scholarly journals Development and validation of comprehensive closed formulas for atmospheric delay and altimetry correction in ground-based GNSS-R

2021 ◽  
Author(s):  
Thalia Nikolaidou ◽  
Marcelo Santos ◽  
Simon Williams ◽  
Felipe Geremia-Nievinski
Keyword(s):  
Elevation Angle ◽  
Satellite System ◽  
Radio Waves ◽  
Atmospheric Refraction ◽  
Refraction Effect ◽  
Receiving Antenna ◽  
Coastal Sea ◽  
Global Navigation Satellite ◽  
Development And Validation ◽  
Atmospheric Delays

Radio waves used in Global Navigation Satellite System Reflectometry (GNSS-R) are subject to atmospheric refraction, even for ground-based tracking stations in applications such as coastal sea-level altimetry. Although atmospheric delays are best investigated via ray-tracing, its modification for reflections is not trivial. We have developed closed-form expressions for atmospheric refraction in ground-based GNSS-R and validated them against raytracing. We provide specific expressions for the linear and angular components of the atmospheric interferometric delay and corresponding altimetry correction, parameterized in terms of refractivity and bending angle. Assessment results showed excellent agreement for the angular component and good for the linear one. About half of the delay was found to originate above the receiving antenna at low satellite elevation angles. We define the interferometric slant factor used to map interferometric zenithal delays to individual satellites. We also provide an equivalent correction for the effective satellite elevation angle such that the refraction effect is nullified. Lastly, we present the limiting conditions for negligible atmospheric altimetry correction (sub-cm), over domain of satellite elevation angle and reflector height. For example, for 5-meter reflector height, observations below 20° elevation angle have more than 1-centimeter atmospheric altimetry error.

scholarly journals Development and validation of comprehensive closed formulas for atmospheric delay and altimetry correction in ground-based GNSS-R

2021 ◽  
Author(s):  
Thalia Nikolaidou ◽  
Marcelo Santos ◽  
Simon Williams ◽  
Felipe Geremia-Nievinski
Keyword(s):  
Elevation Angle ◽  
Satellite System ◽  
Radio Waves ◽  
Atmospheric Refraction ◽  
Refraction Effect ◽  
Receiving Antenna ◽  
Coastal Sea ◽  
Global Navigation Satellite ◽  
Development And Validation ◽  
Atmospheric Delays

Radio waves used in Global Navigation Satellite System Reflectometry (GNSS-R) are subject to atmospheric refraction, even for ground-based tracking stations in applications such as coastal sea-level altimetry. Although atmospheric delays are best investigated via ray-tracing, its modification for reflections is not trivial. We have developed closed-form expressions for atmospheric refraction in ground-based GNSS-R and validated them against raytracing. We provide specific expressions for the linear and angular components of the atmospheric interferometric delay and corresponding altimetry correction, parameterized in terms of refractivity and bending angle. Assessment results showed excellent agreement for the angular component and good for the linear one. About half of the delay was found to originate above the receiving antenna at low satellite elevation angles. We define the interferometric slant factor used to map interferometric zenithal delays to individual satellites. We also provide an equivalent correction for the effective satellite elevation angle such that the refraction effect is nullified. Lastly, we present the limiting conditions for negligible atmospheric altimetry correction (sub-cm), over domain of satellite elevation angle and reflector height. For example, for 5-meter reflector height, observations below 20° elevation angle have more than 1-centimeter atmospheric altimetry error.

scholarly journals Measurement of the Sea Surface Height with Airborne GNSS Reflectometry and Delay Bias Calibration

2021 ◽  
Vol 13 (15) ◽  
pp. 3014
Author(s):  
Feng Wang ◽  
Dongkai Yang ◽  
Guodong Zhang ◽  
Jin Xing ◽  
Bo Zhang ◽  
...  
Keyword(s):  
Wind Speed ◽  
Arrival Time ◽  
Elevation Angle ◽  
Satellite System ◽  
Sea Surface Height ◽  
Antenna Pattern ◽  
Sea Surface ◽  
Observation Method ◽  
Global Navigation Satellite ◽  
The Impact

Sea surface height can be measured with the delay between reflected and direct global navigation satellite system (GNSS) signals. The arrival time of a feature point, such as the waveform peak, the peak of the derivative waveform, and the fraction of the peak waveform is not the true arrival time of the specular signal; there is a bias between them. This paper aims to analyze and calibrate the bias to improve the accuracy of sea surface height measured by using the reflected signals of GPS CA, Galileo E1b and BeiDou B1I. First, the influencing factors of the delay bias, including the elevation angle, receiver height, wind speed, pseudorandom noise (PRN) code of GPS CA, Galileo E1b and BeiDou B1I, and the down-looking antenna pattern are explored based on the Z-V model. The results show that (1) with increasing elevation angle, receiver height, and wind speed, the delay bias tends to decrease; (2) the impact of the PRN code is uncoupled from the elevation angle, receiver height, and wind speed, so the delay biases of Galileo E1b and BeiDou B1I can be derived from that of GPS CA by multiplication by the constants 0.32 and 0.54, respectively; and (3) the influence of the down-looking antenna pattern on the delay bias is lower than 1 m, which is less than that of other factors; hence, the effect of the down-looking antenna pattern is ignored in this paper. Second, an analytical model and a neural network are proposed based on the assumption that the influence of all factors on the delay bias are uncoupled and coupled, respectively, to calibrate the delay bias. The results of the simulation and experiment show that compared to the meter-level bias before the calibration, the calibrated bias decreases the decimeter level. Based on the fact that the specular points of several satellites are visible to the down-looking antenna, the multi-observation method is proposed to calibrate the bias for the case of unknown wind speed, and the same calibration results can be obtained when the proper combination of satellites is selected.

Performance Assessment of GNSS-R Polarimetric Observations for Sea Level Monitoring

2021 ◽  
Author(s):  
Mahmoud Rajabi ◽  
Mstafa Hoseini ◽  
Hossein Nahavandchi ◽  
Maximilian Semmling ◽  
Markus Ramatschi ◽  
...  
Keyword(s):  
Time Series ◽  
Circular Polarization ◽  
Sea Level ◽  
Tide Gauge ◽  
Satellite System ◽  
Sea Surface ◽  
Analysis Tool ◽  
Lower Accuracy ◽  
Coastal Sea ◽  
Global Navigation Satellite

<p>Determination and monitoring of the mean sea level especially in the coastal areas are essential, environmentally, and as a vertical datum. Ground-based Global Navigation Satellite System Reflectometry (GNSS-R) is an innovative way which is becoming a reliable alternative for coastal sea-level altimetry. Comparing to traditional tide gauges, GNSS-R can offer different parameters of sea surface, one of which is the sea level. The measurements derived from this technique can cover wider areas of the sea surface in contrast to point-wise observations of a tide gauge.  </p><p>We use long-term ground-based GNSS-R observations to estimate sea level. The dataset includes one-year data from January to December 2016. The data was collected by a coastal GNSS-R experiment at the Onsala space observatory in Sweden. The experiment utilizes three antennas with different polarization designs and orientations. The setup has one up-looking, and two sea-looking antennas at about 3 meters above the sea surface level. The up-looking antenna is Right-Handed Circular Polarization (RHCP). The sea-looking antennas with RHCP and Left-Handed Circular Polarization (LHCP) are used for capturing sea reflected Global Positioning System (GPS) signals. A dedicated reflectometry receiver (GORS type) provides In-phase and Quadrature (I/Q) correlation sums for each antenna based on the captured interferometric signal. The generated time series of I/Q samples from different satellites are analyzed using the Least Squares Harmonic Estimation (LSHE) method. This method is a multivariate analysis tool which can flexibly retrieve the frequencies of a time series regardless of possible gaps or unevenly spaced sampling. The interferometric frequency, which is related to the reflection geometry and sea level, is obtained by LSHE with a temporal resolution of 15 minutes. The sea level is calculated based on this frequency in six modes from the three antennas in GPS L1 and L2 signals.</p><p>Our investigation shows that the sea-looking antennas perform better compared to the up-looking antenna. The highest accuracy is achieved using the sea-looking LHCP antenna and GPS L1 signal. The annual Root Mean Square Error (RMSE) of 15-min GNSS-R water level time series compared to tide gauge observations is 3.7 (L1) and 5.2 (L2) cm for sea-looking LHCP, 5.8 (L1) and 9.1 (L2) cm for sea-looking RHCP, 6.2 (L1) and 8.5 (L2) cm for up-looking RHCP. It is worth noting that the GPS IIR block satellites show lower accuracy due to the lack of L2C code. Therefore, the L2 observations from this block are eliminated.</p>

scholarly journals High-rate altimetry in SNR-based GNSS-R: Proof-of-concept of a synthetic vertical array

2021 ◽  
Author(s):  
Mauricio Kenji Yamawaki ◽  
Felipe Geremia-Nievinski ◽  
João Francisco Monico
Keyword(s):  
Sea Level ◽  
Signal To Noise Ratio ◽  
Satellite System ◽  
High Rate ◽  
Proof Of Concept ◽  
Radio Waves ◽  
Vertical Array ◽  
Remote Sensing Technique ◽  
Single Antenna ◽  
Global Navigation Satellite

Global Navigation Satellite System Reflectometry (GNSS-R) has emerged as a promising remote sensing technique for coastal sea level monitoring. The GNSS-R based on signal-to-noise ratio (SNR) observations employs a single antenna and a conventional receiver. It performs best for low elevation satellites, where direct and reflected radio waves are very similar in polarization and direction of arrival. One of the disadvantages of SNR-based GNSS-R for sea level altimetry is its low temporal resolution, which is of the order of one hour for each independent satellite pass. Here we present a proof-of-concept based on a synthetic vertical array. It exploits the mechanical movement of a single antenna at high rate (about 1 Hz). SNR observations can then be fit to a known modulation, of the order of the antenna sweeping rate. We demonstrate that centimetric altimetry precision can be achieved in a 5-minute session. [©2021 IEEE]

scholarly journals Coastal sea level rise at Senetosa (Corsica) during the Jason altimetry missions

Ocean Science ◽  
2020 ◽  
Vol 16 (5) ◽  
pp. 1165-1182 ◽  
Author(s):  
Yvan Gouzenes ◽  
Fabien Léger ◽  
Anny Cazenave ◽  
Florence Birol ◽  
Pascal Bonnefond ◽  
...  
Keyword(s):  
High Resolution ◽  
Sea Level Rise ◽  
Sea Level ◽  
Leading Edge ◽  
Satellite System ◽  
Careful Examination ◽  
Coastal Zones ◽  
Coastal Sea ◽  
Potential Contributor ◽  
Global Navigation Satellite

Abstract. In the context of the ESA Climate Change Initiative project, we are engaged in a regional reprocessing of high-resolution (20 Hz) altimetry data of the classical missions in a number of the world's coastal zones. It is done using the ALES (Adaptive Leading Edge Subwaveform) retracker combined with the X-TRACK system dedicated to improve geophysical corrections at the coast. Using the Jason-1 and Jason-2 satellite data, high-resolution, along-track sea level time series have been generated, and coastal sea level trends have been computed over a 14-year time span (from July 2002 to June 2016). In this paper, we focus on a particular coastal site where the Jason track crosses land, Senetosa, located south of Corsica in the Mediterranean Sea, for two reasons: (1) the rate of sea level rise estimated in this project increases significantly in the last 4–5 km to the coast compared to what is observed further offshore, and (2) Senetosa is the calibration site for the TOPEX/Poseidon and Jason altimetry missions, which are equipped for that purpose with in situ instrumentation, in particular tide gauges and a Global Navigation Satellite System (GNSS) antenna. A careful examination of all the potential errors that could explain the increased rate of sea level rise close to the coast (e.g., spurious trends in the geophysical corrections, imperfect inter-mission bias estimate, decrease of valid data close to the coast and errors in waveform retracking) has been carried out, but none of these effects appear able to explain the trend increase. We further explored the possibility that it results from real physical processes. Change in wave conditions was investigated, but wave setup was excluded as a potential contributor because the magnitude was too low and too localized in the immediate vicinity of the shoreline. A preliminary model-based investigation about the contribution of coastal currents indicates that it could be a plausible explanation of the observed change in sea level trend close to the coast.

Atmospheric refraction effects in space vehicle tracking

1964 ◽  
Vol 54 (6B) ◽  
pp. 2185-2197
Author(s):  
R. A. Bowers
Keyword(s):  
Elevation Angle ◽  
Space Vehicle ◽  
Double Precision ◽  
Radio Waves ◽  
Atmospheric Refraction ◽  
Frequency Tracking ◽  
Analytic Expressions ◽  
Tracking Devices ◽  
Ray Bending ◽  
Derivatives Of

Abstract Refraction of radio waves in the atmosphere is becoming a topic of increasing concern to space scientists as tracking systems of extremely high precision are put into operation. Already ray bending and retardation of signal are many times greater than instrumental inaccuracies in measuring arrival time and elevation angle at the various tracking sites. A number of methods are presently in use for computation of the effects of atmospheric refraction on tracker measurements but all which have come to the writer's attention involve interpolation from tables, double precision methods on digital computers, or needlessly involved formulation. In this paper the mathematics of earthquake seismology are used to derive new analytic expressions for the effects of atmospheric refraction on the measurements of conventional radio frequency tracking devices. These expressions are concise, accurate, and rapidly evaluated in single precision. Expressions are also derived for the effects of refraction on time derivatives of the measurements, a subject which is virtually ignored in the literature.

scholarly journals Simulations of direct and reflected waves trajectories for in situ GNSS-R experiments

2014 ◽  
Vol 7 (1) ◽  
pp. 1001-1062 ◽  
Author(s):  
N. Roussel ◽  
F. Frappart ◽  
G. Ramillien ◽  
C. Desjardins ◽  
P. Gegout ◽  
...  
Keyword(s):  
Electromagnetic Waves ◽  
Specular Reflection ◽  
Elevation Angle ◽  
Test Site ◽  
Satellite System ◽  
Geometric Problem ◽  
Reflected Waves ◽  
The North ◽  
The Earth ◽  
Global Navigation Satellite

Abstract. The detection of Global Navigation Satellite System (GNSS) signals that are reflected off the surface, together with the reception of direct GNSS signals offers a unique opportunity to monitor water level variations over land and ocean. The time delay between the reception of the direct and the reflected signal gives access to the altitude of the receiver over the reflecting surface. The field of view of the receiver is highly dependent on both the orbits of the GNSS satellites and the configuration of the study site geometries. A simulator has been developed to determine the accurate location of the reflection points on the surface by modelling the trajectories of GNSS electromagnetic waves that are reflected on the surface of the Earth. Only the geometric problem have been considered using a specular reflection assumption. The orbit of the GNSS constellations satellite (mainly GPS, GLONASS and Galileo), and the position of a fixed receiver are used as input. Three different simulation modes are proposed depending on the choice of the Earth surface (local sphere or ellipsoid) and the consideration of topography likely to cause masking effects. Atmospheric delay effects derived from adaptive mapping functions are also taken into account. This simulator was developed to determine where the GNSS-R receivers should be located to monitor efficiently a given study area. In this study, two test sites were considered. The first one at the top of the Cordouan lighthouse (45°35'11'' N; 1°10'24'' W; 65 m) and the second one in the shore of the Geneva lake (46°24'30'' N; 6°43'6'' E, with a 50 m receiver height). This site is hidden by mountains in the South (altitude up to 2000 m), and overlooking the lake in the North (altitude of 370 m). For this second test site configuration, reflections occur until 560 m from the receiver. The geometric differences between the positions of the specular reflection points obtained considering the Earth as a sphere or as an ellipsoid were found to be on average 44 cm for satellites elevation angle greater than 10° and 1 m for satellite elevation angle between 5° and 10°. The simulations highlight the importance of the DEM integration: differences with and without integrating the DEM were found to be about 3.80 m with the minimum elevation angle equal to 5° and 1.4 m with the minimum elevation angle set to 10°. The correction of the tropospheric effects on the signal leads to geometric differences about 24 m maximum for a 50 m receiver height whereas the maximum is 43 cm for a 5 m receiver height. These errors deeply increase with the receiver height. By setting it to 300 m, the geometric errors reach 103 m for satellite elevation angle lower than 10°. The tests performed with the simulator presented in this paper highlight the importance of the choice of the Earth representation and also the non-negligible effect of the troposphere on the specular reflection points positions. Various outputs (time-varying reflection point coordinates, satellites positions and ground paths, wave trajectories, Fresnel first surfaces, etc.) are provided either as text or KML files for a convenient use.

scholarly journals Impacts of forest spatial structure on variation of the multipath phenomenon of navigation satellite signals

2019 ◽  
Vol 61 (1) ◽  
pp. 3-21 ◽  
Author(s):  
Michał Brach ◽  
Krzysztof Stereńczak ◽  
Leszek Bolibok ◽  
Łukasz Kwaśny ◽  
Grzegorz Krok ◽  
...  
Keyword(s):  
Forest Structure ◽  
Ground Truth ◽  
Satellite System ◽  
Forest Stand ◽  
Navigation Satellite ◽  
Radio Waves ◽  
Ground Truth Data ◽  
Significant Difference ◽  
Gnss Measurements ◽  
Global Navigation Satellite

AbstractThe GNSS (Global Navigation Satellite System) receivers are commonly used in forest management in order to determine objects coordinates, area or length assessment and many other tasks which need accurate positioning. Unfortunately, the forest structure strongly limits access to satellite signals, which makes the positioning accuracy much weak comparing to the open areas. The main reason for this issue is the multipath phenomenon of satellite signal. It causes radio waves reflections from surrounding obstacles so the signal do not reach directly to the GNSS receiver’s antenna. Around 50% of error in GNSS positioning in the forest is because of multipath effect. In this research study, an attempt was made to quantify the forest stand features that may influence the multipath variability. The ground truth data was collected in six Forest Districts located in different part of Poland. The total amount of data was processed for over 2,700 study inventory plots with performed GNSS measurements. On every plot over 25 forest metrics were calculated and over 25 minutes of raw GNSS observations (1500 epochs) were captured. The main goal of this study was to find the way of multipath quantification and search the relationship between multipath variability and forest structure. It was reported that forest stand merchantable volume is the most important factor which influence the multipath phenomenon. Even though the similar geodetic class GNSS receivers were used it was observed significant difference of multipath values in similar conditions.

A distribution model of the GNSS code noise and multipath error considering both elevation angle and orbit type

2018 ◽  
Vol 233 (5) ◽  
pp. 1900-1915 ◽  
Author(s):  
Guochao Fan ◽  
Chengdong Xu ◽  
Jing Zhao ◽  
Xueen Zheng
Keyword(s):  
Prior Information ◽  
Elevation Angle ◽  
Satellite System ◽  
Distribution Model ◽  
Orbit Type ◽  
Integrity Monitoring ◽  
Multipath Error ◽  
Receiver Autonomous Integrity Monitoring ◽  
Orbit Types ◽  
Global Navigation Satellite

Commonly, the code noise and multipath error is considered to fully obey the Gaussian distribution. While in the cases with different elevation angles and orbit types, the assumption may be inappropriate. Based on an empirical study, by considering both the elevation angle and the orbit type, a new code noise and multipath distribution model is proposed to describe a more accurate code noise and multipath distribution in this paper. Actual code noise and multipath data from 10 observation stations during two months are researched, and the parameters and elevation angle range of code noise and multipath distribution model are determined. The code noise and multipath distribution model is verified to be more accurate than the model presented in the Global Navigation Satellite System Evolutionary Architecture Study report, according to the analysis on the code noise and multipath overbounding, position error overbounding, and the availability of receiver autonomous integrity monitoring. This model provides more accurate prior information for receiver autonomous integrity monitoring, especially its availability.

Positioning stability improvement with inter-system biases on multi-GNSS PPP

2018 ◽  
Vol 12 (3) ◽  
pp. 239-248 ◽  
Author(s):  
Byung-Kyu Choi ◽  
Hasu Yoon
Keyword(s):  
Precise Point Positioning ◽  
Elevation Angle ◽  
Satellite System ◽  
Comprehensive Analysis ◽  
Convergence Time ◽  
Dual Frequency ◽  
Position Accuracy ◽  
Satellite Visibility ◽  
Global Navigation Satellite ◽  
Accuracy And Stability

Abstract The availability of multiple signals from different Global Navigation Satellite System (GNSS) constellations provides opportunities for improving positioning accuracy and initial convergence time. With dual-frequency observations from the four constellations (GPS, GLONASS, Galileo, and BeiDou), it is possible to investigate combined GNSS precise point positioning (PPP) accuracy and stability. The differences between GNSS systems result in inter-system biases (ISBs). We consider several ISB values such as GPS-GLONASS, GPS-Galileo, and GPS-BeiDou. These biases are compliant with key parameters defined in the multi-GNSS PPP processing. In this study, we present a unified PPP method that sets ISB values as fixed or constant. A comprehensive analysis that includes satellite visibility, position dilution of precision, position accuracy is performed to evaluate a unified PPP method with constrained cut-off elevation angles. Compared to the conventional PPP solutions, our approach shows more stable positioning at a constrained cut-off elevation angle of 50 degrees.

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