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

Abstract

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 triplefrequency 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.

Quasi-4-dimension ionospheric modeling and its application in PPP

“…It should be noted that the receiver biases are absorbed by the ionospheric delay to remove the rank deficiency, thus special attention should be given to the SID modeling for inconsistent receiver networks. Shi et al (2012b) and Zhao et al (2018) presented a sophisticated ionospheric parameter constrain model, i.e., DEterministic plus Stochastic Ionosphere models for GNSS (DESIGN), and it was demonstrated that the ionospheric delay can be separated from the receiver biases in this case (Gu et al 2020;Zhang et al 2021). Typically, the SID modeling performs much better than that of GIM since it uses the LOS ionospheric delay in modelling directly, thus avoiding the errors induced by the elevation mapping function and the constant-height thin-layer model .…”

GNSS satellite inter-frequency clock bias estimation and correction based on IGS clock datum: a unified model and result validation using BDS-2 and BDS-3 multi-frequency data

“…From the above discussion, it is concluded that the uncombined model provides a better way to realize an overall estimation of both satellite PIFCB and CIFCB which are consistent with the IGS clocks. However, the uncombined model for IFCB or DCB estimation and correction was merely validated by triple-frequency data in previous studies (Guo and Geng 2017;Liu et al 2018;Pan et al 2018a, b;Fan et al 2019;Gu et al 2020). When data on more than three frequencies are considered, numerous IFCBs that can be formed from any three frequencies are not unified in the uncombined model.…”

Initial assessment of single- and dual-frequency BDS-3 RTK positioning

“…BDS-3 retains B1I and B3I of BDS-2 to realise the transition from BDS-2 to BDS-3. On this basis, BDS-3 also transmits three new frequency signals to achieve compatibility and interoperability with other GNSSs, namely, B1C at 1575.42 MHz, B2a at 1176.45 MHz, and B2b at 1207.14 MHz (CSNO 2019aGu et al 2020).…”