Satellite Differential Code Bias Estimation Research Articles

Estimating BDS-3 Satellite Differential Code Biases with the Single-Frequency Uncombined PPP Model.

Differential Code Bias (DCB) is a crucially systematic error in satellite positioning and ionospheric modeling. This study aims to estimate the BeiDou-3 global navigation satellite system (BDS-3) satellite DCBs by using the single-frequency (SF) uncombined Precise Point Positioning (PPP) model. The experiment utilized BDS-3 B1 observations collected from 25 International GNSS Service (IGS) stations located at various latitudes during March 2023. The results reveal that the accuracy of estimating B1I-B3I DCBs derived from single receiver exhibits latitude dependence. Stations in low-latitude regions show considerable variability in the root mean square (RMS) of absolute offsets for satellite DCBs estimation, covering a wide range of values. In contrast, mid- to high-latitude stations demonstrate a more consistent pattern with relatively stable RMS values. Moreover, it has been observed that the stations situated in the Northern Hemisphere display a higher level of consistency in the RMS values when compared to those in the Southern Hemisphere. When incorporating estimates from all 25 stations, the RMS of the absolute offsets in satellite DCBs estimation consistently remained below 0.8 ns. Notably, after excluding 8 low-latitude stations and utilizing data from the remaining 17 stations, the RMS of absolute offsets in satellite DCBs estimation decreased to below 0.63 ns. These enhancements underscore the importance of incorporating a sufficient number of mid- and high-latitude stations to mitigate the effects of ionospheric variability when utilizing SF observations for satellite DCBs estimation.

GPS satellite differential code bias estimation with current eleven low earth orbit satellites

GPS satellite differential code bias estimation with current eleven low earth orbit satellites

Estimation and Analysis of GNSS Differential Code Biases (DCBs) Using a Multi-Spacing Software Receiver

In the use of global navigation satellite systems (GNSS) to monitor ionosphere variations by estimating total electron content (TEC), differential code biases (DCBs) in GNSS measurements are a primary source of errors. Satellite DCBs are currently estimated and broadcast to users by International GNSS Service (IGS) using a network of GNSS hardware receivers which are inside structure fixed. We propose an approach for satellite DCB estimation using a multi-spacing GNSS software receiver to analyze the influence of the correlator spacing on satellite DCB estimates and estimate satellite DCBs based on different correlator spacing observations from the software receiver. This software receiver-based approach is called multi-spacing DCB (MSDCB) estimation. In the software receiver approach, GNSS observations with different correlator spacings from intermediate frequency datasets can be generated. Since each correlator spacing allows the software receiver to output observations like a local GNSS receiver station, GNSS observations from different correlator spacings constitute a network of GNSS receivers, which makes it possible to use a single software receiver to estimate satellite DCBs. By comparing the MSDCBs to the IGS DCB products, the results show that the proposed correlator spacing flexible software receiver is able to predict satellite DCBs with increased flexibility and cost-effectiveness than the current hardware receiver-based DCB estimation approach.

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.

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.

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.

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.

Multi-GNSS triple-frequency differential code bias (DCB) determination with precise point positioning (PPP)

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 fur 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.

Improving performance of GPS satellite DCB estimation for regional GPS networks using long-term stability

Compensation for differential code bias (DCB) is necessary because it is the major source of errors in total electron content (TEC) measurements. The DCB estimation performance is degraded when only the regional GPS network is used. Because DCB estimation is highly correlated with ionospheric modeling, this degradation is particularly evident for measurements concentrated in an area of high TEC concentration. This study proposes a DCB estimation method that uses the long-term stability of the DCB to improve the estimation performance of the regional GPS network. We estimate satellite DCBs by assuming their constancy over seven months. This extended period increases the number of measurements used in DCB estimation and changes the local time distribution of collected measurements. As a result, the unbalanced distribution of specific ionospheric conditions disappears. Tests are performed using both global and regional networks, and the estimation performance is evaluated based on the position error and pseudorange residuals. First, the difference between the global and regional networks when using the conventional method is analyzed. Second, proposed methods are applied to regional networks. The proposed method can improve the DCB estimation performance, and the results are similar to those obtained using one-day global network data.

Estimation and analysis of Galileo differential code biases

When sensing the Earth’s ionosphere using dual-frequency pseudorange observations of global navigation satellite systems (GNSS), the satellite and receiver differential code biases (DCBs) account for one of the main sources of error. For the Galileo system, limited knowledge is available about the determination and characteristic analysis of the satellite and receiver DCBs. To better understand the characteristics of satellite and receiver DCBs of Galileo, the IGGDCB (IGG, Institute of Geodesy and Geophysics, Wuhan, China) method is extended to estimate the satellite and receiver DCBs of Galileo, with the combined use of GPS and Galileo observations. The experimental data were collected from the Multi-GNSS Experiment network, covering the period of 2013–2015. The stability of both Galileo satellite and receiver DCBs over a time period of 36 months was thereby analyzed for the current state of the Galileo system. Good agreement of Galileo satellite DCBs is found between the IGGDCB-based DCB estimates and those from the German Aerospace Center (DLR), at the level of 0.22 ns. Moreover, high-level stability of the Galileo satellite DCB estimates is obtained over the selected time span (less than 0.25 ns in terms of standard deviation) by both IGGDCB and DLR algorithms. The Galileo receiver DCB estimates are also relatively stable for the case in which the receiver hardware device stays unchanged. It can also be concluded that the receiver DCB estimates are rather sensitive to the change of the firmware version and that the receiver antenna type has no great impact on receiver DCBs.

Two-step method for the determination of the differential code biases of COMPASS satellites

The differential code bias (DCB) in satellites of the Global Navigation Satellite Systems (GNSS) should be precisely corrected when designing certain applications, such as ionospheric remote sensing, precise point positioning, and time transfer. In the case of COMPASS system, the data used for estimating DCB are currently only available from a very limited number of global monitoring stations. However, the current GPS/GLONASS satellite DCB estimation methods generally require a large amount of geographically well-dis- tributed data for modeling the global ionospheric vertical total electron content (TEC) and are not particularly suitable for current COMPASS use. Moreover, some satellites with unstable DCB (i.e., relatively large scatter) may affect other satellite DCB estimates through the zero-mean reference that is currently imposed on all satellites. In order to overcome the inadequacy of data sources and to reduce the impact of unsta- ble DCB, a new approach, designated IGGDCB, is developed for COMPASS satellite DCB determination. IGG stands for the Institute of Geodesy and Geophysics, which is located in Wuhan, China. In IGGDCB, the ionospheric vertical TEC of each individual station is independently modeled by a gener- alized triangular series function, and the satellite DCB refer- ence is selected using an iterative DCB elimination process. By comparing GPS satellite DCB estimates calculated by the IGGDCB approach based on only a handful (e.g., seven) of tracking stations against that calculated by the currently existing methods based on hundreds of tracking stations, we are able to demonstrate that the accuracies of the IGGDCB- based DCB estimates perform at the level of about 0.13 and 0.10 ns during periods of high (2001) and low (2009) solar activity, respectively. The iterative method for DCB reference selection is verified by statistical tests that take into account the day-to-day scatter and the duration that the satellites have spent in orbit. The results show that the impact of satellites with unstable DCB can be considerably reduced using the IGGDCB method. It is also confirmed that IGGDCB is not only specifically valid for COMPASS but also for all other GNSS.