Receiver Differential Code Biases Research Articles

Estimating satellite and receiver differential code bias using a relative Global Positioning System network

Abstract. Precise total electron content (TEC) is required to produce accurate spatial and temporal resolution of global ionosphere maps (GIMs). Receivers and satellite differential code biases (DCBs) are one of the main error sources in estimating precise TEC from Global Positioning System (GPS) data. Recently, researchers have been interested in developing models and algorithms to compute DCBs of receivers and satellites close to those computed from the Ionosphere Associated Analysis Centers (IAACs). Here we introduce a MATLAB code called Multi Station DCB Estimation (MSDCBE) to calculate satellite and receiver DCBs from GPS data. MSDCBE based on a spherical harmonic function and a geometry-free combination of GPS carrier-phase, pseudo-range code observations, and weighted least squares was applied to solve observation equations and to improve estimation of DCB values. There are many factors affecting the estimated values of DCBs. The first one is the observation weighting function which depends on the satellite elevation angle. The second factor is concerned with estimating DCBs using a single GPS station using the Zero Difference DCB Estimation (ZDDCBE) code or using the GPS network used by the MSDCBE code. The third factor is the number of GPS receivers in the network. Results from MSDCBE were evaluated and compared with data from IAACs and other codes like M_DCB and ZDDCBE. The results of weighted (MSDCBE) least squares show an improvement for estimated DCBs, where mean differences from the Center for Orbit Determination in Europe (CODE) (University of Bern, Switzerland) are less than 0.746 ns. DCBs estimated from the GPS network show better agreement with IAAC than DCBs estimated from precise point positioning (PPP), where the mean differences are less than 0.1477 and 1.1866 ns, respectively. The mean differences of computed DCBs improved by increasing the number of GPS stations in the network.

Differential code bias estimation based on uncombined PPP with LEO onboard GPS observations

Differential Code Bias (DCB) is an essential correction that must be provided to the Global Navigation Satellite System (GNSS) users for precise position determination. With the continuous deployment of Low Earth Orbit (LEO) satellites, DCB estimation using observations from GNSS receivers onboard the LEO satellites is drawing increasing interests in order to meet the growing demands on high-quality DCB products from LEO-based applications, such as LEO-based GNSS signal augmentation and space weather research. Previous studies on LEO-based DCB estimation are usually using the geometry-free combination of GNSS observations, and it may suffer from significant leveling errors due to non-zero mean of multipath errors and short-term variations of receiver code and phase biases. In this study, we utilize the uncombined Precise Point Positioning (PPP) model for LEO DCB estimation. The models for uncombined PPP-based LEO DCB estimation are presented and GPS observations acquired from receivers onboard three identical Swarm satellites from February 1 to 28, 2019 are used for the validation. The results show that the average Root Mean Square errors (RMS) of the GPS satellite DCBs estimated with onboard data from each of the three Swarm satellites using the uncombined PPP model are less than 0.18 ns when compared to the GPS satellite DCBs obtained from IGS final daily Global Ionospheric Map (GIM) products. Meanwhile, the corresponding average RMS of GPS satellite DCBs estimated with the conventional geometry-free model are 0.290, 0.210, 0.281 ns, respectively, which are significantly larger than those obtained with the uncombined PPP model. It is also noted that the estimated GPS satellite DCBs by Swarm A and C satellites are highly correlated, likely attributed to their similar orbit type and space environment. On the other hand, the Swarm receiver DCBs estimated with uncombined PPP model, with Standard Deviation (STD) of 0.065, 0.037 and 0.071 ns, are more stable than those obtained from the official Swarm Level 2 products with corresponding STD values of 0.115, 0.101, and 0.109 ns, respectively. The above indicates that high-quality DCB products can be estimated based on uncombined PPP with LEO onboard observations.

Estimation and Analysis of IRNSS Satellites Differential Code Biases using Real Data

IRNSS is a regional navigation system developed by the Indian Space Research Organization (ISRO) for precise position and navigation services over the Indian sub-continent. However, the IRNSS measurements are being affected by the many residuals or biases. Differential Code Biases (DCB) are very significant in the precise measurement of ionosphere Total Electron Content (TEC). In this paper, DCB of all available IRNSS satellites and receiver is derived from the pseudorange measurements of IRNSS on L5 and S-band signals. Results show that the estimated daily mean DCB of IRNSS satellites is in the range between -0.60 nanoseconds(ns) and 0.606 ns. Further, the receiver DCB is obtained as 7.904 ns.

A distributed method to estimate RDCB and SDCB using a GPS receiver network

In this paper, a distributed method to estimate satellite and receiver differential code biases (DCBs) separately utilizing a network of global positioning system (GPS) receivers is proposed. The proposed method consists of many local filters and a single fusion module. Each local filter estimates vertical ionospheric delays (VIDs) and the combined DCBs (CDCBs) by utilizing dual-frequency code and carrier-phase measurements from each receiver. The fusion module gathers the combined DCB estimates and their estimation errors from all the local filters. Then it discriminates the satellite DCBs (SDCBs) and the receiver DCBs (RDCBs) separately. By an experiment, it is shown that the RMS difference of SDCBs and RDCBs between the proposed method and the IGS product are around 0.374 m and 0.424 m, respectively.

Use of modified carrier-to-code leveling to analyze temperature dependence of multi-GNSS receiver DCB and to retrieve ionospheric TEC

Deriving the ionospheric total electron content (TEC) from the global navigation satellite systems (GNSS) measurements typically assumes the receiver differential code biases (RDCBs) to remain unchanged within at least 1 day. However, the RDCBs sometimes can exhibit remarkable intraday variability, probably due to the ambient temperature fluctuation. The modified carrier-to-code leveling (MCCL) method enables one to eliminate the adverse impact of the short-term variations of RDCBs (called RDCB offsets) on the retrieval of ionospheric TECs. In this study, we extend the GPS-only MCCL method to the multi-GNSS case and further carry out a series of investigations. First, in terms of the Pearson correlation coefficient (PCC), the dependence of multi-GNSS RDCB offsets upon ambient temperature is verified. As suggested by the results, a strong linear correlation exists between the estimated RDCB offsets and measured temperature values. The percentages of the stations analyzed with the absolute PCC values above 0.5 are 76.5%, 94.1% and 64.2% for GPS, BDS and Galileo, respectively. Second, the global ionospheric map provided by the center for orbit determination in Europe (CODE), the JASON altimeter and the difference of slant TEC (dSTEC) are chosen as the references for evaluating the performance of MCCL-derived TECs. After removing the significant RDCB offsets, an improvement of 69.7%, 93.4% and 87.6% for GPS, BDS and Galileo has been achieved in the dSTEC validation, respectively.

An Enhanced Mapping Function with Ionospheric Varying Height

Mapping function (MF) converts the line-of-sight slant total electron content (STEC) into the vertical total electron content (VTEC), and vice versa. In an MF, an essential parameter is the ionospheric effective height. However, the inhomogeneous ionosphere makes this height vary spatially and temporally, meaning it is not a global constant. In the paper, we review several mapping functions and propose a mapping function that utilizes the ionospheric varying height (IVH). We investigate impacts of the IVH on mapping errors and on the ionospheric modeling, as well as on the satellite and receiver differential code biases (DCBs). Our analysis results indicate that the mapping errors using IVH are smaller than those from the fixed height of 450 km. The integral height achieves smaller mapping errors than using a fixed height of 450 km, an improvement of about 8% when compared with the fixed height of 450 km. And 35% smaller mapping errors were found using HmF2 at the lower latitude. Also, the effects of IVH on the satellite DCBs are about 0.1 ns, and larger impacts on the receiver DCBs at 1.0 ns.

FY-3D and FY-3C onboard observations for differential code biases estimation

With the development of Low Earth Orbit satellites, differential code biases (DCBs) estimation based on onboard observations has been widely studied. In this study, onboard observations of BDS and GPS satellites by the Chinese Fengyun-3D (FY-3D) and Fengyun-3C (FY-3C) satellites are applied to estimate BDS and GPS DCBs. Since only the code observations of C1C and C2W for GPS, and C2I and C7I for BDS are tracked by FY-3D and FY-3C, the DCB types of GPS C1C-C2W and BDS C2I-C7I are estimated with code multipath considered. First, the DCB estimates based on FY-3D onboard observations are analyzed. When jointly processing BDS + GPS onboard observations, the stability of satellite and receiver DCBs for both BDS and GPS has better consistency with the DCB products of the German Aerospace Center (DLR) and the Chinese Academy of Science than that for the single-system solutions (BDS-only solution and GPS-only solution). This is reasonable because more onboard observations are used in BDS + GPS solution, which can improve the strength of the DCB estimation. The variations of receiver DCB are analyzed as a function of geomagnetism and solar activity, but little relationship between them has been found. Compared with the FY-3C solution, the FY-3D solution can achieve a more stable satellite DCB with a stability improvement of 33%, 48%, 62% and 56% for GPS, BDS GEO, IGSO, and MEO satellites, respectively. Meanwhile, the receiver DCB of FY-3D is more stable than that of FY-3C as well. These improvements of satellite and receiver DCBs can be due to the enhancement of FY-3D GNSS Occultation Sounder (GNOS) instrument, which provides more observations with higher quality. Furthermore, both FY-3D and FY-3C onboard observations are processed together to estimate BDS and GPS DCBs. Compared with the FY-3D solution, the stability of satellite DCB can be improved by 16%, 9% and 7% for GPS, BDS GEO and IGSO satellites DCB, respectively, when both FY-3D and FY-3C onboard observations are jointly processed. The impact of DCB estimation on estimating the vertical total electron content (VTEC) is also investigated. Compared with FY-3D GPS-only and BDS + GPS solutions, the VTEC estimates along the FY-3D orbit can achieve more realistic results for FY-3D + FY-3C solution.

Ionosphere Sensing With a Low-Cost, Single-Frequency, Multi-GNSS Receiver

The global navigation satellite system (GNSS) data are beneficial for sensing the earth’s ionosphere by virtue of their temporal continuity and spatial coverage. In recent years, GNSS (GPS, GLONASS, BDS, and GALILEO) has developed rapidly, with BDS and GALILEO offering position, navigation, and timing services and the ongoing modernization of GPS and GLONASS. The customary approach to sensing the ionosphere normally uses the dual- or multifrequency (DF) data provided by geodetic-grade receivers and consists of two sequential steps. The first step is retrieving ionospheric observables using the carrier-to-code leveling technique. In the second step, using the thin-layer ionospheric model, one can isolate the main vertical total electron content (VTEC) for ionosphere sensing as well as the by-product of the satellite differential code biases (SDCBs) and the receiver differential code biases. In this paper, we proposed a multi-GNSS single-frequency (SF) precise point positioning approach enabling the simultaneous retrieval of VTEC and SDCBs with low-cost receivers. The root mean square of the VTEC differences between the values retrieved from the multi-GNSS SF method and DF method is approximately 0.5 total electron content unit in each system.

Calibration errors in determining slant Total Electron Content (TEC) from multi-GNSS data

The global navigation satellite system (GNSS) is presently a powerful tool for sensing the Earth's ionosphere. For this purpose, the ionospheric measurements (IMs), which are by definition slant total electron content biased by satellite and receiver differential code biases (DCBs), need to be first extracted from GNSS data and then used as inputs for further ionospheric representations such as tomography. By using the customary phase-to-code leveling procedure, this research comparatively evaluates the calibration errors on experimental IMs obtained from three GNSS, namely the US Global Positioning System (GPS), the Chinese BeiDou Navigation Satellite System (BDS), and the European Galileo. On the basis of ten days of dual-frequency, triple-GNSS observations collected from eight co-located ground receivers that independently form short-baselines and zero-baselines, the IMs are determined for each receiver for all tracked satellites and then for each satellite differenced for each baseline to evaluate their calibration errors. As first derived from the short-baseline analysis, the effects of calibration errors on IMs range, in total electron content units, from 1.58 to 2.16, 0.70 to 1.87, and 1.13 to 1.56 for GPS, Galileo, and BDS, respectively. Additionally, for short-baseline experiment, it is shown that the code multipath effect accounts for their main budget. Sidereal periodicity is found in single-differenced (SD) IMs for GPS and BDS geostationary satellites, and the correlation of SD IMs over two consecutive days achieves the maximum value when the time tag is around 4 min. Moreover, as byproducts of zero-baseline analysis, daily between-receiver DCBs for GPS are subject to more significant intra-day variations than those for BDS and Galileo.

Modeling and performance analysis of precise time transfer based on BDS triple-frequency un-combined observations

In this study, a model of precise time transfer is developed based on the triple-frequency un-combined observations of the BeiDou navigation satellite system, known as UC-PPP. In this model, except for the traditional position, troposphere delay and receiver clock parameters, ionosphere delays are estimated as unknown parameters by adding the prior, spatial and temporal constraints. In addition, receiver differential code biases (DCB) are also estimated as unknown parameters. The standard triple-frequency ionosphere-free model is also introduced, named as IF-PPP. To assess the performance of the model, datasets with short baseline and common external time frequency are used. The results show that the triple-frequency UC-PPP model can be used for precise time transfer, with accuracy and stability identical to those of the IF-PPP model. The model can also provide the receiver DCB and ionosphere total electron content products.

Rapid local ionosphere modeling based on Precise Point Positioning over Iran: A case study under 2014 solar maximum

Presently, the ionosphere effect is the main source of the error in the Global Positioning System (GPS) observations. This effect can largely be removed by using the two-frequency measurements, while to obtain the reasonable results in the single-frequency applications, an accurate ionosphere model is required. Since the global ionosphere models do not meet our needs everywhere, the local ionosphere models are developed. In this paper, a rapid local ionosphere model over Iran is presented. For this purpose, the GPS observations obtained from 40 GPS stations of the Iranian Permanent GPS Network (IPGN) and 16 other GPS stations around Iran have been used. The observations have been selected under 2014 solar maximum, from the days 058, 107, 188 and 271 of the year 2014 with different geomagnetic activities. Moreover, ionospheric observables based on the precise point positioning (PPP) have been applied to model the ionosphere. To represent our ionosphere model, the B-spline basis functions have been employed and the variance component estimation (VCE) method has been used to regularize the problem.To show the efficiency our PPP-derived local ionosphere model with respect to the International GNSS Service (IGS) global models, these models are applied on the single point positioning using single-frequency observations and their results are compared with the precise coordinates obtained from the double-differenced solution using dual-frequency observations. The results show that the 95th percentile of horizontal and vertical positioning errors of the single-frequency point positioning are about 3.1 and 13.6 m, respectively, when any ionosphere model are not applied. These values significantly improve when the ionosphere models are applied in the solutions. Applying CODE’s Rapid Global ionosphere map (CORG), improvements of 59% and 81% in horizontal and vertical components are observed. These values for the IGS Global ionosphere map (IGSG) are 70% and 82%, respectively. The best results are obtained from our local ionosphere model, where 84% and 87% improvements in horizontal and vertical components are observed. These results confirm the efficiency of our local ionosphere model over Iran with respect to the global models. As a by-product, the Differential Code Biases (DCBs) of the receivers are also estimated. In this line, we found that the intra-day variations of the receiver DCBs could be significant. Therefore, these variations must be taken into account for the precise ionosphere modeling.

Estimation and analysis of differential code biases for BDS3/BDS2 using iGMAS and MGEX observations

In this contribution, the BDS3 differential code biases (DCBs) are estimated by using the iGMAS and MEGX networks and the performance of both satellite and receiver DCBs for BDS3 is evaluated with the observational data during the period of DOY 1–180, 2017. The characteristics of BDS3 and BDS2 DCB are compared, and the code inter-system biases (ISB) between BDS3 and BDS2 are also analyzed in detail. The comparison of our estimated BDS C2I-C6I and C2I-C7I DCBs and the DLR and IGG products shows a good agreement. For BDS2, the mean differences are within $$ \pm \,0.2\,{\text{ns}} $$ and STDs are within 0.15 ns. However, the BDS3 presents a larger difference, with the mean difference of about 0.35 ns, because fewer stations are included in the DLR/IGG processing. The comparison of BDS3 and BDS2 DCB shows that the receiver DCB differences between BDS3 and BDS2 are close to zero for the same network, i.e., iGMAS or MGEX. In other words, there is no significant systematic bias between BDS3 and BDS2 receiver DCB. However, when the iGMAS and MGEX networks are processed together, we found that the receiver DCB differences between BDS3 and BDS2 are not close to zero and present an obvious systematic bias between different networks. The further analysis of code ISB between BDS3 and BDS2 also shows a similar phenomenon. Therefore, the receiver DCB of BDS3 and BDS2 should be separately estimated or calibrated when iGMAS and MGEX networks are processed together. We also analyze the receiver DCB and code ISB between Galileo FOC and IOV satellites and found that there is no such systematic bias between Galileo FOC and IOV satellites. A 180-day analysis of estimated BDS3 and BDS2 DCB shows that the satellite DCBs of BDS3 are fairly stable, with a mean STD of about 0.18 ns. For BDS2, the IGSO DCBs are the most stable with a mean STD of about 0.09 ns, and the GEO DCBs exhibit the worst stability with a mean STD of about 0.18 ns. The mean STDs of receiver DCBs for BDS3 and BDS2 are 0.38 and 0.41 ns, respectively, and the STD of receiver DCBs of BDS3 is smaller than that of BDS2 at most stations.

Revisit the calibration errors on experimental slant total electron content (TEC) determined with GPS

The calibration errors on experimental slant total electron content (TEC) determined with global positioning system (GPS) observations is revisited. Instead of the analysis of the calibration errors on the carrier phase leveled to code ionospheric observable, we focus on the accuracy analysis of the undifferenced ambiguity-fixed carrier phase ionospheric observable determined from a global distribution of permanent receivers. The results achieved are: (1) using data from an entire month within the last solar cycle maximum, the undifferenced ambiguity-fixed carrier phase ionospheric observable is found to be over one order of magnitude more accurate than the carrier phase leveled to code ionospheric observable and the raw code ionospheric observable. The observation error of the undifferenced ambiguity-fixed carrier phase ionospheric observable ranges from 0.05 to 0.11 total electron content unit (TECU) while that of the carrier phase leveled to code and the raw code ionospheric observable is from 0.65 to 1.65 and 3.14 to 7.48 TECU, respectively. (2) The time-varying receiver differential code bias (DCB), which presents clear day boundary discontinuity and intra-day variability pattern, contributes the most part of the observation error. This contribution is assessed by the short-term stability of the between-receiver DCB, which ranges from 0.06 to 0.17 TECU in a single day. (3) The remaining part of the observation errors presents a sidereal time cycle pattern, indicating the effects of the multipath. Further, the magnitude of the remaining part implies that the code multipath effects are much reduced. (4) The intra-day variation of the between-receiver DCB of the collocated stations suggests that estimating DCBs as a daily constant can have a mis-modeling error of at least several tenths of 1 TECU.

Global Ionosphere Mapping and Differential Code Bias Estimation during Low and High Solar Activity Periods with GIMAS Software

Ionosphere research using the Global Navigation Satellite Systems (GNSS) techniques is a hot topic, with their unprecedented high temporal and spatial sampling rate. We introduced a new GNSS Ionosphere Monitoring and Analysis Software (GIMAS) in order to model the global ionosphere vertical total electron content (VTEC) maps and to estimate the GPS and GLObalnaya NAvigatsionnaya Sputnikovaya Sistema (GLONASS) satellite and receiver differential code biases (DCBs). The GIMAS-based Global Ionosphere Map (GIM) products during low (day of year from 202 to 231, in 2008) and high (day of year from 050 to 079, in 2014) solar activity periods were investigated and assessed. The results showed that the biases of the GIMAS-based VTEC maps relative to the International GNSS Service (IGS) Ionosphere Associate Analysis Centers (IAACs) VTEC maps ranged from −3.0 to 1.0 TECU (TEC unit) (1 TECU = 1 × 1016 electrons/m2). The standard deviations (STDs) ranged from 0.7 to 1.9 TECU in 2008, and from 2.0 to 8.0 TECU in 2014. The STDs at a low latitude were significantly larger than those at middle and high latitudes, as a result of the ionospheric latitudinal gradients. When compared with the Jason-2 VTEC measurements, the GIMAS-based VTEC maps showed a negative systematic bias of about −1.8 TECU in 2008, and a positive systematic bias of about +2.2 TECU in 2014. The STDs were about 2.0 TECU in 2008, and ranged from 2.2 to 8.5 TECU in 2014. Furthermore, the aforementioned characteristics were strongly related to the conditions of the ionosphere variation and the geographic latitude. The GPS and GLONASS satellite and receiver P1-P2 DCBs were compared with the IAACs DCBs. The root mean squares (RMSs) were 0.16–0.20 ns in 2008 and 0.13–0.25 ns in 2014 for the GPS satellites and 0.26–0.31 ns in 2014 for the GLONASS satellites. The RMSs of receiver DCBs were 0.21–0.42 ns in 2008 and 0.33–1.47 ns in 2014 for GPS and 0.67–0.96 ns in 2014 for GLONASS. The monthly stability of the GPS satellite DCBs was about 0.04 ns (0.07 ns) in 2008 (2014) and that for the GLONASS satellite DCBs was about 0.09 ns in 2014. The receiver DCBs were less stable than the satellite DCBs, with a mean value of about 0.16 ns (0.47 ns) in 2008 (2014) for GPS, and 0.48 ns in 2014 for GLONASS. It can be demonstrated that the GIMAS software had a high accuracy and reliability for the global ionosphere monitoring and analysis.

The influence of grounding on GPS receiver differential code biases

The Global Positioning System (GPS) has become an effective tool for estimating ionospheric total electron content (TEC). One of the critical factors affecting ionospheric TEC estimation from GPS data is the differential code biases (DCBs) inherent in both GPS receivers and satellites. To investigate the factor that affects the receiver DCB, we consider the relationship between the receiver DCB and the grounding of an antenna. GPS data from 9 stations in South Korea from three periods (the years 2009, 2014, and 2017) were used in the analysis. It was found that a significant jump (∼8–13 ns, or ∼ 23–37 TECU) in hourly DCB time series occurred simultaneously at the two different sites when an antenna is changed from a grounded to the non-grounded state. Thus, our study clearly identifies that the grounding of GPS equipment is a factor of the receiver DCB changes.

A modified carrier-to-code leveling method for retrieving ionospheric observables and detecting short-term temporal variability of receiver differential code biases

Sensing the ionosphere with the global positioning system involves two sequential tasks, namely the ionospheric observable retrieval and the ionospheric parameter estimation. A prominent source of error has long been identified as short-term variability in receiver differential code bias (rDCB). We modify the carrier-to-code leveling (CCL), a method commonly used to accomplish the first task, through assuming rDCB to be unlinked in time. Aside from the ionospheric observables, which are affected by, among others, the rDCB at one reference epoch, the Modified CCL (MCCL) can also provide the rDCB offsets with respect to the reference epoch as by-products. Two consequences arise. First, MCCL is capable of excluding the effects of time-varying rDCB from the ionospheric observables, which, in turn, improves the quality of ionospheric parameters of interest. Second, MCCL has significant potential as a means to detect between-epoch fluctuations experienced by rDCB of a single receiver.

Enhanced Polar Outflow Probe Ionospheric Radio Occultation Measurements at High Latitudes: Receiver Bias Estimation and Comparison With Ground‐Based Observations

AbstractThis paper presents validation of ionospheric Global Positioning System (GPS) radio occultation measurements of the GPS Attitude, Positioning, and Profiling Experiment occultation receiver (GAP‐O). GAP is one of eight instruments comprising the Enhanced Polar Outflow Probe (e‐POP) instrument suite on board the Cascade Smallsat and Ionospheric Polar Explorer (CASSIOPE) satellite. One of the main error sources for certain GAP‐O data products is the receiver differential code bias (rDCB). A minimization of standard deviations (MSD) technique has shown the most promise for rDCB estimation, with estimates ranging primarily from −40 to −28 total electron content units (TECU = 1016 el m−2; 21.6 to 15.1 ns), including a long‐term decrease in rDCB magnitude and variability over the first 3 years of instrument operation. In application of the MSD method, the sensitivity of bias estimates to ionospheric shell height are as large as 4.5 TECU per 100 km. MSD calculations also agree well with the “assumption of zero topside TEC” method for rDCB estimate at satellite apogee. Bias‐corrected topside TEC of GAP‐O was validated by statistical comparison with topside TEC obtained from ground‐based GPS TEC and ionosonde measurements. Although GAP‐O and ground‐based topside TEC had similar variability, GAP‐O consistently underestimated the ground‐derived topside TEC by up to 7 TECU. Ionospheric electron density profiles obtained from Abel inversion of GAP‐O occultation TEC showed good agreement with F region densities of ground‐based incoherent scatter radar measurements. Comparison of GAP‐O and ionosonde measurements revealed correlation coefficients of 0.78 and 0.79, for peak F region density and altitude, respectively.

Estimation and analysis of multi-GNSS differential code biases using a hardware signal simulator

In ionospheric modeling, the differential code biases (DCBs) are a non-negligible error source, which are routinely estimated by the different analysis centers of the International GNSS Service (IGS) as a by-product of their global ionospheric analysis. These are, however, estimated only for the IGS station receivers and for all the satellites of the different GNSS constellations. A technique is proposed for estimating the receiver and satellites DCBs in a global or regional network by first estimating the DCB of one receiver set as reference. This receiver DCB is then used as a ‘known’ parameter to constrain the global ionospheric solution, where the receiver and satellite DCBs are estimated for the entire network. This is in contrast to the constraint used by the IGS, which assumes that the involved satellites DCBs have a zero mean. The ‘known’ receiver DCB is obtained by simulating signals that are free of the ionospheric, tropospheric and other group delays using a hardware signal simulator. When applying the proposed technique for Global Positioning System legacy signals, mean offsets in the order of 3 ns for satellites and receivers were found to exist between the estimated DCBs and the IGS published DCBs. It was shown that these estimated DCBs are fairly stable in time, especially for the legacy signals. When the proposed technique is applied for the DCBs estimation using the newer Galileo signals, an agreement at the level of 1–2 ns was found between the estimated DCBs and the manufacturer’s measured DCBs, as published by the European Space Agency, for the three still operational Galileo in-orbit validation satellites.

Improved Modeling of Global Ionospheric Total Electron Content Using Prior Information

The Ionosphere Working Group of the International GNSS Service (IGS) has been a reliable source of global ionospheric maps (GIMs) since 1998. Modeling of the global ionospheric total electron content (TEC) is performed daily by several Ionosphere Associate Analysis Centers (IAACs). Four IAACs (CODE, ESA, CAS and WHU) use the spherical harmonic (SH) expansion as their primary method for modeling GIMs. The IAACs generally solve a normal equation to obtain the SH coefficients and Differential Code Biases (DCBs) of satellites and receivers by traditional least-squares estimation (LSE) without any prior knowledge. In this contribution, an improved method is proposed and developed for global ionospheric modeling based on utilizing prior knowledge. Prior values of SH coefficients and DCBs of satellites and receivers, as well as the variance factor and covariance matrix, could be obtained from the ionospheric modeling on the previous day. The parameters can subsequently be updated through GNSS measurements to achieve higher accuracy. Comparisons are carried out between WHU products based either on priori information or original LSE and IGS final products, other IAAC products, and JASON data for the year 2014. The results indicate that there is improved consistency between WHU GIMs and IGS final GIMs, other IAAC products, and JASON data, particularly in comparison with ESA and UPC products, with the probabilities of achieving better consistency with these products exceeding 95%. Moreover, WHU-produced DCBs of satellites also have slightly improved consistency with IGS final GIMs and IAAC products.

Estimation and analysis of the short-term variations of multi-GNSS receiver differential code biases using global ionosphere maps

Care should be taken to minimize the adverse impact of differential code biases (DCBs) on global navigation satellite systems (GNSS)-derived ionospheric information determinations. For the sake of convenience, satellite and receiver DCB products provided by the International GNSS Service (IGS) are treated as constants over a period of 24 h (Li et al. (2014)). However, if DCB estimates show remarkable intra-day variability, the DCBs estimated as constants over 1-day period will partially account for ionospheric modeling error; in this case DCBs will be required to be estimated over shorter time period. Therefore, it is important to further gain insight into the short-term variation characteristics of receiver DCBs. In this contribution, the IGS combined global ionospheric maps and the German Aerospace Center (DLR)-provided satellite DCBs are used in the improved method to determine the multi-GNSS receiver DCBs with an hourly time resolution. The intra-day stability of the receiver DCBs is thereby analyzed in detail. Based on 1 month of data collected within the multi-GNSS experiment of the IGS, a good agreement within the receiver DCBs is found between the resulting receiver DCB estimates and multi-GNSS DCB products from the DLR at a level of 0.24 ns for GPS, 0.28 ns for GLONASS, 0.28 ns for BDS, and 0.30 ns for Galileo. Although most of the receiver DCBs are relatively stable over a 1-day period, large fluctuations (more than 9 ns between two consecutive hours) within the receiver DCBs can be found. We also demonstrate the impact of the significant short-term variations in receiver DCBs on the extraction of ionospheric total electron content (TEC), at a level of 12.96 TECu (TEC unit). Compared to daily receiver DCB estimates, the hourly DCB estimates obtained from this study can reflect the short-term variations of the DCB estimates more dedicatedly. The main conclusion is that preliminary analysis of characteristics of receiver DCB variations over short-term intervals should be finished prior to estimate daily multi-GNSS receiver DCB products.