Dual-frequency GPS Data Research Articles

The implementation of dual frequency positioning for ionospheric effects correction

Brazil is located in a tropical region near the equator line, where the solar incidence is more intense. For this reason, the effect of ionospheric refraction on satellite signals is more expressive. In order to mitigate this effect, the use of dual frequency positioning technique is effective in the position solution, reducing distortions caused by ionospheric refraction. In this article, dual frequency GPS data was analyzed, in order to prove its effectiveness in correcting the ionospheric error in comparison with single frequency GPS data.

A method of real-time long-baseline time transfer based on the PPP-RTK

Long-baseline time transfer can nowadays reach rather high frequency stability based on post-processed batch least-squares adjustment using the Precise Point Positioning (PPP) or Integer-PPP (IPPP) methods. For real-time PPP users, time transfer results are degraded due to the filter-based processing mode, and the degraded accuracy of the real-time satellite orbits and clocks compared to the final ones. The Real-Time Kinematic (RTK) time transfer can significantly reduce the satellite-related errors, but has limits on the baseline length similar to the RTK positioning. Also, the delivery of raw observations instead of State-Space Representation (SSR) products could result in pressure on data transfer and difficulties related to latency and prediction. In this study, the PPP-RTK technique, which combines the advantages of the PPP and the RTK methods, is tested for real-time long-baseline time transfer. As an alternative approach to the above two methods, it allows for the time transfer of long baselines, while not relying on external high-sampling and high-precision satellite clocks. By delivering the satellite clocks and satellite phase biases produced within the PPP-RTK regional network, time differences can be estimated between users and the reference network station, with which stable time transfer between users separated by long baselines can be realized. Using dual-frequency GPS and Galileo data, the PPP-RTK time transfer is tested using approximately a thousand-kilometer-scale network in Europe. The time transfer results between two hydrogen masers, i.e., those on the 884 km baseline BRUX-ONSA and the 920 km baseline WTZR-ONSA, are computed. At an averaging time of 105 s, Modified Allan Deviation (MDEV) at the level of sub-10-15 to 10-15 can be reached when processing the user coordinates in the station fixed, static, or kinematic modes. The median clock residuals can converge to 1 ns and 0.3 ns within 2 min and 15 min, respectively, in the kinematic mode, while in the static and fixed modes the convergence times are shorter. With the augmentation of 150 Low Earth Orbit (LEO) satellites having simulated observations, the clock residuals can converge to 1 ns and 0.3 ns within 30 s and 3.5 min, respectively, for all the three estimation modes.

A single station ionospheric empirical model using GPS-TEC observations based on nonlinear least square estimation method

This article presents a nonlinear least square estimation method based on the continuous TEC values at single stations from long-time recorded dual-frequency GPS data of International GNSS Service (IGS) stations to facilitate single-station empirical total electron content (TEC) modelling. The Nonlinear Polynomial GPS-TEC Model (NPGTM) at each of the four different stations (namely Ellesmere Island (alrt), Canada; Lhasa (lhaz), China; New Norcia (nnor), Australia; and East Ongle Island (syog) over the Antarctica) was constructed by the nonlinear least square estimation method using GPS-TEC data from 2005 to 2016 and validated with 2017–2018 datasets over the same locations in the dependencies of universal time (UT), solar activity (PI index), geomagnetic activity (Ap index) and day of year (DOY). The model was designed for quiet and moderate geomagnetic conditions (i.e. Ap ≤ 30 and F10.7 ≤ 160 sfu). Compared with IRI-2016 model values in 2017 to 2018, the accuracy of NPGTM model values is improved by 132% in high latitude area, 84% in medium latitude area and 88% in low latitude area. Evaluation results show that the NPGTM model values are in good agreement with GPS-TEC observations in high, medium and low latitude regions, which is much better than the IRI-2016 model values.

Evaluation of single-frequency receivers for studying crustal deformation at the longitudinal Valley fault, eastern Taiwan

Applications of low-cost single-frequency continuous GPS receivers for monitoring volcano and landslide activities as well as to complement dual-frequency receivers have been demonstrated to produce stable and accurate positioning. In studies of crustal deformation, the relative distance between monitoring stations may vary from several kilometers to tens of kilometers, hence the differential single-frequency observations cannot model the ionospheric delay or other distance dependent errors. The 55 low-cost single-frequency continuous stations have been deployed together with 52 continuous dual-frequency stations in southeastern Taiwan since 2008. All of the single-frequency stations have applied corrections using dual-frequency stations to eliminate the distance dependent errors. Comparing velocity estimates from 8 co-located, the differences in horizontal and vertical components are less than 3 mm/yr and 6 mm/yr, respectively. Our study shows that the combination of single- and dual-frequency GPS data can provide robust results to study the fault slip behavior on the Longitudinal Valley fault.

Analysis of Total Electron Content (TEC) Near Real Time Using Dual Frequency GPS Data (Study Case: Surabaya)

Ionosphere is part of the atmospheric layer located between 50 to 1000 km above the earth's surface which consists of electrons that can influence the propagation of electromagnetic waves in the form of additional time in signal propagation, this depends on Total Electron Content (TEC) in the ionosphere and frequency GPS signal. In high positioning precision with GPS, the effect of the ionosphere must be estimated so that ionospheric correction can be determined to eliminate the influence of the ionosphere on GPS observation. Determination of ionospheric correction can be done by calculating the TEC value using dual frequency GPS data from reference stations or models. In making the TEC model, a polynomial function is used for certain hours. The processing results show that the maximum TEC value occurs at noon at 2:00 p.m. WIB for February 13, 2018 with a value of 35,510 TECU and the minimum TEC value occurs in the morning at 05.00 WIB for February 7, 2018 with a value of 2,138 TECU. The TEC model spatially shows the red color in the area of Surabaya and its surroundings for the highest TEC values during the day around 13.00 WIB to 16.00 WIB.

Precision analysis of troposphere sensing using GPS single-frequency signals

Various studies have been performed to investigate the accuracy of troposphere zenith wet delays (ZWDs) determined from GPS. Most of these studies use dual-frequency GPS data of large-scale networks with long baselines to determine the absolute ZWDs. For small-scale networks the estimability of the absolute ZWDs deteriorates due to high correlation between the solutions of the ZWDs and satellite-specific parameters as satellite clocks. However, as relative ZWDs (rZWDs) can always be estimated, irrespective of the size of the network, it is of interest to understand how the large-scale network rZWD-performance of dual-frequency GPS using an ionosphere-float model compares to the small-scale network rZWD-performance of single-frequency GPS using an ionosphere-weighted model. In this contribution such an analysis is performed using undifferenced and uncombined network parametrization modelling. In this context we demonstrate the ionosphere weighted constraints, which allows the determination of the rZWDs independent from signals on the second frequency. Based on an analysis of both simulated and real data, it is found that under quiet ionosphere conditions, the accuracy of the single-frequency determined rZWDs in the ionosphere-weighted network is comparable to that of the large-scale dual-frequency network without ionospheric constraints. Making use of the real data from two baselines of 15 days, it was found that the absolute differences of the rZWDs applying the two strategies are within 1 cm in over 90% and 95% of the time for ambiguity-float and -fixed cases, respectively.

Geometry-based cycle slip and data gap repair for multi-GNSS and multi-frequency observations

Carrier phase observations are commonly used in high-precision GNSS positioning applications, such as precise point positioning and real-time kinematic positioning, due to their millimeter precisions. Hence, it is a crucial module to handle cycle slips and short-time signal interruptions when phase observations are involved, which otherwise will lead to a time-consuming re-initialization. With the gradual GNSS modernization, jointly using observations from multi-GNSS and multi-frequency tends to be a hotspot application pattern for high-accuracy positioning. In this contribution, we will present a geometry-based ionosphere-weighted approach to estimate integer cycle slips in an integrated adjustment, which is universally applicable to arbitrary number of frequencies of GNSS systems. Different from the traditional methods, where cycle slips are processed in a satellite-by-satellite mode based on geometry-free combinations, we take full advantage of the mutual correlations between multi-frequency, between satellites and between systems embodied in the receiver coordinate parameters. When it is unable to effectively fix the full set of cycle slips, we further propose to partially fix the subset of cycle slips that can be reliably fixed. Performance of the proposed method is validated by extensive experiments using undifferenced dual/triple-frequency BDS data, dual-frequency GPS data and triple-frequency BDS $$+$$ dual-frequency GPS data. The results show that the proposed method can effectively fix continuous cycle slips in case of small/large sampling intervals and connect the data gaps up to a few minutes with high success rates.

Precise orbit determination of the Fengyun-3C satellite using onboard GPS and BDS observations

The GNSS Occultation Sounder instrument onboard the Chinese meteorological satellite Fengyun-3C (FY-3C) tracks both GPS and BDS signals for orbit determination. One month’s worth of the onboard dual-frequency GPS and BDS data during March 2015 from the FY-3C satellite is analyzed in this study. The onboard BDS and GPS measurement quality is evaluated in terms of data quantity as well as code multipath error. Severe multipath errors for BDS code ranges are observed especially for high elevations for BDS medium earth orbit satellites (MEOs). The code multipath errors are estimated as piecewise linear model in 2{^{circ }}times 2{^{circ }} grid and applied in precise orbit determination (POD) calculations. POD of FY-3C is firstly performed with GPS data, which shows orbit consistency of approximate 2.7 cm in 3D RMS (root mean square) by overlap comparisons; the estimated orbits are then used as reference orbits for evaluating the orbit precision of GPS and BDS combined POD as well as BDS-based POD. It is indicated that inclusion of BDS geosynchronous orbit satellites (GEOs) could degrade POD precision seriously. The precisions of orbit estimates by combined POD and BDS-based POD are 3.4 and 30.1 cm in 3D RMS when GEOs are involved, respectively. However, if BDS GEOs are excluded, the combined POD can reach similar precision with respect to GPS POD, showing orbit differences about 0.8 cm, while the orbit precision of BDS-based POD can be improved to 8.4 cm. These results indicate that the POD performance with onboard BDS data alone can reach precision better than 10 cm with only five BDS inclined geosynchronous satellite orbit satellites and three MEOs. As the GNOS receiver can only track six BDS satellites for orbit positioning at its maximum channel, it can be expected that the performance of POD with onboard BDS data can be further improved if more observations are generated without such restrictions.

A new differential code bias (C1–P1) estimation method and its performance evaluation

The current satellite clock products are computed using the ionosphere-free phase (L1/L2) and code (P1/P2) observations. Thus, if users conduct undifferenced positioning using these clock products together with C1 and P2 observations, the differential code bias (DCB) (C1---P1) should be properly compensated. The influence of DCB (C1---P1) on the undifferenced ambiguity solutions is investigated. Based on the investigation, we propose a new DCB (C1---P1) estimation method. Using it, the satellite DCB (C1---P1) can be computed. A 30-day (DOY 205---234, 2012) dual-frequency GPS data set is processed to estimate the DCB (C1---P1). Comparing the estimated results with that of IGS DCB products, the accuracy is better than 0.13 m. The performances of DCB (C1---P1) in the code-based single-point positioning, precise point positioning (PPP) convergence and wide-lane uncalibrated phase delay (UPD) estimation are investigated using the estimated DCB (C1---P1). The results of the code-based single-point positioning show that the influence of DCB (C1---P1) on the up direction is more evident than on the horizontal directions. The accuracy is improved by 50 % and reaches to decimeter level with DCB (C1---P1) application. The performance of DCB (C1---P1) in PPP shows that it can accelerate PPP convergence through improving the accuracy of the code observation. The computed UPD values show that influence of DCB (C1---P1) on UPD of each satellite is different, and some values are larger than 0.3 cycles.

Traveling ionospheric disturbances triggered by the 2009 North Korean underground nuclear explosion

Abstract. Underground nuclear explosions (UNEs) can induce acoustic-gravity waves, which disturb the ionosphere and initiate traveling ionospheric disturbances (TIDs). In this paper, we employ a multi-step and multi-order numerical difference method with dual-frequency GPS data to detect ionospheric disturbances triggered by the North Korean UNE on 25 May 2009. Several International GNSS Service (IGS) stations with different distances (400 to 1200 km) from the epicenter were chosen for the experiment. The results show that there are two types of disturbances in the ionospheric disturbance series: high-frequency TIDs with periods of approximately 1 to 2 min and low-frequency waves with period spectrums of 2 to 5 min. The observed TIDs are situated around the epicenter of the UNE, and show similar features, indicating the origin of the observed disturbances is the UNE event. According to the amplitudes, periods and average propagation velocities, the high-frequency and low-frequency TIDs can be attributed to the acoustic waves in the lower ionosphere and higher ionosphere, respectively.

Georeferencing experiments with UAS imagery

Abstract. Comparing typical airborne mapping systems with Unmanned Airborne Systems (UAS) developed for mapping purposes, there are several advantages and disadvantages of both systems. The unquestionable benefits of UAS are the much lower costs of equipment and the simple operation; though, the regulations to fly UAS greatly vary by country. Low cost, however, means small sensor size and low weight, thus, sensors usually lack the quality, negatively impacting the accuracy of UAS data and, consequently, any derived mapping products. This work compares the performance of three different positioning approaches used for UAS image geolocation. The first one is based on using dual-frequency GPS data, post-processed in kinematic mode. The second approach uses the single frequency, code only GPS data that was acquired and processed by a geotagger, attached to mapping camera. Finally, the third one employs indirect image georeferencing, based on aerial triangulation using ground controls. As expected, the quality of data provided by the inexpensive GPS receiver (geotagger) is not suitable for mapping purposes. The two other approaches provided similar and reliable results, confirming that commonly used indirect georeferencing, which usually assures good solution, can be replaced by direct georeferencing. The latter technique results not only in reduction of field work, e.g. Ground Control Points (GCPs) surveying, but is appropriate for use with other sensors, such as active imaging technology, LiDAR, further extending UAS application potential.

Decimeter-level positioning in dynamic applications with a single GPS receiver

Although the ongoing GPS modernization studies provide better autonomous positioning accuracy (i.e. a few meters), this accuracy level is not enough for many surveying applications. Depending on the developments in satellite-based positioning technology and GNSS data availability and analysis techniques, some new approaches and algorithms have been proposed in the world of global positioning to enhance the autonomous positioning accuracy. In this study, a precise positioning technique, named “self-differential method”, is introduced using the dual frequency GPS data collected by a single geodetic-grade GPS receiver. The technique uses iono-free carrier phase observations, precise satellite ephemerides and satellite clock data. In order to validate the performance of the introduced method in a dynamic environment two kinematic tests were conducted at Halic Bay in Istanbul, Turkey. The results show that the method is capable of achieving decimeter level of positioning accuracy without the need of an additional reference station or any other data while reducing the field operational costs.

Urban area GPS positioning accuracy using ASG-EUPOS POZGEO service as a function of session duration

ABSTRACT GNSS observations carried out in a network of Continuously Operating Reference Station (CORS) are a complex systems which offer post-processing as well as corrections sent in realtime. In Poland, such a system has been in operation since June 2008, known as the Polish Active Geodetic Network (ASG-EUPOS). Usually the measurements performed in real time characterized lower accuracy than static measurements. For users who demand the highest precision results the post-processing services are provided. The paper presents an analysis of the position determination accuracy using ASG-EUPOS POZGEO service. It is well known that the final accuracy is e.g. the measuring conditions, time of observations or number of measured frequencies dependent. We processed 4 consecutive days of GPS data to determine how the accuracy of derived positional coordinates depends on the length of the observing session, the characteristics of horizon visibility on points and the used in post-processing observations (L1 or L1+L2). The POZGEO results show that horizontal accuracies of about 1-2 cm and vertical accuracies of 4 cm are achievable provided 0.5 hours dual frequency GPS data. The accuracy clearly decreases for point measured under conditions of strongly limited satellite availability

Geodetic observations and modeling of time-varying deformation at Taal Volcano, Philippines

We investigate active crustal deformation patterns associated with magmatic activity at Taal Volcano, an active tholeiitic volcano located in southwestern Luzon, Philippines. We present comparisons of elastic and combined elastic–viscoelastic modeling results with deformation observed by continuous GPS measurements on and near the volcano. Continuous dual-frequency and single-frequency (L1) GPS data between 1998 and 2005 provide evidence for smoothly transitioning periods of inflation and deflation centered under the volcano. Within deformation phases that typically last 3–9months (with rates exceeding 200mmyr−1), prominent inflationary phases were observed in February–November 2000 and June 2004–March 2005. The 2000 period of inflation was characterized by up to 145mmyr−1 surface extension and 220mmyr−1 of uplift of the center of Volcano Island relative to the northern caldera rim, while the 2005 inflation was characterized by as much as 116mmyr−1 horizontal extension of the volcanic edifice and 180mmyr−1 uplift. Inversions of observed surface deformation to determine the source location points to a relatively stable spherical source, situated under Volcano Island's central crater, at depths of ~5km (based on the preferred Mogi model). Using this source geometry, we develop axisymmetric finite element models with annuli of concentric shells around the magma reservoir, embedded within a multi-layered elastic lithosphere. Using simply varying pressure histories as input, a variety of forward models are fit to the time history of continuously observed deformation for GPS stations located on Volcano Island. Though the inferred source geometry, volume and near-source rheological properties are non-unique, they represent more physically appropriate material properties than those assumed in simple elastic half-space models. The sources inferred using viscoelastic shell models suggest simpler pressure histories and reduced overall pressure changes, relative to equivalent elastic half-space models.

Validation of Approximation Techniques for Local Total Electron Content Mapping

The aim of this study was to assess the performance of several approximation techniques for ionospheric total electron content (TEC) mapping. Approximation techniques based on data-fitting with local or general two-dimensional polynomials, local planes or distance-dependent interpolation were applied and tested. For the ionosphere modeling, dual-frequency GPS data from Polish GBAS system (ASG-EUPOS) were used, and TEC was estimated together with hardware delays from phasesmoothed pseudoranges. Next, grids of vertical TEC values with spatial resolution of 0.25 degrees in both latitude and longitude were generated using the evaluated approximation techniques. Subsequently the grids were used to create regional TEC maps with 5-minute temporal resolution, and also to create ionospheric delay corrections for GPS positioning. The quality of the resulting ionospheric maps was tested twofold, firstly by comparison to high-quality CODE global ionosphere maps (GIM), which were generated using data from about 150 GPS sites of the International GNSS Service (IGS). Secondly, by creating double-differenced ionospheric delay corrections and comparing them to reference values derived from the reference network data processing. For the correction tests, two perpendicular baselines directed North-South (N-S) and West-East (W-E) and reaching up to 100 km were selected. The approximation methods were analyzed with a special emphasis on the diverse ionospheric conditions. For the testing, a quiet ionosphere day of 20 March 2012 and an active ionosphere day of 9 March 2012 were selected. The results show that the regional models properly represent the changing ionosphere, with the best results provided by data-fitting into local functions.

Enhanced Precise Point Positioning for GNSS Users

This paper summarizes the main results obtained during the development of an Enhanced Precise Point Positioning (EPPP) Global Navigation Satellite Systems multifrequency user algorithm. The main innovations include the application of precise ionospheric corrections to facilitate the resolution of undifferenced carrier phase ambiguities, ambiguity validation, and integrity monitoring. The performance of the EPPP algorithm in terms of accuracy, convergence time, and integrity is demonstrated with actual GPS and simulated Galileo data. This can be achieved with very limited bandwidth requirements for EPPP users (less than 300 b/s for dual-frequency GPS data).

Kinematic Precise Orbit Determination for LEO Satellites Using Space-borne Dual-frequency GPS Measurements

As a special approach to orbit determination for satellites with spaceborne GPS receivers, the kinematic Precise Orbit Determination (POD) is independent of any mechanical model (e.g., the Earth gravity field, atmospheric drag, solar radiation pressure, etc.), and thus especially suitable for the orbit determination of Low Earth Orbiting (LEO)satellites perturbed strongly bythe atmosphere. In this paper, based on the space-borne dual-frequency GPS data, we study the kinematic POD, discuss the pre-processing of the data, and construct an algorithm of zero-difference kinematic POD. Using the observational data from GRACE (Gravity Recovery And Climate Experiment) satellites covering the whole month of February 2008, we verify the effectiveness and reliability of this algorithm. The results show that the kinematic POD may attain an accuracy of about 5cm (with respect to satellite laser ranging data), which is at the same level as the dynamic and reduced-dynamic PODs

High Dimensional Integer Ambiguity Resolution: A First Comparison between LAMBDA and Bernese

The LAMBDA method for integer least-squares ambiguity resolution has been widely used in a great variety of Global Navigation Satellite System (GNSS) applications. The popularity of this method stems from its numerical efficiency and its guaranteed optimality in the sense of maximising the success probability of integer ambiguity estimation. In the past two decades, the LAMBDA method has been typically used in cases where the number of ambiguities is less than several tens. With the advent of denser network processing and the availability of multi-frequency, multi-GNSS systems, it is important to understand LAMBDA's performance in high dimensional spaces. In this contribution, we will address this issue using real GPS data based on the Bernese software. We have embedded the LAMBDA method into the Bernese software and compared their ambiguity resolution performances. Twelve day dual-frequency GPS data with a sampling interval of 30 s was used in the experiment, which was collected from a network of 19 stations in the Perth area of Western Australia with an average baseline length of 380 km. Different experimental scenarios were examined and tested with different observation spans, which represent the different ambiguity dimensions. The results showed that LAMBDA is still efficient even when the number of ambiguities is more than 100, and that the baseline repeatability obtained with the ambiguities resolved from the LAMBDA method agreed well with that of Bernese. Therefore, for future dense network processing, the easy-to-use LAMBDA method should be considered as an alternative to baseline-per-baseline methods as those used in e.g. the Bernese software.

Ionospheric perturbations associated with two recent major earthquakes (M>5.0)

In this paper, dual-frequency GPS data recorded at Varanasi (geographic latitude 25°16′ N, longitude 82°59′ E) have been analyzed to study the ionospheric perturbations in total electron content (TEC) due to two recent major earthquakes (M>5.0) whose main shocks occurred on 25 February and 12 March 2010. A monthly median of the TEC and associated inter-quartile range, upper bound and lower bound are utilized as a reference to identify abnormal signals during these two earthquakes. The results show anomalous depletions in the TEC. These pre-earthquake ionospheric anomalies appear within 6 days prior to the earthquakes. We have also analyzed the ELF and VLF spectra observed from the DEMETER micro-satellite above the epicenter of the earthquake to support the ionospheric anomalies prior to the earthquakes. A possible mechanism responsible for the ionospheric anomalies due to earthquakes is also discussed.

Application of ionospheric tomography inversion to GPS data to study ionospheric electron-density distribution over China

Abstract: Temporal variations of ionospheric electron-density (IED) distributions over China are inversed by applying the computerized ionospheric tomography (CIT) technique to dual-frequency GPS data of the Crustal Movement Observation Network of China (CMONOC) in 2003. Characteristics of the diurnal variations of IED, especially the development and disappearance of the equatorial anomaly structure and the variations of the ionospheric vertical structure, are investigated. The result shows that it is feasible to sound and investigate the temporal-spatial variations of IED by using CIT technique and the high-accuracy GPS data, but the accuracy and reliability are limited by insufficiency of GPS data, reconstruction methods, and CIT models.