Antonio Rius

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49ranked-venue papers
3as first author
4since 2021 · last 2025
0000-0002-5947-2649ORCID · verified

Domains — the database's venue-derived domains; a paper can count in several

Applied, interdisciplinary, general and emerging computing · 49 · 3 first-author · 4 since 2021
YearPublicationVenuePosition
2025 Toward the Exploitation of HydroGNSS Coherent Channel: High Sampling Rate Products
abstract
HydroGNSS is a European Space Agency (ESA) 2-satellite mission scheduled for launch in the second half of 2025, equipped to continuously operate dual-frequency, dual-polarization GNSS reflectometry (GNSS-R) receivers. It will also utilize a high-rate complex signal mode, called “coherent channel,” to capture both the in-phase and quadrature components of signals reflected at the specular point during most of the duty cycle. This operation will result in a substantial volume of high-resolution GNSS-R data being available for analysis and applications. The three variables to be provided by the HydroGNSS coherent channel are described here and validated with CYGNSS raw intermediate frequency (IF) signals. The coherence coefficient (CC) and the normalized amplitude (NA), developed from the peak phasors using 4-ms coherent integration time, were compared to the “full entropy” available in the CYGNSS calibrated raw IF product. NA has a similar sensitivity to water surfaces as the full entropy and is not significantly affected by the coherent integration time. CC exhibits a higher sensitivity to small water bodies, yet it strongly depends on the coherent integration time. We also present a new product, the high sampling rate reflectivity (HSRR). It is here defined and compared to CYGNSS${L}1$low rate reflectivity as well as to the high sampling rate (hsr) CYGNSS calibrated raw IF reflectivity, showing a correlation above 0.92. Its effectiveness has been further validated by a physical model, and its uncertainty was preliminarily assessed using data from two nearby tracks. The results demonstrate that HSRR can be a valuable tool for retrieving geophysical parameters, offering a much finer resolution than the 1–2-Hz product.
Jilun Peng, Estel Cardellach, Weiqiang Li 0001, Sernerni Ribo, Antonio Rius
IEEE Trans. Geosci. Remote. Sens.5
2024 Coherent Combination of GPS III L1 C/A and L1C Signals for GNSS Reflectometry
abstract
With the evolution of Global Navigation Satellite System (GNSS), more GNSS satellites and civilian signals are available for GNSS Reflectometry (GNSS-R). Developments of new onboard processing strategies can improve the observation performance of spaceborne GNSS-R. To this end, this article proposes a new processing method by coherently combining reflected Global Positioning System (GPS) III L1 C/A and L1C signals. By exploiting the additional signal component, the signal-to-noise ratio of the reflected signal can be significantly improved. Moreover, taking advantage of the narrower auto-correlation function of the combined signal, the spatial resolution and the performance on geophysical applications can be significantly improved. The proposed method has been validated by processing cyclone GNSS (CYGNSS) raw intermediate frequency data including the direct and reflected signals from GPS III satellites. The results indicate that the signal-to-noise ratio (SNR) of the combined reflected waveform can be improved by ~2 dB compared to the L1 C/A waveform. Moreover, the SNR of the combined signal can be improved more efficiently using a longer coherent integration interval compared to the L1 C/A signal. Preliminary altimetric results demonstrate a 35.3%-61.6% improvement in the ranging standard deviation, and a 22.4%-64.4% improvement in the median absolute deviation, compared to L1 C/A measurements. Additionally, the correlation coefficient between combined measurements and wind speed improves by 26.3% on average compared to L1 C/A measurements, and 45.7% for high winds. This article presents a novel GNSS-R onboard signal processing method with improved performance, which can provide a reference for the design of future GNSS-R instruments.
Hao Du 0010, Yang Nan 0004, Weiqiang Li 0001, Estel Cardellach, Sernerni Ribo, Antonio Rius
IEEE Trans. Geosci. Remote. Sens.6
2022 Towards a Low Cost Drone-Based Soil Moisture Sensor for Precision Agriculture
abstract
This paper presents de development plans of a combined P&L-band reflectometry sensor using signals of opportunity.
Sernerni Ribo, Estel Cardellach, Weiqiang Li 0001, J. Peng, Antonio Rius
IGARSS5
2022 Standard Deviation of Spaceborne GNSS-R Ocean Scatterometry Measurements
abstract
This article analyzes the contribution of the delay-Doppler map (DDM) observation noise to the uncertainty of global navigation satellite system reflectometry (GNSS-R) ocean scatterometry observables and the retrieved wind speeds. For this purpose, the parameter$K^{p}$, which is commonly used in the traditional microwave scatterometer, is introduced to characterize the relative standard deviation (RSD) of the GNSS-R normalized bistatic radar cross section (NBRCS) measurement. Based on the noise covariance of the DDM measurements, the analytic expressions of RSD are derived for two cases, i.e., the NBRCS computed with one single DDM bin at the specular point and the NBRCS computed from$M\,\,\times \,\,N$DDM bins around the specular point. By analyzing the dependence of the RSD on different system, geometry, and instrument parameters, the simplified models of RSD are derived empirically. As a simple application of the proposed models, the wind speed retrieval errors are computed using parameters from the Cyclone GNSS (CYGNSS) mission. It shows that the wind speed retrieval error due to thermal noise and speckle can be an important error source for the overall wind speed retrieval performance, especially at high wind speed and with the high incidence angle GNSS-R measurements.
Yang Nan 0004, Weiqiang Li 0001, Shirong Ye, Hao Du 0010, Estel Cardellach, Antonio Rius, Jingnan Liu
IEEE Trans. Geosci. Remote. Sens.6
2020 Assessment of Spaceborne GNSS-R Ocean Altimetry Performance Using CYGNSS Mission Raw Data
abstract
This article assesses the ocean altimetry performance of spaceborne Global Navigation Satellite Systems reflectometry (GNSS-R) by processing the raw data sets collected by the Cyclone GNSS (CYGNSS) constellation. These raw data sets, i.e., the intermediate frequency signal streams before any receiver processing, are processed on the ground with a software receiver, from which the reflected waveforms of GPS L1, Galileo E1, and BeiDou-3 B1 band open service (OS) signals are generated following the conventional GNSS-R approach. By using different retracking algorithms, the bistatic delays of the reflected signals are derived from these waveforms, in which the retracking biases are removed with the specular point (SP) delay and power information computed from the corresponding waveform model. After applying a set of standard delay corrections, the bistatic delay observations are converted into sea surface height (SSH) measurements and compared with the mean SSH model. Both the random error (precision) and systematic effects (accuracy) are characterized with intratrack and intertrack analyses of the bistatic delay measurements. The two-way ranging precision can reach up to 3.9 and 2.5 m with 1-s GPS and Galileo group delay measurement (a factor of ~2 better for altimetry solution), and its evolution with the signal-to-noise ratio shows good consistency with the theoretical model. A significant delay dispersion of 3.0 m between different tracks is found, which is mainly attributed to the receiver orbit error and ionospheric correction residuals. These results can provide useful inputs for the development of future GNSS-R missions dedicated to ocean altimetry applications.
Weiqiang Li 0001, Estel Cardellach, Fran Fabra, Sernerni Ribo, Antonio Rius
IEEE Trans. Geosci. Remote. Sens.5
2019 Applications of Spaceborne GNSS-R over Inland Waters and Wetlands
abstract
This work aims to demonstrate the applications of spaceborne Global Navigation Satellite System reflectometry (GNSS-R) over inland waters and wetlands. Raw samples of the GNSS signals reflected from lakes, rivers and wetlands have been recorded occasionally by the TechDemoSat-1 (TDS-1) and Cyclone GNSS (CYGNSS) missions. Strong coherent reflections have been found in the GNSS-R signals from open inland water bodies (lakes and rivers), which would make possible to perform precise surface altimetry measurements using both group delay and carrier phase from reflected signals. In addition, it is also found that GNSS signals reflected off densely vegetated wetlands also present some coherent features from the evolution of their carrier phase, showing the potential of the GNSS-R technique to monitor extremely dense wetlands from spaceborne platforms.
Weiqiang Li 0001, Estel Cardellach, Fran Fabra, Sernerni Ribo, Antonio Rius
IGARSS5
2019 Effects of PRN-Dependent ACF Deviations on GNSS-R Wind Speed Retrieval
abstract
In global navigation satellite systems reflectometry (GNSS-R), the autocorrelation property of the transmitted GNSS signal is an important factor in the delay-Doppler map of the scattered power. The autocorrelation functions (ACFs) of the GPS Level 1 (L1) coarse/acquisition signals exhibit sidelobes. For some of the pseudorandom noise (PRN) codes, the high-amplitude sidelobes are located within one chip from the main lobe and, thus, broaden or narrow its width. These PRN-dependent ACF deviations can introduce significant biases into the GNSS-R scatterometric observables and the wind speed measurements. Simulation results for Cyclone GNSS (CYGNSS) mission show that the ACF deviation induced wind speed error can be larger than 10% (e.g., 2-3 m/s for 20 m/s and 7-8 m/s for 40 m/s wind speeds). These effects can be corrected efficiently by applying empirical factors on the CYGNSS L1 observables.
Weiqiang Li 0001, Estel Cardellach, Fran Fabra, Sernerni Ribo, Antonio Rius
IEEE Geosci. Remote. Sens. Lett.5
2018 Altimetry Over Sea Ice Using Coherent Gnss Reflections
abstract
This work is to demonstrate spaceborne altimetry over sea ice using coherent component of reflected Global Navigation Satellite System (GNSS) signal. The raw samples of sea ice reflected GNSS signal collected by the UK TechDemoSat-l (TDS-l) mission are processed. Strong coherent components are found in sea ice reflected GNSS signal received in space at different elevation angles, which would make it possible to perform precise surface altimetry measurements using the carrier phase information of the reflected signals. In addition, the coherent reflected signals can be integrated coherently for a longer period to increase the signal to noise ratio, which would make it possible to demonstrate the interferometric GNSS-R (iGNSS-R) altimetry technique in space without very high gain antenna. In this presentation, the altimetric results of coherent GNSS reflections with both carrier phase and code phase will be discussed.
Estel Cardellach, Fran Fabra, Sernerni Ribo, Antonio Rius, Weiqiang Li 0001, Manuel Martín-Neira
IGARSS4
2018 Polarimetric Gnss Radio-Occultations Aboard Paz: Commissioning Phase and Preliminary Results
abstract
The experiment called Radio-Occultation and Heavy Precipitation aboard PAZ (ROHP-PAZ) is the first attempt to perform spaceborne polarimetric radio-occultations (PRO) with signals transmitted by the Global Navigation Satellite Systems (GNSS). The GNSS payload aboard PAZ, initially intended for precise orbit determination, was extended with a dedicated two-polarization Radio-Occultation (RO) antenna pointing to the limb of the Earth and the receiver was upgraded to track occulting signals. The experiment is a proof-of-concept for heavy rain measurements using polarimetric GNSS RO. The PAZ satellite was launched in February 22, 2018. Preliminary results from the commissioning phase will be presented.
Estel Cardellach, Sergio Tomás, Antonio Rius, Chi O. Ao, M. de la Torre-Iuarez, Ramon Padullés, F. Joseph Turk, Bill Schreiner
IGARSS3
2018 Bi-Static Reflectometry Using Soop for Atmospheric Applications
abstract
We present a new passive bi-static radar measurement concept that employs digital satellite TV signals transmitted from geostationary orbit as signals of opportunity to measure precipitation. We also present experimental results using artificial targets, and provide results on measured Doppler frequencies as well.
Sernerni Ribo, Victor Moreno, Estel Cardellach, Fran Fabra, Weiqiang Li 0001, Antonio Rius
IGARSS6
2018 Revisiting the GNSS-R Waveform Statistics and Its Impact on Altimetric Retrievals
abstract
This paper analyzes the ocean altimetry precision of global navigation satellite systems' reflectometry (GNSS-R) by characterizing the noise statistics of the measured waveform. For this purpose, we first investigate the dependence of the altimetry precision on the statistics of the observed waveform and then derive an analytical model of the waveform statistics after incoherent averaging. The main data set used for altimetry analysis and model validation is the GPS L5 signals obtained from an airborne experiment. Two different delay estimators, based on the leading-edge derivative (DER) and the waveform fitting (FIT) over the leading edge, have been implemented. Later, the relationship between the statistics of the observed waveform and the altimetry precision is derived and validated for both the estimators with the airborne data. Then, the analytical model of the statistics of the incoherently averaged waveform is built from the correlation properties of the complex waveform, and also validated with both airborne and the TechDemoSat-1 spaceborne data. After that, the proposed waveform statistics and altimetry precision models are applied to spaceborne cases with different orbit altitudes. The altimetry performance of different onboard processing methods, i.e., conventional GNSS-R and interferometric GNSS-R, and delay estimators, i.e., DER and FIT, are preliminarily assessed. Finally, the dependence of altimetry precision on different parameters is analyzed and a simplified model of altimetry precision is proposed for the spaceborne case.
Weiqiang Li 0001, Antonio Rius, Fran Fabra, Estel Cardellach, Sernerni Ribo, Manuel Martín-Neira
IEEE Trans. Geosci. Remote. Sens.2
2017 Wetland GNSS-R measurements from aircraft
abstract
Characterizing, understanding, and projecting changes in atmospheric methane and terrestrial water storage require information about wetland dynamics, which remains a major gap in existing knowledge. Despite recent advances in satellite monitoring techniques, dynamic wetland mapping needs to be improved for more accurate global inventories and also to monitor variabilities at sub-km scale over multiple decades. It has been shown that Global Navigation Satellite Systems (GNSS) Reflectometry (GNSS-R) signatures off inundated wetlands can be identified under different vegetation conditions including a dense rice canopy and a thick forest with tall trees, where optical sensors and monostatic radars provide limited capabilities. In this study, we will further investigate the capabilities of the GNSS-R technique for wetland monitoring from aircraft platforms.
Estel Cardellach, Fran Fabra, Weiqiang Li 0001, Sernerni Ribo, Antonio Rius, Rashmi Shah, Clara C. Chew, Son V. Nghiem, Maximilian Semmling
IGARSS5
2017 WAVPY: A GNSS-R open source software library for data analysis and simulation
abstract
Due to the launch of a number of dedicated GNSS-R satellite missions during the last years, there is a potential raise of research interest in this field. This paper presents an analysis and simulation tool for the GNSS-R community: wavpy. More than just a simple waveform simulator, this library provides a set of object-oriented classes dedicated to each of the different elements that characterize a GNSS-R scenario. Then, the user can focus on just a particular piece of analysis or, by exploiting their combined synergies, to perform a more comprehensive simulation exercise.
Fran Fabra, Estel Cardellach, Weiqiang Li 0001, Antonio Rius
IGARSS4
2017 Prediction of GNSS-R altimetry precision based on waveform statistics
abstract
This work is to analyse the ocean altimetry precision of Global Navigation Satellite Systems Reflectometry (GNSS-R) based on the statistics of observed waveform. The GPS L5 signals obtained from an airborne experiment are used for this study. The altimetry precision is analysed for two specific algorithms, based on the leading edge derivative (DER) and the leading edge fitting (FIT), in which the relationship between the altimetry precision and the waveform statistics is established and validated. Then, we introduce an analytical model of the statistics of the incoherently averaged waveform, which has been validated with both airborne and spaceborne data. Finally, as an example, the altimetry precision is predicted for the GEROS-ISS mission, and preliminary results are presented.
Weiqiang Li 0001, Antonio Rius, Fran Fabra, Estel Cardellach, Sernerni Ribo, Manuel Martín-Neira
IGARSS2
2017 Advances in GNSS-R altimetry
abstract
Since the nadir 1-second altimetry precision was first estimated to be of 56 cm when the PARIS concept was developed back in 1993 (it was assumed the interferometric processing of GPS P-code signals and a 4×4 m×m receiving antenna at 700 km orbital altitude) [1], many detailed analyses and experiments have been conducted leading to far more optimistic values, as low as some 15 cm (using the interferometric processing and a 1 m2antenna from 400 km altitude). This paper presents the instrument and concept advances that have allowed such improved expectations.
Manuel Martín-Neira, Michael Kern, Salvatore D'Addio, Jason Hatton, Antonio Rius, Weiqiang Li 0001, Sernerni Ribo, Fran Fabra, Estel Cardellach, Jens Wickert, Maximilian Semmling
IGARSS5
2017 Calibration aspects of the software PARIS interferometric receiver
abstract
The Software PARIS Interferometric Receiver (SPIR) was conceived as a multiple beam-forming GNSS-Reflectometry receiver capable of implementing different signal processing strategies (clean-replica, interferometric, etc.) in order to demonstrate the synoptic capabilities for sea-surface altimetry using the interferometric GNSS-R technique. The instrument has been designed as a 16-channel very-high speed (320 MB/s) hardware recording receiver followed by a software post-processor, implementing the beam-forming and signal processing. The presence of 16 channels together with the beam-forming capabilities requires to characterize the quantization offsets, instrument time-keeping and relative instrumental delays between the different channels in order to have a well-functioning instrument. In this paper we present several calibration aspects of SPIR.
Sernerni Ribo, Fran Fabra, Estel Cardellach, Weiqiang Li 0001, Antonio Rius
IGARSS5
2016 Altimetric performance of the GEROS experiment at the ISS
abstract
The GNSS rEflectometry, Radio Occultation and Scatterometry onboard the International Space Station (GEROS-ISS) is an innovative experiment for climate research, proposed in 2011 within a call of the European Space Agency (ESA) for installation at the ISS. This international proposal was the only one selected for further studies by ESA out of ~25 submitted ones. In this work, an updated assessment of the instrument performance for the near-nadir altimetry (GNSS-R) mode and scatterometry is assessed, including the effect of the inter-modulation signals, and the expected degradation due to presence of radio-frequency interference coming from DME/TACAN systems. These results correspond to the study lead by Airbus Defence and Space-Spain, one of the two parallel Phase A studies conducted by ESA.
Adriano Camps, Hyuk Park 0001, Raul Onrubia Ibáñez, Daniel Pascual, Jorge Querol, Alberto Alonso Arroyo, Francisco-Javier Benito, Ana Andrés-Beivide, Sergio Moreno, Xabier Ballesteros, Marc Segarra, Roger Vilaseca, Antonio Rius, Manuel Martín-Neira
IGARSS13
2016 Synoptic capabilities of the GNSS-R interferometric technique with the SPIR instrument
abstract
We present in this paper the work done to test the synoptic capabilities of the GNSS-R interferometric technique as a means towards sea surface altimetry estimation, which is an integrated part of the assessment of the GEROS-ISS mission. For this purpose, a new software receiver has been developed and tested: SPIR. With the lessons learned after a first flight campaign, some system modifications were performed and a second experimental campaign has been recently carried on. Initial results show interferometric waveforms that present the quality required for altimetric analysis.
Fran Fabra, Estel Cardellach, Sernerni Ribo, Weiqiang Li 0001, Antonio Rius, Jaan Praks, Erkka Rouhe, Jaakko Seppänen, Manuel Martín-Neira
IGARSS5
2016 The Software PARIS Interferometric Receiver
abstract
The Software PARIS Interferometric Receiver (SPIR) is a multichannel GNSS-R recording receiver. It is capable to record the GNSS signals at L1, L2 or L5 bands from eight up-looking and eight down-looking antenna elements simultaneously at a rate of 80 MHz. A software post-processor processes the recorded data off-line to obtain altimetric estimates. Its development has been carried out in order to validate experimentally the synoptic capabilities of GNSS-R using the PARIS Interferometric Technique and to allow the comparison of different GNSS-R processing techniques on exactly the same set of recorded data. The paper presents the instrument's main characteristics and preliminary results.
Sernerni Ribo, Juan Carlos Arco-Fernández, Oleguer Nogués-Correig, Fran Fabra, Estel Cardellach, Antonio Rius, Manuel Martín-Neira
IGARSS6
2015 Impact of the elevation angle in the coherence time as a function of the sea wave height
abstract
For a given geometry, the coherence time of a GNSS-R waveform can be initially related to the significant wave height. However, when the coherence time is analyzed, several issues shall be considered, such as the geometry (i.e altitude, elevation angle). This work presents a review of the coherence time and its dependence on the geometry. In addition, the impact that the SWH has on both the coherence time and elevation angles is analyzed. Real data from different scenarios (spaceborne, airborne, and ground based) are used in this study.
Francisco Martín 0002, Adriano Camps, Manuel Martín-Neira, Salvatore D'Addio, Fran Fabra, Antonio Rius, Hyuk Park 0001
IGARSS6
2015 Significant wave height retrieval based on the effective number of incoherent averages
abstract
The effectiveness of incoherent averaging depends on the level of correlation between consecutive waveforms, which can vary with the geometry and with the sea state conditions. In addition it is also dependent on the lag position, since the level of correlation is not the same for all the lags. An initial estimation of the lag correlation can be done by means the ratio (R) between the actual number of incoherent averages and the effective number of incoherent averages. This work is structured in two parts: In the first part the concept of using of the ratio R as a new observable to estimate the significant wave height is detailed. In the second part, data from the TIGRIS experiment is used in order to relate the R with the significant wave height, comparing its performance with the performance obtained with the coherence time.
Francisco Martín 0002, Adriano Camps, Manuel Martín-Neira, Salvatore D'Addio, Fran Fabra, Antonio Rius, Hyuk Park 0001
IGARSS6
2015 Mitigation of Direct Signal Cross-Talk and Study of the Coherent Component in GNSS-R
abstract
In Global Navigation Satellite System Reflectometry (GNSS-R), power waveforms or Delay-Doppler Maps (DDM) are incoherently averaged to reduce the standard deviation of the fluctuations caused by the speckle and thermal noise. This letter proposes a simple and innovative processing concept based on the computation of the variance of the complex waveforms. By this approach, the coherent part of the signal is subtracted from the incoherent averaged waveform. It can be useful, for example, in scenarios where reflected signal is contaminated by the direct signal, as ground-based scenarios or in future experiments such as GEROS-ISS due to the nearby multipath of direct signals.
Francisco Martín 0002, Adriano Camps, Fran Fabra, Antonio Rius, Manuel Martín-Neira, Salvatore D'Addio, Alberto Alonso Arroyo
IEEE Geosci. Remote. Sens. Lett.4
2015 Sensitivity of PAZ LEO Polarimetric GNSS Radio-Occultation Experiment to Precipitation Events
abstract
A Global Navigation Satellite System (GNSS) radio occultation (RO) experiment is being accommodated in the Spanish low Earth orbiter for Earth Observation PAZ. The RO payload will provide globally distributed vertical thermodynamic profiles of the atmosphere suitable to be assimilated into weather numerical prediction models. The Ground Segment services of the U.S. National Oceanographic and Atmospheric Administration and standard-RO processing services by University Corporation for Atmospheric Research (USA) will be available under best effort basis. Moreover, the mission will run, for the first time, a double-polarization GNSS RO experiment to assess the capabilities of polarimetric GNSS RO for sensing heavy rain events. This paper introduces the Radio-Occultation and Heavy Precipitation experiment aboard PAZ and performs a theoretical analysis of the concept. The L-band GNSS polarimetric observables to be used during the experiment are presented, and their sensitivity to moderate to heavy precipitation events is evaluated. This study shows that intense rain events will induce polarimetric features above the detectability level.
Estel Cardellach, Sergio Tomás, Santi Oliveras, Ramon Padullés, Antonio Rius, Manuel de la Torre Juárez, F. Joseph Turk, Chi O. Ao, E. Robert Kursinski, Bill Schreiner, Dave Ector, Lidia Cucurull
IEEE Trans. Geosci. Remote. Sens.5
2014 Typhoon observations using the interferometric GNSS-R technique
abstract
Typhoon motoring using Global Navigation Satellite System (GNSS) signals is a new application of the GNSS-R technique, with increasing interest in the last years. Examples of that can be the CYGNSS (Cyclone Global Navigation Satellite System) spaceborne mission proposed by NASA, or the TIGRIS (Typhoon Investigation using GNSS-R Interferometric Signals) experiment, conducted in the framework of ESA-China cooperation. This paper focuses on the TIGRIS experiment, presenting the preliminary results obtained using the interferometric GNSS-R (iGNSS-R) technique.
Francisco Martín 0002, Adriano Camps, Hyuk Park 0001, Fran Fabra, Antonio Rius, Manuel Martín-Neira, Salvatore D'Addio, Weiqiang Li 0001, Dongkai Yang
IGARSS5
2014 Consolidating the Precision of Interferometric GNSS-R Ocean Altimetry Using Airborne Experimental Data
abstract
This paper revises the precision of altimetric measurements made with signals of the Global Navigation Satellite Systems (GNSS) reflected (GNSS-R) off the sea surface. In particular, we investigate the performance of two different GNSS-R techniques, referred to here as the clean-replica and interferometric approaches. The former has been used in GNSS-R campaigns since the late 1990s, while the latter has only been tested once, in 2010, from an 18-m-high bridge in static conditions and estuary waters. In 2011, we conducted an airborne experiment over the Baltic Sea at 3-km altitude to test the interferometric concept in dynamic and rougher conditions. The campaign also flew a clean-replica GNSS-R instrument with the purpose of comparing both approaches. We have analyzed with detail the data sets to extract and validate models of the noise present in both techniques. After predicting the noise models and verifying these with aircraft data, we used them to obtain the precision of altimetric measurements and to extrapolate the performance analysis to spaceborne scenarios. The main conclusions are that the suggested noise model agrees with measured data and that the GNSS-R interferometric technique is at least two times better in precision than a technique based on using a clean replica of the publicly available GPS code. This represents a factor of at least four times finer along-track resolution. A precision of 22 cm in 65-km along-track averaging should be achievable using near-nadir interferometric GNSS-R observations from a low earth orbiter.
Estel Cardellach, Antonio Rius, Manuel Martín-Neira, Fran Fabra, Oleguer Nogués-Correig, Sernerni Ribo, Juha Kainulainen, Adriano Camps, Salvatore D'Addio
IEEE Trans. Geosci. Remote. Sens.2
2014 Experimental Results of an X-Band PARIS Receiver Using Digital Satellite TV Opportunity Signals Scattered on the Sea Surface
abstract
A bistatic radar at X-band (11 GHz) using opportunity signals (Passive Reflectometry and Interferometry System (PARIS) concept implementing the interferometric technique) has been developed and tested in a coastal-based experimental setup. Digital satellite TV signals broadcast from geostationary orbit have been used as sources of opportunity, and correlation waveforms have been collected at different receiver bandwidths. Calibration algorithms to compensate instrumental errors have improved our observables and allowed us to obtain delay measurements with a precision of about 10 cm for wind speeds in the range of 3 m/s. A statistical analysis of the measurement noise is used to determine the quality of the obtained observables. This paper also discusses the opportunities of the PARIS concept applied at higher frequency band and with stronger signals.
Sernerni Ribo, Juan Carlos Arco-Fernández, Santi Oliveras, Estel Cardellach, Antonio Rius, Christopher Buck
IEEE Trans. Geosci. Remote. Sens.5
2013 Altimetry performance and error budget of the PARIS in-orbit demonstration mission
abstract
Reflectometry using Global Navigation Satellite System's signals of opportunity (GNSS-R) was originally conceived for mesoscale altimetry [1], although its applicability to sea state determination, soil moisture, vegetation, snow monitoring... has already been demonstrated. In December 2012 the Phase A studies of ESA's PAssive Reflectometry and Interferometry System In-orbit Demonstration (PARIS IoD) mission ended. In conventional GNSS-R the GNSS signals scattered over the Earth's surface are cross-correlated with a locally generated replica of the transmitted signal shifted in frequency (Δfd) and in delay (Δτ). PARIS is called an interferometric GNSS-R (iGNSS-R) system because the direct and the scattered signals are cross-correlated in order to use the whole signal's bandwidth, and improve the altimetric precision, despite the large bandwidth signals are not publicly available. This work presents a methodology to evaluate the performance of iGNSS-R altimeters. It is then applied to a PARIS IoD-like case, in which the receivers' bandwidths have been optimized in terms of altimetric resolution.
Adriano Camps, Daniel Pascual, Hyuk Park 0001, Francisco Martín 0002, Antonio Rius, Sernerni Ribo, Francisco-Javier Benito, Ana Andrés, Paula Saameno, Gavin Staton, Manuel Martín-Neira, Salvatore D'Addio, Philip Willemsen
IGARSS5
2013 Delay Tracking in Spaceborne GNSS-R Ocean Altimetry
abstract
Tracking, in radar altimetry, is the positioning of the waveforms in the correlation window. This letter presents a tracking strategy in spaceborne altimetry using global navigation satellite system reflectometry. First, the tracking procedure is illustrated, and the tracking parameters are discussed one by one: the determination of the correlation window, the accuracy of specular delay guess, and the tracking-refresh period. Based on the results, the proposed European Space Agency Passive Reflectometry and Interferometry System In-Orbit Demonstrator tracking case study is examined.
Hyuk Park 0001, Enric Valencia, Adriano Camps, Antonio Rius, Sernerni Ribo, Manuel Martín-Neira
IEEE Geosci. Remote. Sens. Lett.4
2012 PAU instrument aboard INTA MicroSat-1: Flight model tests
abstract
This work presents the flight model of a PAU version to be flown in INTA's (Instituto Nacional de Técnicas Aeroespaciales, Spanish Aerospace Center) MicroSat-1 and the tests performed. PAU is a hybrid GNSS-Reflectometer / Microwave Radiometer developed to assess the impact of the sea state on the L-band brightness temperatures and on the GNSS-R observables (the Delay Doppler Maps or DDMs). The DDMs can be used in the future to perform the sea state correction in the L-band radiometric measurements, and therefore, improve the quality of the sea surface salinity retrievals. This work also describes a sensitivity test, a Doppler test, and a preliminary field experiment to evaluate the performance.
Alberto Alonso Arroyo, Adriano Camps, Daniel Pascual, Hyuk Park 0001, Antonio Alcayde, Sergio Chavero, Pedro Martinez, Luis Crespo, Manuel Angulo, Antonio Rius
IGARSS10
2012 Interferometric GNSS-R achievable altimetric performance and compression/denoising using the wavelet transform: An experimental study
abstract
Reflectometry using Global Navigation Satellite System's (GNSS) opportunity signals was originally conceived for altimetry [1]. However, when the GNSS signals scatter over the Earth's surface (or propagates through the atmosphere), the amplitude and polarization characteristics change, which can be used for many other remote sensing applications such as sea state, water level, soil moisture, vegetation height, snow depth monitoring, atmospheric profiling... ([2], [3] among many others). In [4] and [5], recent experimental results from an ESA-sponsored airborne campaign carried out in June and November 2011 in the Baltic sea are presented using conventional and interferometric GNSS-R, respectively. In this work the properties of the measured interferometric GNSS-R waveforms are studied, and the wavelet transform is applied to compress and denoise the waveforms. This is of interest for future missions, such as ESA's proposal of PARIS IoD, to reduce the amount of data to be stored on board and downloaded to Earth.
Adriano Camps, Francisco Martín 0002, Hyuk Park 0001, Enric Valencia, Antonio Rius, Salvatore D'Addio
IGARSS5
2012 Submeter ocean altimetry with GPS L1 C/A signal
abstract
The ultimate accuracy and precision of conventional1 and interferometric2Global Positioning Satellite System Rerflectometry (GNSS-R) techniques for mesoscale ocean altimetry are still a matter of debate in the scientific community. The results obtained depend on the techniques used to identify the point of the specular delay in the waveform, and to perform the different delay corrections to derive the geometric delay. Also, the geometric model assumed for the scenario determines the accuracy of the altimeter range. This work presents the results of two ESA-sponsored airborne experiments using conventional GNSS-R showing subdecimeter altimetric precision with the Global Positioning System (GPS) L1 C/A code only. The Relative Mean Dynamic Topography (RMDT) obtained in both experiments is compared with results derived from traditional radar altimetry provided by Jason 2. The Root Mean Square (RMS) of the RMDT difference between both measurement systems is 48 cm for the first flight, and 198 cm for the second flight. Additionally, results from the second flight experiment show the capability of the proposed technique to retrieve sea slope measurements by superposing the ground track with EM96 geoid undulations.
Hugo Carreno-Luengo, Hyuk Park 0001, Adriano Camps, Fran Fabra, Antonio Rius
IGARSS5
2012 PARIS Interferometric Technique proof of concept: Sea surface altimetry measurements
abstract
We report preliminary results of an aircraft experiment aimed to proof the PARIS Interferometric Technique. The experiment was performed in the Gulf of Finland during a two hours flight. We installed a PARIS Interferometric Receiver together with a GOLD-RTR instrument to collect reflected C/A, P(Y) and M-code GPS signals. The collected data has been analyzed to produce altimetric observables with both techniques.
Antonio Rius, Fran Fabra, Sernerni Ribo, Juan Carlos Arco-Fernández, Santi Oliveras, Estel Cardellach, Adriano Camps, Oleguer Nogués-Correig, Juha Kainulainen, Erkka Rouhe, Manuel Martín-Neira
IGARSS1
2012 Phase Altimetry With Dual Polarization GNSS-R Over Sea Ice
abstract
This paper evaluates the potential use of reflected signals from Global Navigation Satellite Systems as a source of opportunity for the retrieval of absolute ellipsoidal heights over sea ice. Accurate estimation of the surface level would be helpful for the determination of the ice thickness, a key parameter for classification and characterization of sea ice masses. Our analysis is based on altimetric estimations from the coherent differential phase between direct and both cross- and co-polar reflected signals. For this purpose, GPS waveforms have been collected from a fixed platform in Greenland, monitoring the complete process of sea ice formation and melting during a 7-month period. The variability of coherent phase samples and polarimetric measurements are compared with in situ observations to make a realistic rough characterization of the ice cover. The retrieved sea ice surface height estimates are then evaluated against an Arctic tide model, ice surface temperature from moderate-resolution imaging spectroradiometer, and the laser altimetry product from ICESat.
Fran Fabra, Estel Cardellach, Antonio Rius, Sernerni Ribo, Santi Oliveras, Oleguer Nogués-Correig, Maria Belmonte Rivas, Maximilian Semmling, Salvatore D'Addio
IEEE Trans. Geosci. Remote. Sens.3
2011 PAU instrument aboard INTA MicroSat-1: A GNSS-R demonstration mission for sea state correction in L-band radiometry
abstract
Global Navigation Satellite System (GNSS) Reflectometry was originally proposed for mesoscale altimetry, but today its feasibility for sea state, soil moisture, vegetation and snow height has already been demonstrated. This paper describes a GNSS-Reflectometer develop to perform the sea state correction in L-band radiometric measurements, and therefore, improve the quality of the sea surface salinity retrievals. The instrument is currently being developed as a secondary payload to be launched aboard INTA (Instituto Nacional de Técnicas Aerospaciales, Spanish Aerospace Center) MicroSat-1. The basic principles of operation and the instrument development status are presented.
Adriano Camps, Juan Fernando Marchan-Hernandez, Enric Valencia, Isaac Ramos-Pérez, Xavier Bosch-Lluis, Nereida Rodriguez-Alvarez, Hyuk Park 0001, Antonio Alcayde, A. Mollfulleda, J. Galindo, Pedro Martinez, Sergio Chavero, Manuel Angulo, Antonio Rius
IGARSS14
2011 Preliminary error budget of a GNSS-R spaceborne mission
abstract
Reflectometry using Global Navigation Satellite System's (GNSS) opportunity signals was originally conceived for altimetry [1], but it has been demonstrated today that it can be applied to sea state determination, soil moisture, vegetation, snow monitoring... So far, GPS signals scattered over the Earth's surface have been cross-correlated with a local replica of the transmitted signal (typically the only GPS available: the C/A code) shifted in frequency (Δfd) and in delay (τ). However, to achieve the full potential (bandwidth) of these signals the direct and reflected signals can be directly cross-correlated, but in this case, high gain antennas are required to increase the signal-to-noise ratio. Therefore these antennas must be steerable so as to track the direct satellite and the specular reflection point. This is the concept of the European Space Agency PARIS In Orbit Demonstrator (IoD) mission [2], a new concept that was demonstrated experimentally for the first time in 2010 [3]. This work deals with the analysis of the preliminary instrument error budget of this mission to address the critical design parameters.
Adriano Camps, Hyuk Park 0001, Enric Valencia, Antonio Rius
IGARSS4
2011 An empirical approach towards characterization of dry snowlayers using GNSS-R
abstract
We present in this paper an empirical approach for the characterization of the internal layering of dry snow masses by means of GNSS-R. A forward model has been designed for reconstructing reflected waveforms given a dry snow profile and geometry (elevation and elevation-rate), as a sum of multiple responses from different layers. To extract the internal information, Fourier transforms of time series of waveforms are computed to generate lag-holograms. The frequency stripes that appear are related to the depths of the contributing snow layers. The same analysis has been done with real data, showing with agreement with the models.
Fran Fabra, Estel Cardellach, Oleguer Nogués-Correig, Santi Oliveras, Sernerni Ribo, Antonio Rius, Giovanni Macelloni, Simone Pettinato, Salvatore D'Addio
IGARSS6
2011 One-bit digital cross-correlation in the PARIS-IOD
abstract
The use of opportunity signals to make altimetric measurements is known as the PARIS (PAssive Reflectometry and Interferometry System) concept. Signals transmitted by the GPS satellite constellation reach the PARIS receiver by the direct path and are collected by a zenith looking antenna. Signals reflected on the Earth's surface reach the PARIS receiver as well and are collected by a nadir looking antenna. The instrument measures the relative delay between the instants of arrival of the direct and reflected signals. By knowing the positions of transmitters and receivers the distance to the scattering surface can be retrieved. The presented work aims to clarify if one-bit correlation can be successfully used in the PARIS-IOD, and under what limitations. It can be concluded that an upper bound has been found for the SNR of the signals at the PARIS-IOD if one-bit quantization is used and a linear cross-correlation with the same shape as the analog correlation is desired. That is, it is not possible to increase the signal SNR at any desired level without distorting the cross-correlation waveform if one-bit digitalization is used. Simulation results have been presented confirming the upper bound for the SNR of the signals.
Sernerni Ribo, Oleguer Nogués-Correig, Antonio Rius
IGARSS3
2010 Polarimetric GNSS Radio-Occultations for heavy rain detection
abstract
A Global Navigation Satellite System (GNSS) Radio-Occultation (RO) experiment is being accommodated in the Spanish Low Earth Orbiter (LEO) for Earth Observation PAZ. The RO-payload will provide globally distributed vertical thermodynamic profiles of the Atmosphere in Near Real-Time (NRT) suitable to be assimilated into Weather Numerical Prediction Models. The NRT operability will be dispensed by the Ground Segment services of the U.S.A. National Oceanographic and Atmospheric Administration (NOAA). Moreover, the mission will run, for the first time from Space, a double-polarization GNSS experiment, to assess the capabilities of polarimetric GNSS-RO for detection of heavy rain events.
Estel Cardellach, Antonio Rius, Fernando Cerezo, Miguel Angel Garcia-Primo, Manuel de la Torre Juárez, Lidia Cucurull, Dave Ector
IGARSS2
2010 Monitoring sea-ice and dry snow with GNSS reflections
abstract
GPS reflected signals have become a source of opportunity for remote sensing of the Earth's suface. In this work, we present several capabilities of this technique in two different polar environments: Greenland and Antarctica. The first part is dedicated to the retrieval of sea-ice properties, giving emphasis to the study of the coherent phase for altimetric and roughness estimations, and polarimetric measurements for the determination of the ice salinity variation. The results show good agreement with a tide model and daily ice charts. On the second part, some preliminary results and analysis strategies to retrieve dry snow signatures are presented.
Fran Fabra, Estel Cardellach, Oleguer Nogués-Correig, Santi Oliveras, Sernerni Ribo, Antonio Rius, Maria Belmonte Rivas, Maximilian Semmling, Giovanni Macelloni, Simone Pettinato, Renato Zasso, Salvatore D'Addio
IGARSS6
2010 The proof of concept for 3-cm Altimetry using the Paris Interferometric Technique
abstract
A proof-of-concept instrument for PARIS-IOD, based on a full-custom dedicated GNSS-Reflections receiver has been developed, and the novel interferometric concept tested in several experiments using signals generated by a SPIRENT equipment. The preliminary analysis has resulted in the detection of 1-cm delay-jumps, using 33 group-delay observables of 1 second, with an associated dispersion of the order of 2-cm. A signal-to-noise degradation of the order of ~3 dB with respect to the one expected for the Bridge Experiment would keep the 1-second sigma error below 3-cm.
Oleguer Nogués-Correig, Sernerni Ribo, Juan Carlos Arco-Fernández, Estel Cardellach, Antonio Rius, Enric Valencia, José Miguel Tarongí, Adriano Camps, Hans van der Marel, Manuel Martín-Neira
IGARSS5
2010 Altimetric Analysis of the Sea-Surface GPS-Reflected Signals
abstract
We describe the development and implementation of a method for extracting altimetric information using the Passive Reflectometry and Interferometry System (PARIS), i.e., from GPS signals after their reflection off the sea surface. We have formalized one idea laid out in the description of a bistatic system for ocean altimetry using the GPS signal, by Hajj and Zuffada (Jet Propulsion Laboratory), and have extended it to real situations encountered in PARIS aircraft experiments. Second, we have developed the corresponding algorithms to produce real-time altimetric observables to be used in dedicated digital signal processors. Finally, we have applied this method to estimate sea-surface height from one flight experiment in the North Sea off the coast of Norway.
Antonio Rius, Estel Cardellach, Manuel Martín-Neira
IEEE Trans. Geosci. Remote. Sens.1
2008 Combined Airborne Radio-instruments for Ocean and Land Studies (CAROLS)
abstract
The CAROLS, L band radiometer, is built and designed as a copy of EMIRAD II radiometer of DTU team. It is a Correlation radiometer with direct sampling and fully polarimetric (i.e 4 Stockes). It will be used in conjunction with other airborne instruments (in particular the C-Band scatterometer (STORM) and IEEC GPS system, Infrared CIMEL radiometer, one visible camera), in coordination with in situ field campaigns for SMOS CAL/VAL. The instruments are implemented on board the French research airplane ATR42. A validation campaign with four flights was made over south west of France, Hourtin Lake and Bay of Biscay (Atlantic Ocean) in September 2007. In order to qualify the radiometer data, different types of aircraft movements were realized: circle flights, wing and nose wags. Simultaneously to flights, different ground measurements were made over continental surfaces and ocean. First results show a good quality of data over ocean surfaces. For continental surfaces, important Radio-Frequency Interferences (RFI) were observed over a large part of the studied region.
Mehrez Zribi, Danièle Hauser, Mickaël Pardé, Pascal Fanise, Paul Leroy, Monique Dechambre, Alain Weill, Jacqueline Boutin, Gilles Reverdin, Jean-Christophe Calvet, Jean-Pierre Wigneron, Niels Skou, Sten Schmidl Søbjærg, Nicolas Reul, Antonio Rius, Estel Cardellach
IGARSS (2)15
2007 Sea surface slopes' PDF from GNSS reflected signals
abstract
We present a new technique to analyze L-band signals of the Global Navigation Satellite System (GNSS) that have rebounded off the sea surface, with the aim of retrieving information about surface roughness in the form of the Probability Density Function (PDF) of the slopes. Unlike earlier techniques, which parameterize the PDF (usually as normal bivariate distributions), this approach does not constrain the surface slopes' PDF to the shape of a particular analytical distribution. After validating the algorithm by means of end- to-end simulations, we have applied it to real data. The tests on real data show that the retrievals are robust, consistent with the results obtained with standard GNSS-reflection techniques, and in agreement with independent sources of information. Moreover, the retrieved slopes' PDF present non-Gaussian features, such as skewness, that maps with the up-/down- asymmetries introduced by surface forces. This is the first time that GNSS-reflections have sensed and identified the up- and down-wind signature on the surface.
Estel Cardellach, Antonio Rius
IGARSS2
2007 ASAP, towards a PARIS instrument for space
abstract
The technological aspects of the Altimetric and Scatterometric Applications of PARIS (ASAP) sensor are presented in this paper. This sensor is based on the PARIS concept, which makes use of GPS signals reflected on the ocean's surface in order to measure the surface's properties (altitude and roughness). The ASAP instrument is a hardware real-time PARIS receiver with the aim of being an intermediate step between the airborne GOLD-RTR receiver developed at our institute and a future spaceborne PARIS instrument.
Sernerni Ribo, Juan Carlos Arco-Fernández, Estel Cardellach, Oleguer Nogués-Correig, Antonio Rius, María Teresa Álvarez, Jesús Tabero
IGARSS5
2007 A GPS-Reflections Receiver That Computes Doppler/Delay Maps in Real Time
abstract
This paper describes a new instrument that was specially designed and developed to gather global positioning system (GPS) signals after they have been reflected from suitable surfaces (sea, ice, and ground), for Earth remote sensing. The device has been called the GPS open-loop differential real-time receiver (GOLD-RTR). Its main and most innovative feature is its computation and storage, in real time, of complex-valued ($I$and$Q$) cross correlations (waveforms) between GPS L1-C/A signals—received directly and after reflection—and the corresponding models of these signals. Particularly, the GOLD-RTR schedules consecutive coherent integration time slots of 1 ms over which ten parallel correlation channels, with 64 lags each, work simultaneously and continuously with the input raw data sampled at 40 MHz. The total throughput is 10 000 waveforms per second, each waveform being 64 lags long. These real-time correlation resources can be flexibly distributed in several configurations according to the observational requirements, for instance: Doppler/delay maps or up to ten simultaneous reflected waveforms for ten different GPS satellites are examples of what can be done. The further processing of the real-time computed 1-ms waveforms in a flight campaign over the ocean, ice, or ground can be used to obtain geophysical parameters such as sea level and tides, sea surface mean-square slopes, ice roughness and thickness, soil moisture and biomass, or future applications. This paper covers the GOLD-RTR architecture and hardware, signal processing and data storage issues, machine–user interface, laboratory readiness tests, and waveform data samples from the first two jet aircraft campaigns at 9300 m over the sea.
Oleguer Nogués-Correig, Estel Cardellach, Josep Sanz Campderros, Antonio Rius
IEEE Trans. Geosci. Remote. Sens.4
2003 A 3 GPS-channels Doppler-delay receiver for remote sensing applications
abstract
This paper describes the hardware implementation and first tests of a 3 GPS-channels Doppler-delay receiver for remote sensing applications implemented by the Technical University of Catalonia (UPC) for the Institute of Space Studies of Catalonia (IEEC/CSIC). It can be configured for several applications. For altimetry applications: by looking at the differential delay between the correlation peaks ("waveforms") between the pseudo random noise (PRN) sequence from a visible GPS-satellite and the direct and reflected signals collected by one antenna with a broad beam pointing to the zenith, and another one pointing to the sea surface (not necessarily at nadir). For sea state determination: from the shape of the ambiguity function (both in the Doppler and delay). Additionally, the instrument can be configured for GPS occultation experiments, etc. This paper presents the description of the instrument implementation and two preliminary tests performed at the Garraf coast (South of Barcelona city, Spain) and at the Zeeland Bridge (The Netherlands).
Oleguer Nogués-Correig, A. Sumpsi, Adriano Camps, Antonio Rius
IGARSS4
2001 Tomography of the lower troposphere using a small dense network of GPS receivers
abstract
The application of tomographic techniques to the troposphere with GPS signals was demonstrated in previous work using data from the Kilauea permanent network, Hawaii. Local orography of the network considered there, however, played a key role in the resolution capabilities of the technique. The authors explore the possibilities of tomographic reconstruction of the four-dimensional (4D) structure of water vapor using a very small network of global positioning satellite (GPS) receivers with virtually no height differences between the stations. The analyzed campaign consisted of seven GPS receivers located at the Onsala Space Observatory, Onsala, Sweden, and was carried out in August 1998. Traditional meteorological data sources and tools such as the numerical weather model NCAR Mesoscale Model (MM5), satellite data from the National Oceanic and Atmospheric Administration (NOAA), Washington, DC, and data and analysis from the European Center for Medium-Range Weather Forecasting (ECMWF), Reading, UK, have been used to evaluate the results. A good agreement is found between GPS tomography and classical methods, even in meteorological situations with complex vertical structure of water vapor.
Alejandro Flores 0003, Jordi Vilà-Guerau de Arellano, Lubomir Gradinarsky, Antonio Rius
IEEE Trans. Geosci. Remote. Sens.4
1998 Analysis of ionospheric electron density distribution from GPS/MET occultations
abstract
The authors present results from analysis of GPS/MET occultation data obtained from the University Corporation for Atmospheric Research database. They have used high-rate occultation data to study the performance of an earlier 4D ionospheric electron content model-obtained tomographically with the use of the GPS constellation-with satisfactory results. In addition, they have processed UCAR level-one medium-rate occultation data by using the GIPSY package to obtain aligned phases. Under the assumption of local spherical symmetry, this phase information has been processed to yield ray-path bending angles through Doppler-shift analysis, which have then been used to yield profiles of electronic density via the Abel transform. These profiles give important information for preparing future tomographic work, although the limitations imposed by the working assumptions in this approach cannot be ignored.
Antonio Rius, Giulio Ruffini, August Romeo
IEEE Trans. Geosci. Remote. Sens.1
1998 GPS tomography of the ionospheric electron content with a correlation functional
abstract
The authors develop a minimization functional in order to regularize the inverse problem associated with three-dimensional (3D) ionospheric stochastic tomography. This functional is designed to yield, upon minimization, a solution which maximizes the frequency content of the solution below a certain cutoff, while keeping /spl chi//sup 2/ constant. The authors show how this functional can be rewritten in terms of the correlation function of the image, thereby facilitating the algorithmic implementation of the method. They then implement this functional in a Kalman filter and obtain a smoothing algorithm that acts in both space and time. Finally, they use this technique to perform global scale Global Positioning System (GPS) tomography of the ionospheric electron content.
Giulio Ruffini, Alejandro Flores 0003, Antonio Rius
IEEE Trans. Geosci. Remote. Sens.3