Dual-frequency Global Positioning System Data Research Articles

Copernicus Sentinel–1 POD reprocessing campaign

Copernicus Sentinel–1 is a C-Band Synthetic Aperture Radar (SAR) satellite mission within the European Copernicus Programme. The two satellites Sentinel-1A and -1B were launched in April 2014 and 2016, respectively. The Copernicus POD (Precise Orbit Determination) Service is responsible for the determination of orbital and auxiliary products required by the Payload Data Ground Segment (PDGS). Precise orbits are determined based on the dual-frequency GPS (Global Positioning System) data delivered by dedicated geodetic-grade GPS receivers on-board the satellites. Several updates in the operational orbit determination were done during the years including an update of the GPS antenna reference point coordinates. The switch to GPS carrier phase ambiguity-fixing was a major improvement. A reprocessing of the entire mission span of both satellites became necessary to provide a consistent orbit time series for the mission based on state-of-the-art models and processing settings. Due to the lack of independent observation techniques, the Sentinel-1 orbit quality has been assessed by analysing processing metrics, orbit overlaps and orbit comparisons. For this purpose, members of the Copernicus POD Quality Working Group (QWG) provided reprocessed Sentinel-1 orbit time series based on their software packages and their orbit determination settings. A weighted average of all five delivered solutions - a combined orbit - serves as reference for the comparisons. The quality and reliability of this reference orbit depends among others on the number of available orbit solutions and whether a manoeuvre has been performed during the processed day or not. The mean orbit consistency between all orbit solutions is below 1 cm in 3D RMS for the entire mission time interval for both satellites. Only few days show inferior quality due to data gaps or orbit manoeuvres. Following this sophisticated validation process, the reprocessed Sentinel-1 orbits from the Copernicus POD Service have been made available to the user community.

A refined carrier-to-code levelling method for retrieving ionospheric measurements from dual-frequency GPS data

The retrieval of ionosphere measurements (IMs) constitutes the first key step in the process of ionospheric monitoring with the global positioning system (GPS). Carrier-to-code levelling (CCL) is one of the most widely used retrieval methods, mainly because of its simplicity and effectiveness. However, CCL-derived IMs have been proven to be susceptible to so-called levelling errors, which is mainly due to the presence of code multipath effects and the occurrence of short-term variability in receiver code biases (RCBs). To address these levelling errors, we propose a refined CCL (rCCL) method, in which the code multipath and RCB variations are jointly estimated as time-varying parameters and thus removed. Compared to the customary CCL method, this new method has two advantages. First, rCCL is able to exclude the effect of code multipath and time-varying RCBs from IMs, thereby greatly reducing the levelling errors of IM estimates. Second, the RCB variations are estimated for each individual code observation using a single receiver, allowing easy and effective calibration of the short-term variability in RCBs and the linear combination of, for instance, receiver differential code biases (rDCBs).

PPP-RTK based on undifferenced and uncombined observations: theoretical and practical aspects

A synthesis of two prevailing global navigation satellite system positioning technologies, namely the precise point positioning and the network-based real-time kinematic, results in the emergence of the PPP-RTK, enabling single-receiver users to achieve high positioning accuracy with reasonable timeliness through integer ambiguity resolution. The realization of PPP-RTK needs to accomplish two sequential tasks. The first task is to determine a class of corrections including, among others, the satellite phase biases (SPBs) at the network level. With these corrections, the second task, then, is to solve for the ambiguity-fixed, absolute position at the user level. In this contribution, we revisit three variants (geometry-free, geometry-fixed and geometry-plus-satellite-clock-fixed) of the undifferenced and uncombined PPP-RTK network model and then point out their implications for practical use. We also carry out a case study using multi-day, dual-frequency global positioning system data from the crustal movement observation network of China stations, aiming to figure out what are the most appropriate linear combinations of the SPBs to be transmitted to the users from the viewpoint of decorrelation, and to assess the static and kinematic positioning performance.

BeiDou Code Pseudorange Precision Estimation and Time Correlation Analysis from Trimble Net-R9 and ComNav 708 Receivers

Stochastic models describe the observation precisions and their correlations with each other and play an important role in reliable global navigation satellite system ambiguity resolution and precise positioning. However, the characteristics of BeiDou Navigation Satellite System (BDS) observations are still not clear at present. In general, the stochastic model used for BDS is based on empirical models from global positioning system (GPS) knowledge in most cases. In this paper, the zero-baseline dual-frequency GPS and BDS data with different sampling intervals are used to evaluate the precision and time correlation of the BDS code pseudorange observations. The results show that the precisions of BDS and GPS code measurements are almost of the same magnitude. However, the standard deviations of BDS measurements are larger than those of GPS measurements. Inclined geostationary orbit observations suffer from periodic error, which has been confirmed to be unaffected by multipath error in this paper. Traditional elevation-dependent models cannot work well for precise positioning for either GPS or BDS because the elevation dependencies of the two carrier frequencies’ pseudorange observations are not the same. Moreover, BDS observations have a significant time correlation, especially for geostationary orbit satellites. The time correlation coefficients are maintained at ~0.63–0.75 for different receiver types. Consequently, the BDS positioning residuals are significantly larger than those of GPS even if the observations have similar precision.

GPS receiver phase biases estimable in PPP-RTK networks: dynamic characterization and impact analysis

The integer ambiguity resolution enabled precise point positioning (PPP-RTK) has been proven advantageous in a wide range of applications. The realization of PPP-RTK concerns the isolation of satellite phase biases (SPBs) and other corrections from a network of Global Positioning System (GPS) reference receivers. This is generally based on Kalman filter in order to achieve real-time capability, in which proper modeling of the dynamics of various types of unknowns remains crucial. This paper seeks to gain insight into how to reasonably deal with the dynamic behavior of the estimable receiver phase biases (RPBs). Using dual-frequency GPS data collected at six colocated receivers over days 50–120 of 2015, we analyze the 30-s epoch-by-epoch estimates of L1 and wide-lane (WL) RPBs for each receiver pair. The dynamics observed in these estimates are a combined effect of three factors, namely the random measurement noise, the multipath and the ambient temperature. The first factor can be overcome by turning to a real-time filter and the second by considering the use of a sidereal filtering. The third factor has an effect only on the WL, and this effect appears to be linear. After accounting for these three factors, the low-pass-filtered, sidereal-filtered, epoch-by-epoch estimates of L1 RPBs follow a random walk process, whereas those of WL RPBs are constant over time. Properly modeling the dynamics of RPBs is vital, as it ensures the best convergence of the Kalman-filtered, between-satellite single-differenced SPB estimates to their correct values and, in turn, shortens the time-to-first-fix at user side.

TEC and Instrumental Bias Estimation of GAGAN Station Using Kalman Filter and SCORE Algorithm

The standalone Global Positioning System (GPS) does not meet the higher accuracy requirements needed for approach and landing phase of an aircraft. To meet the Category-I Precision Approach (CAT-I PA) requirements of civil aviation, satellite based augmentation system (SBAS) has been planned by various countries including USA, Europe, Japan and India. The Indian SBAS is named as GPS Aided Geo Augmented Navigation (GAGAN). The GAGAN network consists of several dual frequency GPS receivers located at various airports around the Indian subcontinent. The ionospheric delay, which is a function of the total electron content (TEC), is one of the main sources of error affecting GPS/SBAS accuracy. A dual frequency GPS receiver can be used to estimate the TEC. However, line-of-sight TEC derived from dual frequency GPS data is corrupted by the instrumental biases of the GPS receiver and satellites. The estimation of receiver instrumental bias is particularly important for obtaining accurate estimates of ionospheric delay. In this paper, two prominent techniques based on Kalman filter and Self-Calibration Of pseudo Range Error (SCORE) algorithm are used for estimation of instrumental biases. The estimated instrumental bias and TEC results for the GPS Aided Geo Augmented Navigation (GAGAN) station at Hyderabad (78.47°E, 17.45°N), India are presented.

Oscillator Frequency Offset Impact on Software GPS Receivers and Correction Algorithms

Software-based Global Positioning System (GPS) receivers have been recognized as an effective research platform in recent years. The impact of oscillator frequency offset on hardware receiver and software receiver signal processing is contrasted based on a refined signal model and cross correlation function (CCF) analysis. Several online clock error correction algorithms are presented to produce unbiased measurements and clock error estimates with known and unknown front end frequency plans and with and without signal tracking and navigation solutions for single- and dual-frequency receivers on both static and dynamic platforms. The CCF formulation and the clock correction performance are validated using simulated signals and real single- and dual-frequency GPS data. The raw frequency error measurements with 0.02 s time resolution for an oven controlled crystal oscillator (OCXO) using real GPS signal report an Allan deviation (ADEV) of 1.3E-11 and a standard deviation of 1.56E-11.

Ionospheric Electron Concentration Imaging Using Combination of LEO Satellite Data With Ground-Based GPS Observations Over China

Space-based global positioning system (GPS) data onboard low Earth orbit satellites are used together with ground-based GPS observations to simultaneously image ionospheric electron density (IED), and it aims to improve the spatial resolution of ionospheric tomography. High-precision dual-frequency GPS data from the Crustal Movement Observation Network of China and several International GPS Service stations and the Constellation Observation System for Meteorology Ionosphere and Climate (COSMIC) are used to invert a time series of the IED profiles over China and surroundings. Some retrieved electron density profiles are compared with the results from COSMIC occultation data processed by COSMIC Data Analysis and Archival Center, and the peak density in F2 (NmF2) is verified by ionosonde data. Experimental results demonstrate the imaging effectiveness due to COSMIC data used in the inversion, and the potential benefits using COSMIC data in such system are also discussed.

A Preliminary Study on Mapping the Regional Ionospheric TEC Using a Spherical Cap Harmonic Model in High Latitudes and the Arctic Region

The conventional ionosphere total electron content (TEC) models based on geodetic coordinates have asynchronous dimensional resolution, especially in the area close to the pole. This paper presents a novel spherical cap harmonic model for mapping the arctic regional ionospheric TEC in a spherical cap coordinate system. Utilizing a series of IGS (International GNSS Service) products, a set of dual-frequency GPS (Global Positioning System) data from IGS stations in high latitudes is processed and used to map the arctic regional TEC values with the spherical cap harmonic model and the conventional regional TEC models. Together with the global ionosphere mapping (GIM) model from IGS, the TEC mapping accuracies from these models are compared. The comparison results show that the spherical cap harmonic model has a better TEC mapping performance with more homogeneous accuracy distributions in both temporal and spatial domains for the arctic region. In addition, the spectrum components of the coefficient series of the spherical cap harmonic models are demonstrated in this paper.

Test of GPS for permanent ionospheric TEC monitoring at high latitudes

Abstract. The Global Positioning System (GPS) observables are affected by the ionosphere. The dispersive nature of this effect and the use of two frequencies in the GPS observations make possible to measure the ionospheric total electron content (TEC) from dual frequency GPS data. In this work we test the concept of permanent monitoring of TEC using a network of GPS receivers at high latitudes. We have used GPS data from five permanent receivers in Scandinavia, from 1-30 January 1994, with geographic latitudes ranging from 57.4°N to 78.9°N. The results show the capability of the method to monitor the evolution of TEC as a function of time and geographical location. We have detected night-time enhancements almost every night for some of the stations, and we have also been able to produce maps of the instantaneous TEC as a function of both latitude and longitude around the GPS network. We also present some of the current limitations in the use of GPS for estimating TEC at high latitudes such as the difficulties in solving for cycle-slips, and the necessity of reliable values for the receiver and satellite differential instrumental biases.

Test of GPS for permanent ionospheric TEC monitoring at high latitudes

<strong class="journal-contentHeaderColor">Abstract.</strong> The Global Positioning System (GPS) observables are affected by the ionosphere. The dispersive nature of this effect and the use of two frequencies in the GPS observations make possible to measure the ionospheric total electron content (TEC) from dual frequency GPS data. In this work we test the concept of permanent monitoring of TEC using a network of GPS receivers at high latitudes. We have used GPS data from five permanent receivers in Scandinavia, from 1-30 January 1994, with geographic latitudes ranging from 57.4^°N to 78.9^°N. The results show the capability of the method to monitor the evolution of TEC as a function of time and geographical location. We have detected night-time enhancements almost every night for some of the stations, and we have also been able to produce maps of the instantaneous TEC as a function of both latitude and longitude around the GPS network. We also present some of the current limitations in the use of GPS for estimating TEC at high latitudes such as the difficulties in solving for cycle-slips, and the necessity of reliable values for the receiver and satellite differential instrumental biases.

Ionospheric calibration of single frequency VLBI and GPS observations using dual GPS data

The ionospheric effect is one of the main sources of error in Very Long Baseline Interferometry (VLBI) and Global Positioning System (GPS) high precision geodesy. Although the use of two frequencies allows the estimation of this effect, in some cases dual observations are not possible due to the available equipment or the type of observation. This paper presents the ionospheric calibration of single frequency VLBI and GPS observations based on the ionospheric electron content estimated from dual frequency GPS data. The ionospheric delays obtained with this procedure and the VLBI baseline length results have been compared with those obtained with dual frequency data. For the European geodetic VLBI baselines, both solutions agree at the 3–5 parts in 10−9 level. The noise introduced by the GPS-based calibration is in the order of 3 cm for the VLBI observables and of 10 cm for the GPS observables.