Differential Code Bias Products Research Articles

Modeling and performance analysis of precise time transfer based on BDS triple-frequency un-combined observations

In this study, a model of precise time transfer is developed based on the triple-frequency un-combined observations of the BeiDou navigation satellite system, known as UC-PPP. In this model, except for the traditional position, troposphere delay and receiver clock parameters, ionosphere delays are estimated as unknown parameters by adding the prior, spatial and temporal constraints. In addition, receiver differential code biases (DCB) are also estimated as unknown parameters. The standard triple-frequency ionosphere-free model is also introduced, named as IF-PPP. To assess the performance of the model, datasets with short baseline and common external time frequency are used. The results show that the triple-frequency UC-PPP model can be used for precise time transfer, with accuracy and stability identical to those of the IF-PPP model. The model can also provide the receiver DCB and ionosphere total electron content products.

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.

Estimation and evaluation of the triple-frequency GPS satellite inter-frequency clock bias

A new estimation method is presented to detect and remove the potential outliers in the triple-frequency GPS inter-frequency clock bias (IFCB) estimating. The estimated results of the robust estimation (RE) can successfully mitigate the influence of outliers on IFCB estimation, IFCB modelling and IFCB application. The difference between the constant parts of IFCB estimated with observations and the differential code bias (DCB) (P1–P2) and DCB (P1–P5) products is computed and this difference shows that the DCB products cannot completely replace the constant parts of IFCB. The characteristic of the IFCB modeling is discussed based on the 5- year results. The estimated IFCB is evaluated and its impact on the precise point positioning (PPP) is analysed. The PPP results show that the influence of the IFCB on the static positioning is different with that of kinematic mode.

Characteristics and Precision Analysis of BeiDou2 Satellite Differential Code Bias Products

Currently, resolution of the BeiDou2 satellites differential code bias (DCB) is greatly limited by the number of tracking stations and data quality. To improve the precision of calculated DCBs, an adaptive control method, based on elevation angle weight and posteriori variance factor, is proposed. The feasibility and precision of the proposed method are verified via analysis of the DCBs precision and application of single-frequency precise point positioning (SF-PPP). The results show that the long-term variation of the daily BeiDou2 satellite DCB sequence is stable and the precision of DCBs of BeiDou2 satellites in different constellations is different. In addition, it is found by using periodogram and fast Fourier transform (FFT) methods that weekly and daily periodic signals exist in the daily BeiDou2 satellite DCB products. The results of SF-PPP show that root mean square (RMS) horizontal residual is reduced by 10% and convergence time is shortened significantly using DCB products.

Estimation and analysis of the short-term variations of multi-GNSS receiver differential code biases using global ionosphere maps

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.

GPS and BeiDou Differential Code Bias Estimation Using Fengyun-3C Satellite Onboard GNSS Observations

Differential code biases (DCBs) are important parameters in GNSS (Global Navigation Satellite System) applications such as positioning as well as ionosphere remote sensing. In comparison to the conventional approach, which utilizes ground-based observations and parameterizes global ionosphere maps together with DCBs, a method is presented for GPS and BeiDou system (BDS) satellite DCB estimation using onboard observations from the Chinese Fengyun-3C (FY3C) satellite. One month worth of GPS and BDS data during March 2015 was exploited and the GPS C1C-C2W and BDS C2I-C7I DCBs were explored. To improve DCB estimation precision, the dual frequency carrier phase measurements leveled by code measurements were used to form basic observation equation. Code multipath errors of the FY3C onboard GPS/BDS observations were assessed and modeled as grid maps, and their impact on DCB estimation was analyzed. By correcting code multipath errors, the stability of DCB estimates was improved by 5.0%, 3.1%, 16.2% and 13.6% for GPS, and BDS geosynchronous orbit satellites (GEOs), inclined geosynchronous satellite orbit satellites (IGSOs) and medium Earth orbit satellites (MEOs), respectively. The monthly stability of FY3C-based DCBs was at the order of 0.1 ns for GPS satellites, 0.2 ns for BDS GEOs and 0.1 ns for BDS IGSOs and MEOs. By comparison to the ground-based DCB products issued by other institutions, FY3C-based DCBs showed stability degradation for BDS C02 and C05 satellites, while, for other satellites, the stability reached a similar or even superior level. The estimated FY3C receiver DCB stability was at the order of 0.2 ns for both GPS and BDS. In addition to the DCB estimates, the obtained vertical total electron content above the FY3C satellite orbit was also investigated and its realism was examined in physical and numerical aspects.

Influence of the GLONASS inter-frequency bias on differential code bias estimation and ionospheric modeling

Due to the application of frequency division multiple access, the signals of GLONASS satellites suffer from code and carrier phase inter-frequency biases (IFBs). In this study, the effects of GLONASS code IFBs on differential code bias (DCB) estimation and ionospheric modeling are investigated. The observational data from more than 130 MGEX stations for a period of 60 days are used to generate the DCB products, with and without considering the GLONASS code IFB. According to the results, residuals of the DCB estimation without GLONASS code IFB consideration exhibit frequency-dependent systematic errors, errors that can be eliminated when the GLONASS code IFB is taken into account. The GLONASS inter-frequency differential code bias (IFDCB), defined as the difference of the sum of satellite and receiver DCB estimates without and with GLONASS code IFB consideration, is taken to represent the difference between the two DCB estimation types. The IFDCBs are generally in the range of ?4 and ?2 ns for C1P---C2P and C1C---C1P, respectively, and the largest difference of the C1P---C2P IFDCBs between frequency channels is >7 ns. The VTEC products of ionospheric modeling with and without the consideration of the GLONASS code IFB are also generated based on data from 30 days of MGEX and IGS networks. The mean difference and standard deviation between them are 0.53---1.13 and 0.98---1.75 TECU, respectively.

BeiDou satellite’s differential code biases estimation based on uncombined precise point positioning with triple-frequency observable

The differential code bias (DCB) of BeiDou satellite is an important topic to make better use of BeiDou system (BDS) for many practical applications. This paper proposes a new method to estimate the BDS satellite DCBs based on triple-frequency uncombined precise point positioning (UPPP). A general model of both triple-frequency UPPP and Geometry-Free linear combination of Phase-Smoothed Range (GFPSR) is presented, in which, the ionospheric observable and the combination of triple-frequency satellite and receiver DCBs (TF-SRDCBs) are derived. Then the satellite and receiver DCBs (SRDCBs) are estimated together with the ionospheric delay that is modeled at each individual station in a weighted least-squares estimator, and the satellite DCBs are determined by introducing the zero-mean condition of all available BDS satellites. To validate the new method, 90day’s real tracking GNSS data (from January to March in 2014) collected from 9 Multi-GNSS Experiment (MGEX) stations (equipped with Trimble NETR9 receiver) is used, and the BDS satellite DCB products from German Aerospace Center (DLR) are taken as reference values for comparison. Results show that the proposed method is able to precisely estimate BDS satellite DCBs: (1) the mean value of the day-to-day scattering for all available BDS satellites is about 0.24ns, which is reduced in average by 23% when compared with the results derived by only GFPSR. Moreover, the mean value of the day-to-day scattering of IGSO satellites is lower than that of GEO and MEO satellites; (2) the mean value of RMS of the difference with respect to DLR DCB products is about 0.39ns, which is improved by an average of 11% when compared with the results derived by only GFPSR. Besides, the RMS of IGSO and MEO satellites is at the same level which is better than that of GEO satellites.

Determination of differential code biases with multi-GNSS observations

In order to better understand the differential code biases (DCBs) of global navigation satellite system, the IGGDCB method is extended to estimate the intra- and inter-frequency biases of the global positioning system (GPS), GLONASS, BeiDou navigation satellite system (BDS), and Galileo based on observations collected by the multi-GNSS experiment (MGEX) of the international GNSS service (IGS). In the approach of IGGDCB, the local ionospheric total electronic content is modeled with generalized triangular series (GTS) function rather than using a global ionosphere model or a priori ionospheric information. The DCB estimated by the IGGDCB method is compared with the DCB products from the Center for Orbit Determination in Europe (CODE) and German Aerospace Center (DLR), as well as the broadcast timing group delay (TGD) parameters over a 2-year span (2013 and 2014). The results indicate that GPS and GLONASS intra-frequency biases obtained in this work show the same precision levels as those estimated by DLR (about 0.1 and 0.2–0.4 ns for the two constellations, respectively, with respect to the products of CODE). The precision levels of IGGDCB-based inter-frequency biases estimated over the 24-month period are about 0.29 ns for GPS, 0.56 ns for GLONASS, 0.36 ns for BDS, and 0.24 ns for Galileo, respectively. Here, the accuracies of GPS and GLONASS biases are assessed relative to the products of CODE, while those of BDS and Galileo are compared with the estimates of DLR. In addition, the monthly stability indices of IGGDCB-based DCBs are 0.11 (GPS), 0.18 (GLONASS), 0.17 (BDS), and 0.14 (Galileo) ns for the individual constellation.

An enhanced algorithm to estimate BDS satellite’s differential code biases

This paper proposes an enhanced algorithm to estimate the differential code biases (DCB) on three frequencies of the BeiDou Navigation Satellite System (BDS) satellites. By forming ionospheric observables derived from uncombined precise point positioning and geometry-free linear combination of phase-smoothed range, satellite DCBs are determined together with ionospheric delay that is modeled at each individual station. Specifically, the DCB and ionospheric delay are estimated in a weighted least-squares estimator by considering the precision of ionospheric observables, and a misclosure constraint for different types of satellite DCBs is introduced. This algorithm was tested by GNSS data collected in November and December 2013 from 29 stations of Multi-GNSS Experiment (MGEX) and BeiDou Experimental Tracking Stations. Results show that the proposed algorithm is able to precisely estimate BDS satellite DCBs, where the mean value of day-to-day scattering is about 0.19 ns and the RMS of the difference with respect to MGEX DCB products is about 0.24 ns. In order to make comparison, an existing algorithm based on IGG: Institute of Geodesy and Geophysics, China (IGGDCB), is also used to process the same dataset. Results show that, the DCB difference between results from the enhanced algorithm and the DCB products from Center for Orbit Determination in Europe (CODE) and MGEX is reduced in average by 46 % for GPS satellites and 14 % for BDS satellites, when compared with DCB difference between the results of IGGDCB algorithm and the DCB products from CODE and MGEX. In addition, we find the day-to-day scattering of BDS IGSO satellites is obviously lower than that of GEO and MEO satellites, and a significant bias exists in daily DCB values of GEO satellites comparing with MGEX DCB product. This proposed algorithm also provides a new approach to estimate the satellite DCBs of multiple GNSS systems.

A new differential code bias (C1–P1) estimation method and its performance evaluation

The current satellite clock products are computed using the ionosphere-free phase (L1/L2) and code (P1/P2) observations. Thus, if users conduct undifferenced positioning using these clock products together with C1 and P2 observations, the differential code bias (DCB) (C1---P1) should be properly compensated. The influence of DCB (C1---P1) on the undifferenced ambiguity solutions is investigated. Based on the investigation, we propose a new DCB (C1---P1) estimation method. Using it, the satellite DCB (C1---P1) can be computed. A 30-day (DOY 205---234, 2012) dual-frequency GPS data set is processed to estimate the DCB (C1---P1). Comparing the estimated results with that of IGS DCB products, the accuracy is better than 0.13 m. The performances of DCB (C1---P1) in the code-based single-point positioning, precise point positioning (PPP) convergence and wide-lane uncalibrated phase delay (UPD) estimation are investigated using the estimated DCB (C1---P1). The results of the code-based single-point positioning show that the influence of DCB (C1---P1) on the up direction is more evident than on the horizontal directions. The accuracy is improved by 50 % and reaches to decimeter level with DCB (C1---P1) application. The performance of DCB (C1---P1) in PPP shows that it can accelerate PPP convergence through improving the accuracy of the code observation. The computed UPD values show that influence of DCB (C1---P1) on UPD of each satellite is different, and some values are larger than 0.3 cycles.

The realization and convergence analysis of combined PPP based on raw observation

In order to speed up Precise Point Positioning (PPP)’s convergence, a combined PPP method with GPS and GLONASS which is based on using raw observations is proposed, and the positioning results and convergence time have been compared with that of single system. The ionospheric delays and receiver’s Differential Code Bias (DCB) corrections are estimated as unknown parameters in this method. The numerical results show that the combined PPP has not caused significant impacts on the final solutions, but it greatly improved Position Dilution of Precision (PDOP) and convergence speed and enhanced the reliability of the solution. Meanwhile, the convergence speed is greatly influenced by the receiver’s DCB, positioning results in horizontal which are better than 10cm can be realized within 10min. In addition, the ionosphere and DCB products can be provided with high precision.