Satellite Differential Code Biases Research Articles

Denoising ionospheric observables based on multipath error modelling with Tikhonov regularization

Multipath errors, as one of the manifest unmodelled error types introduced by code measurements, are absorbed in ionospheric observables, which results in ionospheric pollution. In this work, in order to cancel out random noise by an adjustment algorithm, the modelling of multipath errors derived from code measurement residuals in undifferentiated and uncombined precise point position (PPP) mode is realized by solving a regularization problem, in which Tikhonov regularization (i.e. the first order difference) is taken into account. Furthermore, the Thomas update algorithm is employed to find the solution and a bootstrap method is used to determine the optimal regularization parameter. After the multipath error model was constructed, it was used to extract the ionospheric observables, thereby enabling the correction of the code measurements. In this research, three ionosphere-retrieval schemes were designed, namely the the alignment of the carrier phase to the code (1) before and (2) after the multipath errors were corrected (CCBM and CCAM), and (3) a PPP solution (PPPS). Based on colocation experiments, the effects of removing errors arising from the multipath effect on the code were comparatively assessed. Large differences were found between the three schemes when used in a short-baseline experimental setting, but only small differences were found with a zero-baseline setup. In the short-baseline experiment, CCAM was more reliable than CCBM, with an improvement in accuracy of about 50%, and reached close agreement with PPPS. In addition, 14 continuously operating reference stations in Hong Kong were selected for ionosphere modelling with differential code bias (DCB) estimations. Similar results were seen, as follows: (1) compared with CCBM, CCAM and PPPS had better modelling accuracies, with an improvement of 60%; (2) CCAM and PPPS had better performance at five fitting stations with respect to CCBM, which resulted in improvements in the accuracies ranging from 60% to 80%; (3) taking five-day-average values of the satellite DCBs, the difference between Center for OrbitDetermination in Europe (CODE) and CCAM was around 0.5 ns, which is consistent with the difference between CODE and PPPS, but about a 2 ns difference was verified between CODE and CCBM.

Estimation of QZSS differential code biases using QZSS/GPS combined observations from MGEX

As an important error source in Global Navigation Satellite System (GNSS) positioning and ionospheric modeling, the differential code biases (DCB) need to be estimated accurately, e.g., the regional Quasi-Zenith satellite system (QZSS). In this paper, the DCB of QZSS is estimated by adopting the global ionospheric modeling method based on QZSS/GPS combined observations from Multi-GNSS experiment (MGEX). The performance of QZSS satellite and receiver DCB is analyzed with observations from day of year (DOY) 275–364, 2018. Good agreement between our estimated QZSS satellite DCB and the products from DLR and CAS is obtained. The bias and root mean square (RMS) of DCB are mostly within ±0.3 ns. The day-to-day fluctuation of the DCB time series is less than 0.5 ns with about 96% of the cases for all satellites. However, the receiver DCB is a little less stable than satellite DCB, and their standard deviations (STDs) are within 1.9 ns. The result shows that the stability of the receiver DCBs is not significantly related to the types of receiver or antenna.

Estimation of differential code biases with Jason-2/3 onboard GPS observations

With the continuous deployment of Low Earth Orbit (LEO) satellites, the estimation of differential code biases (DCBs) based on GNSS observations from LEO has gained increasing attention. Previous studies on LEO-based DCB estimation are usually using the spherical symmetry ionosphere assumption (SSIA), in which a uniform electron density is assumed in a thick shell. In this study, we propose an approach (named the SHLEO method) to simultaneously estimate the satellite and LEO onboard receiver DCBs by modeling the distribution of the global plasmaspheric total electron content (PTEC) above the satellite orbit with a spherical harmonic (SH) function. Compared to the commonly used SSIA method, the SHLEO model improves the GPS satellite DCB estimation accuracy by 13.46% and the stability by 22.34%, respectively. Compared to the GPS satellite DCBs estimated based on the Jason-3-only observations, the accuracy and monthly stability of the satellite DCBs can be improved by 14.42% and 26.8% when both Jason-2 and Jason-3 onboard observations are jointly processed. Compared with the Jason-2 solutions, the GPS satellite DCB estimates based on the fusion of Jason-2 and Jason-3 observations have an improved consistency of better than 18.26% and 9.71% with the products provided by the Center for Orbit Determination in Europe (CODE) and Chinese Academy of Sciences (CAS). Taking the DCB products provided by the German Aerospace Center (DLR) as references, there is no improvement in accuracy of the GPS satellite DCB estimates based on the fusion of Jason-2 and Jason-3 observations than the Jason-2 solutions alone. A periodic variation is found in the time series of both the Jason-3 and Jason-2 onboard receiver DCB estimates. Preliminary analysis of the PTEC distribution based on the estimated SH coefficients are also presented.

Understanding long-term variations in GPS differential code biases

Precise estimation of satellite differential code biases (DCBs) plays a crucial role in precise ionospheric modeling, positioning, and timing. Due to the rank deficiency, a constraint or a datum is required in order to separate the satellite DCBs from the receiver DCBs. A common practice is to impose a zero-mean constraint on all the visible satellites. However, datum selection is affected by satellite replacement and variation of the DCBs. As a result, the long-term variations of current DCB products vary significantly. Taking the DCBs of SVN 44 (PRN 28) as a reference, we analyzed the long-term variations of DCBs over a period of 20 years, between 2000 and 2019. Based on this reference, the results indicate that the change of the zero-mean datum is responsible for the variation of current DCB products. The datum change is attributed to the satellite replacement as well as the discontinuities and their variations. We found that discontinuities for the same satellite vehicle reach 1.8 ns, which is related to satellite changes announced in the Notice Advisory to Navstar Users message and to flex power. The magnitude of the DCBs depends on the satellite type. DCBs for Block IIR-A and IIR-M satellites are close to each other, while DCBs of Block IIR-B satellites are approximately 5 ns larger and DCBs for the Block IIF are 8 ns smaller. In addition, the satellite biases between GPS P1 and C1 are also briefly examined, and the results show that they are also affected by the satellite replacements and discontinuities. However, the satellite bias differences between P1 and C1 for different satellite types are minor.

Estimation of the DCB for the BDS-3 new signals based on BDGIM constraints

The hardware delay difference for different navigation signals in satellite or receiver channels is called Differential Code Bias (DCB). DCB is a major error of global navigation satellite system (GNSS), which may lead to tens of Total Electron Content unit (TECu) ionospheric delay errors or several-meter ranging errors. The basic system of BeiDou Navigation Satellite System has opened services and three new navigation signals, namely B1C, B2a at the end of 2018, and B2b at the end of 2019. As the BeiDou satellite broadcast clock difference is based on the phase center of the B3I signal antenna, it is necessary to estimated the DCB values of the new navigation signals relative to B3I. Considering that BDS broadcasts the BeiDou global ionospheric delay correction model (BDGIM) parameters with the highest precision, the method of solving satellite or receiver DCB based on the BDS-3 BDGIM parameter constraint is proposed and verified. Theoretical analysis shows that the mean square error of daily solution is about 0.63–1.96 ns. The measured data of 25 iGMAS stations from January 1 to 30, 2019, are used for verification. The results show that the solution precision of satellite DCB is better than 1.0 ns and that of receiver DCB is slightly worse. This method does not need the support of external ionospheric products and provides a possibility for online real-time estimating of the satellite and receiver DCB.

A new model for total electron content based on ionospheric continuity equation

With the development of the Global Navigation Satellite System (GNSS), the accuracy and reliability requirements on observations are constantly increasing. The effect of ionospheric disturbance is not negligible, especially for accurate GNSS applications. To reduce the influence of ionospheric delay and disturbance, this study uses the Ionospheric Continuity Equation (ICE) to establish a new model for Total Electron Content (TEC), which takes both photochemical and transportation processes into account and named ICE model. Experimental results show that the ICE model achieves accuracies higher than Spherical Harmonic (SH) and polynomial models on geomagnetism quiet and disturbance days, and more prominent advantages appear at nighttime. By the test of Satellite Differential Code Bias (SDCB) estimation, the deviations of the polynomial and the ICE models are nearly the same whatever the geomagnetic field is quiet or disturbance; however, the estimation accuracy of the ICE model is slightly better than the polynomial model. Spatial and temporal adaptability tests indicate that the ICE model can achieve accuracies of 0.5 TECU and 1 TECU on time scales of approximately 25 min and 100 min, respectively. On the weak disturbance or quiet day, these accuracies can be achieved on the spatial scales of approximately 200 km and 600 km. The credibility of the ICE model is evaluated by Nash–Sutcliffe efficiency. The evaluation results assigned that the ICE model has higher credibility than the SH and polynomial models and better immunity to geomagnetic disturbance.

BDS-3 differential code bias estimation with undifferenced uncombined model based on triple-frequency observation

Since 2015, the new generation global BDS system, i.e., BDS-3, has started its development with five experimental satellites demonstration system and has announced its initial global service officially on December 27, 2018. Among the various characteristics to be analyzed for the new generation BDS satellites, the differential code bias (DCB) is of special attention since that it has a direct dependence on the new signals, i.e., B1C and B2a, and it is one of the most intricacy problems in the ionosphere sensing and positioning with multi-GNSS and multi-frequency observations. To take the full capability of the triple-frequency BDS signals, this paper proposed a new method for the DCB estimation in which the undifferenced uncombined observations are processed in PPP mode. In addition, with the intention to estimate all the unknowns, including the DCB, in a single filter, the DESIGN (deterministic plus stochastic ionosphere model for GNSS) method is applied for the ionospheric delay constrains in this method. In the formula derivation, special attention is given to the DCB and clock parameters due to different frequencies for B1I/B1C, etc. Then, the efficiency of the new method is assessed with observations of 23 iGMAS stations capable for BDS triple-frequency tracking and 21 IGS stations capable for GPS triple-frequency tracking during DOY 001 to 090, 2019. Moreover, the traditional DCB estimation method by employing the geometry-free (GF) combination with the ionospheric delay removed by global ionosphere map product is also performed for comparison purpose. The experimental results suggest that by using the undifferenced uncombined solution, rather than the GF combination, the BDS-2 DCB on B1IB2I and B1CB3I can be improved, especially for the MEO satellites. Regarding to the DLR products, the undifferenced uncombined DCB solution presents a RMS of 0.32 ns and 0.27 ns for B1IB2I and B1CB3I, respectively. Concerning the BDS-3 satellites DCB, it is GF combination that performs better by a factor of 12.7% and 15.2% for B1CB2a and B1CB3I, respectively. This is mainly due to the fact that the undifferenced uncombined DCB solution is sensitive to the limited precision of the BDS-3 orbit and clock. This conclusion is further confirmed by the improvement in the GPS DCB solution with the new method. Compared with the GF combination solution, the STD for daily repeatability improves from 0.088 to 0.061 ns and 0.119 to 0.090 ns for satellite on C1WC2W and C1WC5X, respectively, by using the undifferenced uncombined model.

Estimation of GPS Differential Code Biases Based on Independent Reference Station and Recursive Filter

The differential code bias (DCB) of the Global Navigation Satellite Systems (GNSS) receiver should be precisely corrected when conducting ionospheric remote sensing and precise point positioning. The DCBs can usually be estimated by the ground GNSS network based on the parameterization of the global ionosphere together with the global ionospheric map (GIM). In order to reduce the spatial-temporal complexities, various algorithms based on GIM and local ionospheric modeling are conducted, but rely on station selection. In this paper, we present a recursive method to estimate the DCBs of Global Positioning System (GPS) satellites based on a recursive filter and independent reference station selection procedure. The satellite and receiver DCBs are estimated once per local day and aligned with the DCB product provided by the Center for Orbit Determination in Europe (CODE). From the statistical analysis with CODE DCB products, the results show that the accuracy of GPS satellite DCB estimates obtained by the recursive method can reach about 0.10 ns under solar quiet condition. The influence of stations with bad performances on DCB estimation can be reduced through the independent iterative reference selection. The accuracy of local ionospheric modeling based on recursive filter is less than 2 Total Electron Content Unit (TECU) in the monthly median sense. The performance of the recursive method is also evaluated under different solar conditions and the results show that the local ionospheric modeling is sensitive to solar conditions. Moreover, the recursive method has the potential to be implemented in the near real-time DCB estimation and GNSS data quality check.

Determination of NavIC differential code biases using GPS and NavIC observations

Delay bias between the pseudo range code is called Differential Code Bias (DCB), this is one of the main error sources to estimate the precise Total Electron Content (TEC) in ionosphere. Differential delay biases between the dual frequency band signals in both satellite and receiver are called satellite differential code biases (SDCBs) and receiver differential code biases (RDCBs). The combined satellite and receiver DCBs lead to measure error TEC. SDCBs and RDCBs should be removed from the Global Navigation Satellite System (GNSS) measurements accurately. The DCB estimations of GNSS signals are important for improving GNSS user positioning accuracy in ionospheric and space weather applications. The Navigation with Indian Constellation (NavIC) system has been developed by India to cater to positioning, navigation, timing, and ionosphere and troposphere remote sensing applications. The proposed DCB estimation algorithm is necessary to calibrate the NavIC TEC measurements for both NavIC satellites and receivers. In this work, a Global Positioning System (GPS)-aided NavIC DCB estimation algorithm has been implemented with the help of single station GPS TEC measurements. TEC data were recorded at the same location by the NavIC as well as the GPS receiver (Koneru Lakshamaiah Education Foundation, Guntur, India, 16.47°N, 80.61°E) for the month of September 2016. The SDCB and RDCB estimations for NavIC satellites and receivers located at Guntur, India. The maximum SDCB value of 9.2 TECU was observed for NavIC satellite pseudo range number (PRN) 3. Standard deviations of NavIC satellites were in the range of 0.53–1.11 TECU. The NavIC RDCB was estimated to be 16 TECU. The DCB results were validated with the Fitted Receiver Bias (FRB) method. The implemented DCB estimation algorithm would be useful for improving positional accuracy of NavIC users.

Advantages of Uncombined Precise Point Positioning with Fixed Ambiguity Resolution for Slant Total Electron Content (STEC) and Differential Code Bias (DCB) Estimation

The determination of slant total electron content (STEC) between satellites and receivers is the first step for establishing an ionospheric model. However, the leveling errors, caused by the smoothed ambiguity solutions in the carrier-to-code leveling (CCL) method, degrade the performance of ionosphere modeling and differential code bias (DCB) estimation. To reduce the leveling errors, an uncombined and undifferenced precise point positioning (PPP) method with ambiguity resolution (AR) was used to directly extract the STEC. Firstly, the ionospheric observables were estimated with CCL, PPP float-ambiguity solutions, and PPP fixed-ambiguity solutions, respectively, to analyze the short-term temporal variation of receiver DCB in zero or short baselines. Then, the global ionospheric map (GIM) was modeled using three types of ionospheric observables based on the single-layer model (SLM) assumption. Compared with the CCL method, the slight variations of receiver DCBs can be obviously distinguished using high precise ionospheric observables, with a 58.4% and 71.2% improvement of the standard deviation (STD) for PPP float-ambiguity and fixed-ambiguity solutions, respectively. For ionosphere modeling, the 24.7% and 27.9% improvements for posteriori residuals were achieved for PPP float-ambiguity and fixed-ambiguity solutions, compared to the CCL method. The corresponding improvement for residuals of the vertical total electron contents (VTECs) compared with the Center for Orbit Determination in Europe (CODE) final GIM products in global accuracy was 9.2% and 13.7% for PPP float-ambiguity and fixed-ambiguity solutions, respectively. The results show that the PPP fixed-ambiguity solution is the best one for the GIM product modeling and satellite DCBs estimation.

The phase and code biases of Galileo and BDS-3 BOC signals: effect on ambiguity resolution and precise positioning

The modernization of GPS and GLONASS and the development of BDS and Galileo make a variety of new navigation signals available to the users. The wide range of GNSS signals will result in various biases that need to be considered in data processing. In particular, Galileo and BDS-3 binary offset carrier (BOC) signals employ a new approach called dual-frequency constant envelope multiplexing. In this contribution, the phase and code biases of Galileo and BDS-3 BOC signals were estimated and investigated with the observation of iGMAS and MEGX networks during the period of 2015–2018. Initial analyses of BDS-3 BOC signals indicate that satellite-specific pilot-minus-data code biases are close to zero for BDS-3 B2a and B2b signals, while the ones for B1C signal are not. In addition, the satellite differential code biases (DCBs) between Galileo E5a, E5b and E5ab signals, as well as between BDS-3 B2a and B2b signals, are also close to zero. The estimated phase biases for Galileo E5a, E5b and E5ab signals or BDS-3 B2a and B2b signals are the same values, and the resultant phase biases of the extra-wide-lane (EWL) combination are very close to the zero. Besides, no obvious time-varying inter-frequency clock bias could be observed for both Galileo and BDS-3 satellites. Such characteristics of phase/code biases of the new GNSS signals are valuable for ambiguity resolution and precise positioning. Only one set of code or phase bias product is required for Galileo E5a/b/ab (BDS-3 B2a/b) signals. The satellite DCBs between Galileo E5a, E5b and E5ab signals, as well as between BDS-3 B2a and B2b signals, can be ignored in the data processing. And the EWL ambiguities derived from the Galileo E5a/b/ab or BDS-3 B2a/b observations keep their integer feature and can be fixed to integers without phase bias corrections.

Impact of satellite clock offset on differential code biases estimation using undifferenced GPS triple-frequency observations

The uncombined model using undifferenced triple-frequency observations provides an alternative approach for the precise estimation of differential code biases (DCBs) of GPS satellite and receiver. However, the accuracy of DCB estimation is significantly affected by the satellite clock offset due to their strong correlation. We aim to analyze the impact of the satellite clock offset on the estimation of GPS DCB for different frequency pairs. The relationship between satellite clock offset and DCB estimates is rigorously studied based on the derived full-rank triple-frequency uncombined model. Theoretical analysis indicates that the initial satellite clock bias would affect the size of satellite DCB estimates in a linear way. To test our analysis, precise products released by the international GNSS service (IGS), the Center for Orbit Determination in Europe (CODE) and the German Research Centre for Geosciences (GFZ), are used for data processing and comparison. The channel types 1W, 2W and 5X for both GPS triple-frequency code and phase measurements are chosen for DCB estimation. Results show that the average monthly standard deviation (STD) is 0.06 ns and 0.08 ns for GPS satellite C1W–C2W and C1W–C5X DCB estimates. Different satellite clock products have no significant effect on the STDs. When compared with the DCB computed by CODE and Deutsches Zentrum fur Luft-und Raumfahrt (DLR), the mean RMS values of GPS satellite C1W–C2W and C1W–C5X DCB differences are 0.10 ns and 0.42 ns. Different satellite clock products have a significant effect on the RMSs. Through linear regression analysis, we find that 46% and 27% of initial satellite clock biases would be included in the satellite C1W–C2W DCB and C1W–C5X DCB estimates, respectively. In addition, the satellite clock offset has little impact on the receiver DCB estimates though it significantly affects the satellite DCB estimates.

Estimation and Analysis of BDS-3 Differential Code Biases from MGEX Observations

The third generation of China’s BeiDou Navigation Satellite System (BDS-3) began to provide global services on 27 December, 2018. Differential code bias (DCB) is one of the errors in precise BDS positioning and ionospheric modeling, but the impacts on BDS-2 satellites and receiver DCB are unknown after joining BDS-3 observations. In this paper, the BDS-3 DCBs are estimated and analyzed using the Multi-Global Navigation Satellite System (GNSS) Experiment (MGEX) observations during the period of day of year (DOY) 002–031, 2019. The results indicate that the estimated BDS-3 DCBs have a good agreement with the products provided by the Chinese Academy of Sciences (CAS) and Deutsche Zentrum für Luft- und Raumfahrt (DLR). The differences between our results and the other two products are within ±0.2 ns, with Standard Deviations (STDs) of mostly less than 0.2 ns. Furthermore, the effects on satellite and receiver DCB after adding BDS-3 observations are analyzed by BDS-2 + BDS-3 and BDS-2-only solutions. For BDS-2 satellite DCB, the values of effect are close to 0, and the effect on stability of DCB is very small. In terms of receiver DCB, the value of effect on each station is related to the receiver type, but their mean value is also close to 0, and the stability of receiver DCB is better when BDS-3 observations are added. Therefore, there is no evident systematic bias between BDS-2 and BDS-2 + BDS-3 DCB.

On the application of the raw-observation-based PPP to global ionosphere VTEC modeling: an advantage demonstration in the multi-frequency and multi-GNSS context

The ionospheric delay accounts for one of the major errors that the Global Navigation Satellite Systems (GNSS) suffer from. Hence, the global ionosphere Vertical Total Electron Content (VTEC) map has been an important atmospheric product within the International GNSS Service (IGS) since its early establishment. In this contribution, an enhanced method has been proposed for the modeling of the global VTECs, in which the enhancements include two aspects. Firstly, to cope with the rapid development of the newly established Galileo and BeiDou constellations in recent years, we extend the current dual-system (GPS/GLONASS) solution to a quad-system (GPS/GLONASS/Galileo/BeiDou) solution. More importantly, instead of using dual-frequency observations based on the Carrier-to-Code Leveling method, all available triple-frequency signals are utilized with a general raw-observation-based multi-frequency Precise Point Positioning model, which can process dual-, triple- or even arbitrary-frequency observations compatibly and flexibly. Benefiting from this, quad-system slant ionospheric delays can be retrieved based on multi-frequency observations in a more flexible, accurate and reliable way, which are finally used to establish global VTEC models with the spherical harmonic function. In this process, multi-GNSS Differential Code Biases (DCBs) are also estimated as by-products. More than 400 globally distributed stations from the IGS and the Multi-GNSS Experiment (MGEX) networks have been processed in both 2014 (with high solar activity) and 2018 (with low solar activity). Global VTECs have been compared with the IGS final products, and the over-ocean VTECs are validated with the results from the JASON altimeter. The mean RMS values of the VTEC differences are 1.84 (2014) and 1.23 (2018) TECUs with respect to the IGS final products. The standard deviations of the VTEC differences with respect to the JASON results are 4.71 (2014) and 2.82 (2018) TECUs, outperforming all the other products generated with the spherical harmonic function. Additionally, multi-GNSS satellite DCBs have also been validated with the existing products from the Center for Orbit Determination in Europe and MGEX. All the results prove that the proposed method can be used as an effective and accurate approach for global VTEC modeling and DCB estimation, especially in the future multi-frequency and multi-GNSS context.

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.

Combined use of single-frequency data and global ionosphere maps to estimate BDS and Galileo satellite differential code biases

Differential code biases (DCBs) are the most significant systematic errors in global navigation satellite system (GNSS) ionospheric total electronic content (TEC) monitoring and other code-related applications. Currently, the rapidly developing GNSS benefits from the Chinese BeiDou (BDS) and European Galileo systems that continuously offer position, navigation and timing services. In this way, the determination of satellite DCBs (SDCBs), which generally relies on GNSS data collected from dual- or multi-frequency geodetic-grade receivers, is of great importance, especially for the BDS and Galileo systems. However, the use of these geodetic-grade receivers implies a substantial increase in hardware costs. In this paper, we propose a single-frequency (SF) method for the determination of the BDS (C2I–C7I) and Galileo (C1X–C5X) satellite DCBs with the combined use of global ionospheric maps (GIMs) and low-cost SF multi-GNSS receivers, thereby greatly reducing the hardware costs. The mean precision of the satellite DCBs estimated from multi-GNSS data of a standalone SF receiver is approximately 0.35 ns for Galileo and 0.51 ns for BDS, when taking the DCB products published by the Deutsches zentrum für Luft-und Raumfahrt (DLR) as ground truth.

Multi-GNSS contributions to differential code biases determination and regional ionospheric modeling in China

Due to the limited number and uneven distribution globally of Beidou Satellite System (BDS) stations, the contributions of BDS to global ionosphere modeling is still not significant. In order to give a more realistic evaluation of the ability for BDS in ionosphere monitoring and multi-GNSS contributions to the performance of Differential Code Biases (DCBs) determination and ionosphere modeling, we select 22 stations from Crustal Movement Observation Network of China (CMONOC) to assess the result of regional ionospheric model and DCBs estimates over China where the visible satellites and monitoring stations for BDS are comparable to those of GPS/GLONASS. Note that all the 22 stations can track the dual- and triple-frequency GPS, GLONASS, and BDS observations. In this study, seven solutions, i.e., GPS-only (G), GLONASS-only (R), BDS-only (C), GPS + BDS (GC), GPS + GLONASS (GR), GLONASS + BDS (RC), GPS + GLONASS + BDS (GRC), are used to test the regional ionosphere modeling over the experimental area. Moreover, the performances of them using single-frequency precise point positioning (SF-PPP) method are presented. The experimental results indicate that BDS has the same ionospheric monitoring capability as GPS and GLONASS. Meanwhile, multi-GNSS observations can significantly improve the accuracy of the regional ionospheric models compared with that of GPS-only or GLONASS-only or BDS-only, especially over the edge of the tested region which the accuracy of the model is improved by reducing the RMS of the maximum differences from 5–15 to 2–3 TECu. For satellite DCBs estimates of different systems, the accuracy of them can be improved significantly after combining different system observations, which is improved by reducing the STD of GPS satellite DCB from 0.243 to 0.213, 0.172, and 0.165 ns after adding R, C, and RC observations respectively, with an increment of about 12.3%, 29.4%, and 32.2%. The STD of GLONASS satellite DCB improved from 0.353 to 0.304, 0.271, and 0.243 ns after adding G, C, and GC observations, respectively. The STD of BDS satellite DCB reduced from 0.265 to 0.237, 0.237 and 0.229 ns with the addition of G, R and GR systems respectively, and increased by 10.6%, 10.4%, and 13.6%. From the experimental positioning result, it can be seen that the regional ionospheric models with multi-GNSS observations are better than that with a single satellite system model.

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.