ruptures dans un signal angulaire s'appuyant sur un filtre particulaire défini dans le domaine circulaire. Le traitement des signaux GNSS repose traditionnellement sur l'estimation récursive, en boucles fermées, de trois paramètres : le délai de code, la phase et la fréquence porteuse du signal reçu. On montre dans cette thèse que l'estimation de la phase et de la fréquence en boucle fermée est à l'origine d'imprécisions et de perturbations additionnelles. On propose une nouvelle approche pour l'estimation de ces paramètres en boule ouverte. Dans ce cas, les mesures de phase sont des angles, définis entre ‒π et π. Statistiquement, elles peuvent être modélisées par la distribution circulaire de von Mises et l'on utilise donc les outils d'estimation circulaire développés dans cette thèse pour les traiter. On montre l'intérêt de l'approche proposée pour le positionnement et pour l'altimétrie par réflectométrie des signaux GNSS. La précision obtenue est de l'ordre du centimètre, pour des durées d'intégrationd'une milliseconde. On propose également une technique de résolution de l'ambiguïté de phase, utilisable dans une approche mono-récepteur et mono-fréquence.When a value is observed by a temporal series of periodic measurements, such as angle measurements, the statistic tools of the linear domain are no longer adapted to the estimation of the statistical parameters of this series. We propose several filters and a fusion operator adapted to angular random variables estimation. They are developed in a Bayesian framework with the von Mises circular normal distribution. Moreover, we propose a Global Likelihood Ratio circular change estimator which relies on a particle filter defined in the circular domain. GNSS signal procedding traditionnaly relies on the recursive estimation of three parameters in lock loops : the code delay, the phase and the frequency of the received signal carrier. We show in this thesis that the phase and frequency estimations, when realized in a lock loop, cause imprecisions and additional perturbations. We proposea new approach for the estimation of these parameters in an open loop. in this context, the phase measurements are angles defined between ‒π et π. They can be modeled using the von Mises distribution, thus we use the developed circular estimation tools in order to process them. We show the benefit of the proposed approach for positioning and for height estimation using the GNSS-Reflectometry technique. The obtained precision is of the centimeter order, for integration times of one millisecond. We also propose a phase ambiguity resolution technique which can be used in a mono-receiver , mono-frequency approach

Circular Regression Applied to GNSS-R Phase Altimetry

International audienceThis 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