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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. [ABSTRACT FROM AUTHOR]

Differential code biases (DCBs) account for the most significant systematical biases when sensing the earth's ionosphere with GNSS observations and are also important correction parameters in GNSS applications of positioning, navigation and timing. With the continuous modernization of the American GPS and Russian GLONASS systems, and also the rapid developments of the European Galileo and Chinese BeiDou systems, there is a strong demand of precise satellite DCB products for multiple constellations and frequencies. This study proposes a new method for the precise determination of multi-GNSS triple-frequency DCBs, which can be divided into three steps. The first step is to precisely retrieve slant ionospheric delays and "additional code biases" based on a newly established full-rank triple-frequency precise point positioning (PPP) model with raw observations. Both the slant ionospheric delays and "additional code biases" containing the DCBs need to be estimated. Then, an enhanced IGGDCB (IGG stands for Institute of Geodesy and Geophysics) method is used to estimate the DCBs between the first and second frequency bands with the PPP-derived slant ionospheric delays. At last, the previously estimated DCBs between the first and second frequency bands are substituted into the "additional code biases" and DCBs between the first and third frequency bands are estimated. Multi-GNSS slant ionospheric delays from the triple-frequency PPP method are compared with those from the traditional dual-frequency carrier-to-code level (CCL) method, in terms of formal precision and zero-baseline experiment. Quad-system average formal precisions are 0.08 and 0.41 TECU, for PPP and CCL methods, respectively, indicating the obvious improvements of PPP over CCL. One month of data from 60 globally distributed multi-GNSS experiment stations are selected, and totally eight types of DCBs are estimated for GPS, GLONASS, Galileo and BeiDou. Multi-GNSS satellite DCBs generated with the proposed method are compared with the products from different agencies, including Center for Orbit Determination in Europe (CODE), Deutsches zentrum für Luft-und Raumfahrt (DLR) and Chinese Academy of Sciences (CAS). For GPS C1WC2 W DCBs, RMS values with respect to CODE products are 0.24, 0.07 and 0.09 ns for DLR, CAS and IGG (this study), respectively. RMS values are 0.31/0.25 and 0.19/0.15 ns, for GPS C1WC5X and C1WC5Q DCBs and with respect to DLR/CAS, respectively. For GLONASS C1PC2P DCBs, RMS values with respect to CODE are 0.68, 0.49 and 0.33 ns for DLR, CAS and IGG, respectively. For Galileo, RMS values are 0.16/0.20 and 0.13/0.14 ns, for C1XC5X and C1XC7X DCBs and with respect to DLR/CAS, respectively. For BeiDou, RMS values are 0.32/0.25 and 0.34/0.41, for C2IC7I and C2IC6I DCBs and with respect to DLR/CAS. These results show that the proposed method can provide multi-GNSS and multi-frequency satellite DCB estimation with high precision, processing efficiency and flexibility. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A joint-processing model for multi-GNSS (GPS, GLONASS, BDS and GALILEO) precise point positioning (PPP) is proposed, in which raw code and phase observations are used. In the proposed model, inter-system biases (ISBs) and GLONASS code inter-frequency biases (IFBs) are carefully considered, among which GLONASS code IFBs are modeled as a linear function of frequency numbers. To get the full rank function model, the unknowns are re-parameterized and the estimable slant ionospheric delays and ISBs/IFBs are derived and estimated simultaneously. One month of data in April, 2015 from 32 stations of the International GNSS Service (IGS) Multi-GNSS Experiment (MGEX) tracking network have been used to validate the proposed model. Preliminary results show that RMS values of the positioning errors (with respect to external double-difference solutions) for static/kinematic solutions (four systems) are 6.2 mm/2.1 cm (north), 6.0 mm/2.2 cm (east) and 9.3 mm/4.9 cm (up). One-day stabilities of the estimated ISBs described by STD values are 0.36 and 0.38 ns, for GLONASS and BDS, respectively. Significant ISB jumps are identified between adjacent days for all stations, which are caused by the different satellite clock datums in different days and for different systems. Unlike ISBs, the estimated GLONASS code IFBs are quite stable for all stations, with an average STD of 0.04 ns over a month. Single-difference experiment of short baseline shows that PPP ionospheric delays are more precise than traditional leveling ionospheric delays. [ABSTRACT FROM AUTHOR]