Estimation and Analysis of BDS2 and BDS3 Differential Code Biases and Global Ionospheric Maps Using BDS Observations

Following the continuous and stable regional service of BDS2, the BDS3 officially announced its global service in July 2020. To fully take advantage of the new multi-frequency BDS3 signals in ionosphere sensing and positioning, it is essential to understand the characteristics of the differential code bias (DCB) of new BDS3 signals and BDS performance in global ionospheric maps (GIMs) estimation. This article presents an evaluation of the characteristics of 13 types of BDS DCBs and the accuracy of BDS-based GIM based on the data provided by the International GNSS Service (IGS) and International GNSS Monitoring and Assessment System (iGMAS) for the first time. The GIMs and DCBs are estimated by the APM (Innovation Academy for Precision Measurement Science and Technology) method in a time efficient manner, which can be divided into two main steps. The first step is to produce GIMs based on BDS observations at the B1I, B2I and B3I signals, and the second step is to estimate DCBs among the other frequency bands by removing the ionospheric delay using the precomputed GIMs. Good agreement is found between the APM-based satellite DCB estimates and those from the Chinese Academy of Sciences (CAS) and the German Aerospace Center (DLR) at levels of 0.26 ns and 0.18 ns, respectively. The results, spanning one month, show that the stability of BDS DCB estimates among different frequency bands are related to the contributed observations, and the receiver DCB estimates represent larger STD values than the satellite DCB estimates. The differences in receiver DCB estimates between BDS2 and BDS3 are found to be related to the types of receivers and antennas and firmware version, and the bias of the JAVAD receivers reaches 1.03 ns. The results also indicate that the difference in the single-frequency standpoint positioning (SPP) accuracy using GPS-based and BDS-based GIMs for ionospheric delay corrections is less than 0.03 m in both the horizontal and vertical directions.

Epoch-by-epoch estimation and analysis of BeiDou Navigation Satellite System (BDS) receiver differential code biases with the additional BDS-3 observations

The differential code bias (DCB) of the Global Navigation Satellite System (GNSS) is an important error source in ionospheric modeling, which was generally estimated as constants every day. However, the receiver DCB may be changing due to the varying spatial environments and temperatures. In this paper, a method based on the global ionospheric map (GIM) of the Center for Orbit Determination in Europe (CODE) is presented to estimate the BeiDou Navigation Satellite System (BDS) receiver DCB with epoch-by-epoch estimates. The BDS receiver DCBs are analyzed from 30 d of Multi-GNSS Experiment observations. The comparison of estimated receiver DCB of BDS with the DCB provided by the German Aerospace Center (DLR) and the Chinese Academy of Sciences (CAS) shows a good agreement. The root-mean-square (rms) values of receiver DCB are 0.43 and 0.80 ns with respect to the DLR and CAS estimates, respectively. In terms of the intraday variability of receiver DCB, most of the receiver DCBs show relative stability within 1 d with the intraday standard deviation (SD) of less than 1 ns. However, larger fluctuations with more than 2 ns of intraday receiver DCB are found. Besides, the intraday stability of receiver DCB calculated by the third-generation BDS (BDS-3) and the second-generation BDS (BDS-2) observations is compared. The result shows that the intraday stability of BDS-3 receiver DCB is better than that of BDS-2 receiver DCB.

Reply to Comment on Choi et al. Correlation between Ionospheric TEC and the DCB Stability of GNSS Receivers from 2014 to 2016. Remote Sens. 2019, 11, 2657

Choi et al. (2019) suggested that ionospheric total electron content (TEC) and receiver differential code bias (rDCB) stability have a strong correlation during a period of two years from 2014 to 2016. This article is a response to Zhong et al. (2020), who pointed out that the long-term variations of the GPS DCBs are mainly attributed to the satellite replacement rather than the ionospheric variability. In this issue, we investigated the center for orbit determination in Europe (CODE) Global Ionosphere Maps (GIM) products from 2000 to 2020. In this study, changes in TEC and receiver DCB (rDCB) root mean squares (RMS) at Bogota (BOGT) station still have a clear correlation. In addition, there was a moderate correlation between satellite DCB RMS and rDCB RMS. As a result, we suggest that rDCB can be affected simultaneously by GPS sDCB as well as ionospheric activity.

Comment on Choi et al. Correlation between Ionospheric TEC and the DCB Stability of GNSS Receivers from 2014 to 2016. Remote Sens. 2019, 11, 2657

Choi et al. (2019) analyzed the correlation between the ionospheric total electron content (TEC) and the Global Navigation Satellite System (GNSS) receiver differential code bias (DCB) and concluded that the long-term variations of the receiver DCB are caused by the corresponding variations in the ionosphere. Unfortunately, their method is problematic, resulting in conclusions that are not useful. The long-term variations of the Global Positioning System (GPS) DCBs are primarily attributed to the GPS satellite replacement with different satellite block series under the zero-mean constraint condition, rather than the ionospheric variability.

Epoch-by-epoch estimation and analysis of BDS receiver differential code biases with the additional BDS-3 observations

The differential code bias (DCB) of global navigation satellite systems (GNSS) is an important error source in ionospheric modeling, which was generally estimated as constants every day. However, the receiver DCB may be changing due to the varying space environments and temperatures. In this paper, the receiver DCB of BeiDou Navigation Satellite System (BDS) is estimated as the changing parameter within one day with epoch-by-epoch. The BDS receiver DCBs are analyzed from 30 days of multi-GNSS experiment observations. The comparison of estimated receiver DCB of BDS with the DCB provided by German Aerospace Center (DLR) and Chinese Academy of Sciences (CAS) shows a good agreement. The root mean square (RMS) values of receiver DCB are 0.43 and 0.80 ns with respect to DLR and CAS, respectively. In terms of the intra-day variability of receiver DCB, most of the receiver DCBs show relative stability within one day with the intra-day standard deviation (STD) of less than 1 ns. However, larger fluctuations with more than 2 ns of intra-day receiver DCB are found. Besides, the intra-day stability of receiver DCB calculated by the third-generation BDS (BDS-3) and the second-generation BDS (BDS-2) observations is compared. The result shows that the intra-day stability of BDS-3 receiver DCB is better than that of BDS-2 receiver DCB.

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.

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.