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Differential code bias (DCB) of satellite is an error that cannot be ignored in precise positioning, timing, ionospheric modeling, satellite clock correction, and ambiguity resolution. The completion of the third generation of BeiDou Navigation Satellite System (BDS-3) has extended DCB to multichannel code bias observations and observable-specific signal bias (OSB). In this paper, the DCB and OSB products provided by the Chinese Academy of Sciences (CAS) are analyzed and compared. The DCB parameters for the BDS satellites are applied in both single- and dual-frequency single point positioning (SPP), and the results are intensively investigated. Based on the satellite DCB parameters of the BDS, the performance of precise point positioning (PPP) with different frequency combinations is also analyzed in terms of positioning accuracy and convergence time. The standard deviations (STDs) of DCBs at each signal pair fluctuate from 0.2 ns to 1.5 ns. The DCBs of BDS-2 are slightly more stable than those of BDS-3. The mean values and STDs of C2I and C7I OSBs for BDS-2 are at the same level and are numerically smaller than their counterparts for the C6I OSBs. The mean OSBs for each signal of the BDS-3, excluding C2I, fluctuate between 12.35 ns and 12.94 ns, and the STD fluctuates between 2.11 ns and 3.10 ns. The DCBs and OSBs of the BDS-3 of the IGSO satellites are more stable than those of the MEO satellites. The corrections for TGD and DCB are able to improve the accuracy of single-frequency SPP by 44.09% and 44.07%, respectively, and improve the accuracy of dual-frequency SPP by 6.44% and 12.85%, respectively. The most significant improvements from DCB correction are seen in single-frequency positioning with B1I and dual-frequency positioning with B2a+B3I. DCB correction can improve the horizontal and three-dimensional positioning accuracy of the dual-frequency PPP of different ionosphere-free combinations by 13.53% and 13.84% on average, respectively, although the convergence is slowed. [ABSTRACT FROM AUTHOR]

Tropospheric delay (TD) parameter estimation is a critical issue underlying high-precision data processing for global navigation satellite systems (GNSSs). The most widely used TD parameter estimation methods are the random walk (RW) and piece-wise constant (PWC). The RW method can effectively track rapid variations of tropospheric delay, but it may introduce excessive noise. In contrast, the PWC method introduces less noise, but it is less adaptable to cases of large variations of tropospheric delay. To address the problem of how to choose the optimal TD parameter estimation method, this paper investigates the variation patterns of international GNSS service zenith tropospheric delay (IGS ZTD) products and proposes a combined strategy model for TD parameter estimation. Firstly, this paper avoids the day-boundary jumps problem of IGS ZTD products by grouping based on single-day data. Secondly, this paper introduces discrete point areas (DPAs) to measure the magnitude of the ZTD values and uses comprehensive indicators to reflect the variation of ZTD. Next, based on the Köppen-Geiger climate classification, this study selected five different climate classifications with a total of 20 IGS stations as experimental data. The data assessed span from day of year (DOY) 001 to DOY 365 in 2022. This paper then applied 26 different parameter estimation strategies for static precise point positioning (PPP) data processing, and the parameter estimation strategies that were used include the RW and PWC (with the piece-wise constant ranging from twenty minutes to five hundred minutes at twenty-minute intervals). Finally, ZTD and positioning results were obtained using various parameter estimation methods, and a combined strategy model was established. We selected five different climate classifications of IGS stations as validation data and designed three sets of comparative experiments: RW, PWC120, and the combined strategy model, to verify the effectiveness of the combined strategy model. The experimental results revealed that: RW and the combined strategy model have a comparable ZTD accuracy and both are superior to PWC120. The combined strategy model improves the positioning accuracy in the U direction compared to RW and PWC120. In arid (B) and polar (E) regions with a small variation of TD, the PWC120 strategy displayed a better positioning accuracy than the RW strategy; in equatorial (A) and warm-temperate (C) regions, where there are large variations of TD, the RW strategy exhibited a better positioning accuracy than the PWC120 strategy. The combined strategy model can flexibly select the optimal parameter estimation method according to the comprehensive indicator while ensuring ZTD estimation accuracy; it enhances positioning accuracy. [ABSTRACT FROM AUTHOR]

For the same antenna type, numerical differences among the phase center correction (PCC) models released by different institutes can reach several millimeters, which is far beyond the nominal calibration accuracy. This contribution introduces a new method to evaluate the consistency of these PCC models. We first investigated the coupling of phase center offset (PCO) and phase center variation (PCV) through simulation experiments, and the results show that the calibrated PCO values under different strategies may result in large differences, and so do PCV values due to strong coupling with PCO. This is further confirmed by field calibration experiments. Moreover, a new datum parameter is introduced to equivalently transform the PCC models to assess the consistency of PCC models of the same antenna type calibrated under different strategies or by different facilities. It is also essential to perform consistency analysis of PCC models in the coordinate domain. We further investigated these PCC models through a simulated positioning experiment. The results show that millimeter-level consistency of PCC models will lead to the same level of positioning precision in the coordinate domain. Moreover, as a comparison, both baseline positioning and PPP were performed with an antenna-type JAV_RINGANT_G3T NONE based on real observations. Multiday results showed that the average RMS of the positioning differences between PCC models from robot and anechoic chamber calibration is less than 1 mm for the baseline solution and 4 mm for the PPP solution, although the PCC model differences can reach 6 mm in L1 and 4 mm in L2, respectively. Finally, we also investigated the distribution of position biases without PCC or with inaccurate PCC. Considering the actual GPS constellation, we found that position biases have a strong correlation with latitude, if PCV values fluctuate greatly with the users' elevation angle. [ABSTRACT FROM AUTHOR]

The Japanese Quasi-Zenith Satellite System (QZSS) is a regional navigation satellite system covering the entire Asia-Oceania region. Except for the standard satellite navigation signals, QZSS satellites also broadcast L6E augmentation signals with real time GNSS precise orbit every 30 s and clock messages every 1 s, which is very important and necessary for Real-Time precise point positioning (RTPPP) applications. In this paper, the MADOCA real-time services derived from L6E augmentation signals were evaluated for both accuracy and availability compared with IGS final products. To avoid the datum difference of GPS orbit between MADOCA real-time and IGS final products, the 7-parameters Helmert transformation was firstly used in this paper, and then the orbit was evaluated on radial, along, and cross-track directions. On the clock evaluation, the mean satellites clock errors were taken as reference clock error, and then the standard deviation (STD) was calculated for each satellite. Furthermore, the signal in space range errors (SISRE) were also summarized to evaluate the ranging-measurement accuracy. Seven-day evaluation results show that satellite orbit, clock errors, and the final SISRE errors range as being 1.8–3.9 cm, 0.04–0.15 ns (1.2–4.5 cm), and 5–10 cm, respectively. For the one-year long-term evaluation, daily SISRE errors in 2018 show consistent performance with that of seven days. Furthermore, the open source software RTKLIB was used to evaluate the kinematic PPP performance based on the MADOCA real-time products, and it shows that the daily positioning accuracy of the 20 globally distributed IGS stations can reach 4.9, 4.2, 11.7, and 12.1 cm in the east, north, up, and 3D directions, respectively. Hence, it is concluded that the current MADOCA real-time ephemeris products can provide orbit and clock products with SISRE on centimeters level with high interval, which could meet the demands of the RTPPP solution and serve real-time users who can access the MADOCA real-time products via L6E signal or internet. [ABSTRACT FROM AUTHOR]