GPS Signal Propagation Research Articles

Estimated Impacts Induced by The Magnetic Activity Index (Dst) on the Local Total Electronic Content (TEC) in Africa Equatorial Zone

The state of equatorial ionosphere has been studied from the determination of the Total Electron Content (TEC) based on the correction of errors propagation of GPS signals due to ionospheric disturbances using the dual frequency method. In our study, we considered tree stations of the equatorial area (adis, bjco and nklg) in January 2012. Firstly, the monthly survey of the TEC has revealed that the magnetic storm days coincide with the days that the TEC Rinex around 70 UCET. Secondly, the daily survey of the TEC reveals two TEC ( TEC/RINEX and the TEC/CODG) has revealed that during magnetics storms days, the interval between curves of TEC observed between 10: 00PM to 16:00PM (UT) is more important (around 10 UCET) when the Dst is strongly negative whatever the nature of the magnetic storm, and the interval between curves of TEC observed between 17:00 to 20:00PM (UT) is function of the nature of the magnetic storm.

Effect of Higher-Order Ionospheric Delay on Precise Orbit Determination of GRACE-FO Based on Satellite-Borne GPS Technique

Ionospheric delay is one of the main errors in precise orbit determination (POD) of Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) with satellite-borne GPS technique. Effective elimination or reduction of ionospheric delay can improve POD precision. For satellite-borne GPS dual-frequency data, the ionospheric-free linear combination is generally used to eliminate the first-order term, while igoring the influence of higher-order terms. To improve the POD precision of GRACE-FO, this paper presents an effective method to calculate higher-order ionospheric delay of GRACE-FO observation. Dual-frequency GPS receiver observation is used to calculate the total electron content on the signal propagation path. The magnetic field strength is calculated according to international geomagnetic reference field model, and the angle between the GPS signal propagation path and the geomagnetic field is calculated. Finally, the delays of second-order and third-order terms are calculated and introduced into GRACE-FO reduced-dynamic POD. The effect of higher-order ionospheric delay on POD of GRACE-FO is analyzed in detail. The results show that the influence of ionospheric higher-order term on satellite-borne GPS observation is in centimeter level. The orbit precision of GRACE-FO can be improved by adding higher-order ionospheric delay, with improvement order of sub-millimeter level.

GPS: User Position Calculation Including Advanced Troposphere Delay Modeling

Objective of this project is to analyze and mitigate troposphere delays induced in GPS signals, which can result in very large position errors while estimating user position. The standard models currently present do not take into account all the various set of parameters or elements of the troposphere that can cause a significant delay. This project also includes study of troposphere propagation delays that improve the understanding of GPS signal propagation through the troposphere during irregular conditions. This characteristic is very important as it can play crucial role in real time surveying, navigation, precision farming and positioning for emergency services. Due to the tropical nature of the Indian climate the troposphere delay can be observed significantly in India sub-continent. In order to accurately estimate delay troposphere in real time conditions is taken into account, which are provided by the Indian meteorological department, by their automatic weather surveillance systems. GPS data for stations in India is obtained from CORS data for Bangalore, from where we obtain the observation and navigation files used in the calculations. Obtained data is processed and run through various algorithms like least squares satellite position calculation, error mitigation and ray tracing algorithms to mitigate troposphere and better estimate user position. Apart from these algorithms this project also includes a study on various concepts/formulas that help in using the forecasted real time data to be used in snell’s law to estimate delay as part of ray tracing techniques. All the code development in this project is done using MATLAB by math works and GUI is developed for an easier interface. For analysis purposes the data is analyzed with and without the advanced mitigation techniques to show the improvement in position estimation using advanced troposphere mitigation techniques.

Assessing the Performance of GPS Precise Point Positioning Under Different Geomagnetic Storm Conditions during Solar Cycle 24.

The geomagnetic storm, which is an abnormal space weather phenomenon, can sometimes severely affect GPS signal propagation, thereby impacting the performance of GPS precise point positioning (PPP). However, the investigation of GPS PPP accuracy over the global scale under different geomagnetic storm conditions is very limited. This paper for the first time presents the performance of GPS dual-frequency (DF) and single-frequency (SF) PPP under moderate, intense, and super storms conditions during solar cycle 24 using a large data set collected from about 500 international GNSS services (IGS) stations. The global root mean square (RMS) maps of GPS PPP results show that stations with degraded performance are mainly distributed at high-latitude, and the degradation level generally depends on the storm intensity. The three-dimensional (3D) RMS of GPS DF PPP for high-latitude during moderate, intense, and super storms are 0.393 m, 0.680 m and 1.051 m, respectively, with respect to only 0.163 m on quiet day. RMS errors of mid- and low-latitudes show less dependence on the storm intensities, with values less than 0.320 m, compared to 0.153 m on quiet day. Compared with DF PPP, the performance of GPS SF PPP is inferior regardless of quiet or disturbed conditions. The degraded performance of GPS positioning during geomagnetic storms is attributed to the increased ionospheric disturbances, which have been confirmed by our global rate of TEC index (ROTI) maps. Ionospheric disturbances not only lead to the deteriorated ionospheric correction but also to the frequent cycle-slip occurrence. Statistical results show that, compared with that on quiet day, the increased cycle-slip occurrence are 13.04%, 56.52%, and 69.57% under moderate, intense, and super storms conditions, respectively.

Detection of plumes at Redoubt and Etna volcanoes using the GPS SNR method

Detection and characterization of volcanic eruptions is important both for public health and aircraft safety. A variety of ground sensors are used to monitor volcanic eruptions. Data from these ground sensors are subsequently incorporated into models that predict the movement of ash. Here a method to detect volcanic plumes using GPS signals is described. Rather than carrier phase data used by geodesists, the method takes advantage of attenuations in signal to noise ratio (SNR) data. Two datasets are evaluated: the 2009 Redoubt Volcano eruptions and the 2013/2015 eruptions at Mt. Etna. SNR-based eruption durations are compared with previously published seismic, infrasonic, and radar studies at Redoubt Volcano. SNR-based plume detections from Mt. Etna are compared with L-band radar and tremor observations. To place these SNR observations from Redoubt and Etna in context, a model of the propagation of GPS signals through both water/water vapor and tephra is developed. Neither water nor fine ash particles will produce the observed attenuation of GPS signals, while scattering caused by particles >1cm in diameter potentially could.

Modeling investigation of wet tropospheric delay error and precipitable water vapor content in Egypt

A set of 1092 radio soundings was performed at the Egyptian stations in the south of Egypt, near the Mediterranean Sea, and near the Red Sea in 2005. These measurements are mean monthly data that were used to determine the mean vertical profiles of water vapor pressure and its effect on GPS signal propagation (wet tropospheric delay) in the troposphere and lower stratosphere. Temperature data were corrected for errors due to radiation, heat exchange processes, and for the lag errors of the sensor. Due to temperature dependence and other dry bias effects, the humidity errors were also taken into account. The results showed that partial water vapor pressure in Egypt varies from 6.43 to 23.19mb and decreases significantly with height. In addition, the quantity of water vapor pressure above 8km is negligible. Results showed that, in Egypt zenith wet delay varies from 66.84mm to 239.34mm. It can be concluded that, the best model to predict zenith wet tropospheric delay for the atmospheric conditions of Egypt is the Saastamoinen model with a mean error of 11mm and rms of 3.12mm.

Ionosphere influence on success rate of GPS ambiguity resolution in a satellite formation flying

Satellite formation flying is one of the most promising technologies for future space missions. The distribution of sensors and payloads among different satellites provides more redundancy, flexibility, improved communication coverage, among other advantages. One of the fundamental issues in spacecraft formation flying is precise position and velocity determination between satellites. For missions in low Earth orbits, GPS system can meet the precision requirement in relative positioning, since the satellite dynamics is modeled properly. The key for high accuracy GPS relative positioning is to resolve the ambiguities to their integer values. Ambiguities resolved successfully can improve the positioning accuracy to decimetre or even millimetre-level. So, integer carrier phase ambiguity resolution is often a prerequisite for high precision GPS positioning. The determination of relative position was made using an extended Kalman filter. The filter must take into account imperfections in dynamic modeling of perturbations affecting the orbital flight, and changes in solar activity that affects the GPS signal propagation, for mitigating these effects on relative positioning accuracy. Thus, this work aims to evaluate the impact of ionosphere variation, caused by changes in solar activity, in success rate of ambiguity resolution. Using the Ambiguity Dilution of Precision (ADOP) concept, the ambiguity success rate is analyzed and the expected precision of the ambiguity-fixed solution is calculated. Evaluations were performed using actual data from GRACE mission and analyzed for their performance in real scenarios. Analyses were conducted in different configurations of relative position and during different levels of solar activity. Results bring the impact of various disturbances and modeling of solar activity level on the success rate of ambiguity resolution.

Angular Distributions of Discrete Mesoscale Mapping Functions

The paper presents the results of analyses of numerical experiments concerning GPS signal propagation delays in the atmosphere and the discrete mapping functions defined on their basis. The delays were determined using data from the mesoscale non-hydrostatic weather model operated in the Centre of Applied Geomatics, Military University of Technology. A special attention was paid to investigating angular characteristics of GPS slant delays for low angles of elevation. The investigation proved that the temporal and spatial variability of the slant delays depends to a large extent on current weather conditions.

Simulating the Impact of Refractive Transverse Gradients Resulting From a Severe Troposphere Weather Event on GPS Signal Propagation

In this study, the effects of transverse refractive gradients in the ionosphere and in the lower atmosphere on GPS signal paths for both ground-based receivers and receivers on board low Earth orbital satellites are examined. A three-dimensional numerical ray tracing technique, based on geometrical optics, together with the models of the ionosphere, lower atmosphere, and magnetic field, are used to simulate GPS signal propagation. The average transverse refractive gradients were determined from a tropospheric storm event over Melbourne, Australia, on 6th of March, 2010. The traditional GPS ionospheric and atmospheric retrieval methods assume spherical stratification of the refractivity in the atmosphere and typically do not take into consideration the transverse refractivity gradients acting on the GPS signals. The transverse displacements of the GPS signal paths are calculated for both ground-based stations and for low Earth orbit radio occultation paths.

A comparative study of zenith tropospheric delay and precipitable water vapor estimates using scientific GPS processing software and web based automated PPP service

The zenith tropospheric delay (ZTD) is a significant error source which affects the GPS signal propagation time. ZTD time series can directly or indirectly reflect the weather variations. In geodetic studies their computation is important since it improves position accuracy. Sophisticated software packages using network data of ground-based GPS receivers are used for this purpose. During the last years, various web based precise point positioning (PPP) services can provide position solutions. Additional products, such as ZTD estimates, can be derived both from PPP as well as from network solutions. Research institutes and laboratories like JPL provide similar services. This study’s objective is twofold. In a first instance we used the Bernese and GAMIT software packages and the PPP service via the JPL webpage to estimate ZTD values every hour for a period of one month. We selected a geographical area in Greece, where seasonal weather variations are frequent and GPS permanent station infrastructure is available. The estimated ZTD values derived from GPS processing for a single station were compared with the ZTD estimates derived directly from the Saastamoinen model using meteorological data from a co-located meteorological sensor as input to this model. The results show an rms agreement of about 45 mm. The second scope of this study is to compare precipitable water (PW) values between different processing schemes. For this purpose, we used the derived zenith wet delay estimates of each processing scheme and a global formula for the computation of the weighted mean temperature of the atmosphere for our area of study. The rms differences between the web PPP solution and the Bernese derived estimates were 0.35 mm. The rms of the differences between and the web PPP solution and the GAMIT derived estimates of PW were 1.67 mm. We conclude that this difference follows from the zenith hydrostatic delay component that needs to be properly modeled when high accuracy results are required.

The research on measurement and prediction methods of multipath error dispersion in instrumental satellite landing system

The results of research of multipath GPS and GLONASS signal propagation errors while using the standard code-phase filter are provided. An estimate of complex filtering influence on multipath error is performed. The algorithms for detection of interference area with dangerous reflections are designed.

Canonical transform method for GPS/LEO radio occultation

Under the atmospheric multipath conditions, both canonical transform (CT) and full spectrum inversion (FSI) method can solve the problem of calculating bending angle profiles within the multipath area. The atmospheric propagation of GPS signals under atmospheric multipath conditions is simulated using multiple phase screens (MPS) technique. Bending angle profiles computed by CT method are compared with corresponding solutions to Abel integral (taken as the true value). The results show that CT method is close to the true value in the multipath area. The retrieval accuracy of CT method is degraded to some extent when Gaussian noises are added to the phase of simulated signal. About 4500 COSMIC (Constellation Observing System for Meteorology, Ionosphere and Climate) atmPhs profiles from DOY (day of year) 71 to DOY 73 in 2007 are retrieved by CT method. Statistical comparisons of the retrieved refractivity profiles, together with atmPrf data (retrieved by FSI method), with those from corresponding ECMWF (European Centre for Medium-Range Weather Forecasts) analysis show that CT method contains greater systematic negative bias than atmPrf data below 5 km. A possible reason is that the signal aperture is decreased for back-propagating the signal from LEO position to the back-propagation plane in CT method. The small aperture means low accuracy in the refractivity. The influence of signal truncation on both retrieval accuracy and occultation number is also discussed.

Modeling low elevation GPS signal propagation in maritime atmospheric ducts

Using the parabolic wave equation (PWE) method, we model low elevation GPS L1 signal propagation in maritime atmospheric ducts. To consider sea surface impedance, roughness, and the effects of earth's curvature, we propose a new initial field model for the GPS PWE split-step solution. On the basis of the comparison between the proposed model and the conventional initial field model for a smooth, perfectly conducting sea surface on a planar earth, we conclude that both the amplitude and phase of the initial field are influenced by surface impedance and roughness, and that the interference behavior between direct and reflected GPS rays is affected by earth's curvature. The performance of the proposed model is illustrated with examples of low elevation GPS L1 signal propagation in three types of ducts: an evaporation duct, a surface-based duct, and an elevated duct. The GPS PWE is numerically implemented using the split-step discrete mixed Fourier transform algorithm to enforce impedance-type boundary conditions at the rough sea surface. Because the GPS signal is right hand circularly polarized, we calculate its power strength by combining the propagation predictions of the horizontally and the vertically polarized components. The effects of the maritime atmospheric ducts on low elevation GPS signal propagation are demonstrated according to the presented examples, and the potential applications of the GPS signals affected by ducts are discussed.

Magneto‐ionic polarization and GPS signal propagation through the ionosphere

Recent progress in high‐precision GPS measurements research and applications leads to the study of higher‐order ionosphere effects on GPS signal propagation. This paper focuses on second‐order ionospheric effects, which are influenced by the presence of the Earth's magnetic field. Due to the presence of Earth's magnetic field, GPS signals may propagate through the ionosphere in two distinct modes: the ordinary mode and the extraordinary mode. These two modes correspond to different refractive indices, and the difference between these refractive indices affects the computation of the second‐order error introduced by the ionosphere to GPS code and carrier phase approximations. The first objective of this paper is to clarify a misconception about the different modes of GPS signal propagation through the ionosphere: although the GPS signal is predominantly right‐hand circularly polarized, it may propagate through the ionosphere in either the ordinary or the extraordinary mode. The second objective of this paper is to analyze the impact of the different modes of propagation on GPS solutions at different geographical locations.

Higher-order ionospheric error at Arecibo, Millstone, and Jicamarca

[1] The ionosphere is a dominant source of Global Positioning System receiver range measurement error. Although dual-frequency receivers can eliminate the first-order ionospheric error, most second- and third-order errors remain in the range measurements. Higher-order ionospheric error is a function of both electron density distribution and the magnetic field vector along the GPS signal propagation path. This paper expands previous efforts by combining incoherent scatter radar (ISR) electron density measurements, the International Reference Ionosphere model, exponential decay extensions of electron densities, the International Geomagnetic Reference Field, and total electron content maps to compute higher-order error at ISRs in Arecibo, Puerto Rico; Jicamarca, Peru; and Millstone Hill, Massachusetts. Diurnal patterns, dependency on signal direction, seasonal variation, and geomagnetic activity dependency are analyzed. Higher-order error is largest at Arecibo with code phase maxima circa 7 cm for low-elevation southern signals. The maximum variation of the error over all angles of arrival is circa 8 cm.

A case study of using Raman lidar measurements in high-accuracy GPS applications

This paper investigates the impact of rapid small-scale water vapor fluctuations on GPS height determination. Water vapor measurements from a Raman lidar are used for documenting the water vapor heterogeneities and correcting GPS signal propagation delays in clear sky conditions. We use data from four short observing sessions (6 h) during the VAPIC experiment (15 May–15 June 2004). The retrieval of wet delays from our Raman lidar is shown to agree well with radiosonde retrievals (bias and standard deviation (SD) were smaller than 1 and 2.8 mm, respectively) and microwave radiometers (from two different instruments, bias was 6.0/−6.6 mm and SD 1.3/3.8 mm). A standard GPS data analysis is shown to fail in accurately reproducing fast zenith wet delay (ZWD) variations. The ZWD estimates could be improved when mean post-fit phase residuals were removed. Several methodologies for integrating zenith lidar observations into the GPS data processing are also presented. The final method consists in using lidar wet delays for correcting a priori the GPS phase observations and estimating a scale factor for the lidar wet delays jointly with the GPS station position. The estimation of this scale factor allows correcting for a mis-calibration in the lidar data and provides in the same way an estimate of the Raman lidar instrument constant. The agreement of this constant with an independent determination using radiosonde data is at the level of 1–4%. The lidar wet delays were derived by ray-tracing from zenith pointing measurements: further improvement in GPS positioning is expected from slant path lidar measurements that would properly account for water vapor anisotropy.

Assessment of second‐order ionosphere error in GPS range observables using Arecibo incoherent scatter radar measurements

The second‐order ionosphere error in GPS range measurements is determined by the electron densities and the geomagnetic field projection onto the GPS signal propagation direction along the GPS signal propagation path. It can be a delay or an advancement error. This paper presents the second‐order error analysis based on an extensive collection of electron density profiles measured by the Arecibo incoherent scatter radar and geomagnetic field vectors generated using the International Geomagnetic Reference Field model. The results indicate that the 56–500 km altitude range contributes a maximum of −1.1 cm for GPS L1 signals arriving from the zenith at Arecibo. For signals coming from the north and south at 10 degree elevation angles, the maximum errors are 0.9 cm and −3.4 cm, respectively. The maximum of the mean values of the second‐order error computed using the entire data set are −0.55 cm, 0.48 cm, and −1.74 cm for a signal arriving from the zenith, from the north at 10 degrees elevation, and from the south at 10 degrees elevation, respectively. The paper also discusses the diurnal patterns and geomagnetic activity dependency of the second‐order error. Finally, the International Reference Ionosphere model is used to obtain an upper bound estimation of error contributions from the 500–2000 km altitude range.

A Note on the Group Delay and Phase Advance Phenomenon Associated with GPS Signal Propagation through the Ionosphere

The propagation of a GPS signal through the ionosphere causes a group delay in the code signal and an advance of equal magnitude in the carrier signal. This paper explains this phenomenon by extending Jorgensen's derivation for ionospheric effects on a carrier signal modulated by a single-frequency sinusoidal modulation. The explanation is based on an inverse Fourier transform model of the GPS signal at the GPS receiver antenna output and the expression for the delay of a single-frequency wave in the medium. It is much easier to understand than more common explanations in the literature that involve deriving group and phase velocities in the time–space domain.

Estimation of Satellite-Based Augmentation System Grid Size at Low Latitudes in the Indian Zone

The Total Electron Content (TEC) measured from a station situated near the northern crest of the equatorial anomaly is compared with that obtained from models such as the Parameterized Ionospheric Model (PIM 1.6) and International Reference Ionosphere (IRI-95) for well over one solar cycle (1977–1990). The limitations of conversion from vertical to slant TEC and vice versa as required for GPS ionospheric corrections in the equatorial region are discussed. It is found that the correspondence among the vertical TEC at the ionospheric pierce point, geometrically (sec χ) converted slant TEC, and slant TEC along a GPS signal propagation path becomes poor for elevation angles of less than 80 deg. Based on this finding, an optimum grid size for reliable operation of the Satellite-Based Augmentation System (SBAS) in the Indian subcontinent (GAGAN, or GPS and Geo Augmented Navigation) is estimated. The suggested grid size is much smaller than the standard 5 × 5 deg.

Simulation studies of GPS radio occultation measurements

The atmospheric propagation of GPS signals under multipath conditions and their detection are simulated. Using the multiple phase screen method, C/A‐code modulated L1 signals are propagated through a spherically symmetric refractivity field derived from a high‐resolution radio sonde observation. The propagated signals are tracked by a GPS receiver implemented in software and converted to refractivity profiles by the canonical transform technique and the Abel inversion. Ignoring noise and assuming an ideal receiver tracking behavior, the true refractivity profile is reproduced to better than 0.1% at altitudes above 2 km. The nonideal case is simulated by adding between 14 and 24 dB of Gaussian white noise to the signal and tracking the signal with a receiver operating at 50 and 200 Hz sampling frequency using two different carrier phase detectors. In the upper troposphere and stratosphere the fractional refractivity retrieval error is below 0.3% for 50 Hz sampling and below 0.15% for 200 Hz sampling. In the midtroposphere down to altitudes of about 2 km, phase‐locked loop tracking induces negative fractional refractivity biases on the order of −1 to −2% at 50 Hz sampling frequency. Modifications to the receiver tracking algorithm significantly improve the retrieval results. In particular, replacing the carrier loop's two‐quadrant phase extractor with a four‐quadrant discriminator reduces the refractivity biases by a factor of 5; increasing the sampling frequency from 50 to 200 Hz gains another factor of 2.