Differential Code Bias Estimation Research Articles

Effects of Topside Ionosphere Modeling Parameters on Differential Code Bias (DCB) Estimation Using LEO Satellite Observations

Given the potential of low-earth orbit (LEO) satellites in terms of navigation enhancement, accurately estimating the differential code bias (DCB) of GNSS satellites and LEO satellites is an important research topic. In this study, to obtain accurate DCB estimates, the effects of vertical total electron content (VTEC) modeling parameters of the topside ionosphere on DCB estimation were investigated using LEO observations for the first time. Different modeling parameters were set in the DCB estimations, encompassing modeling spacing in the dynamic temporal mode and degree and order (D&O) in spherical harmonic modeling. The DCB precisions were then evaluated, and the impacts were analyzed. Thus, a number of crucial and beneficial conclusions are drawn: (1) The maximum differences in the GPS DCB estimates after adopting different modeling spacings and different D&Os exhibit that the different modeling spacings or D&Os both affect the GPS DCB estimates and their root-mean square (RMS), and the effects of the two are at the same level. (2) The maximum differences in receiver DCBs using different modeling spacings indicate that the modeling spacing has a significant impact on the receiver DCBs, compared with GPS DCBs. Whereas, the maximum differences in receiver DCBs with different modeling D&Os are inferior to the differences in the GPS DCBs. That is, the modeling spacing has a greater impact on the LEO DCBs than those of the modeling D&O. (3) The experimental results indicate that the GPS DCB estimates using a modeling spacing of 12H have higher precisions than the others, whereas LEO receiver DCBs using a spacing of 4H or 6H obtain optimal STD. In terms of modeling D&O, adopting 8D&O in the LEO-based VTEC modeling can attain superior estimates and precisions for both GPS and LEO DCBs. The research conclusions can provide references for LEO-augmented DCB estimation.

A Simple Approach to Determine Single-Receiver Differential Code Bias Using Precise Point Positioning.

In this study, a precise single-receiver differential code bias (DCB) estimation method using the precise point positioning (PPP) model is presented. The first step is to extract the high-precision ionospheric observations, including DCBs, based on the PPP model. Then, the satellite DCBs are corrected using International GNSS Service (IGS) products. Lastly, the algorithm for the minimization of the standard deviation of vertical total electron content (VTECmstd) is employed to determine the value of receiver DCB. To check the method, GNSS data from more than 200 IGS stations around the globe on four days with various geomagnetic and solar activity circumstances are processed. The receiver DCBs are compared to those obtained using previous carried-to-code level (CCL) models. The experimental results show that, compared to the CCL model, the values of VTECmstd for most stations are significantly reduced, the mean number of stations with negative ionospheric measurements is reduced by 40% after correcting the receiver DCBs, and the mean error of estimated receiver DCBs is reduced by approximately 0.6 ns using the PPP model. These results suggest that this method can provide more high-precision receiver DCB estimation.

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.

DCB estimation and analysis using the single receiver GPS/GLONASS observations under various seasons and geomagnetic activities

Global Navigation Satellite Systems (GNSS) have many applications in surveying, geodesy, and everyday life, so the accuracy of observations is very important. To have accurate results, many errors should be corrected, including ionospheric errors. Estimating the Differential Code Bias (DCB) and Total Electron Content (TEC) is essential to reduce ionospheric errors. This study's main aim is to determine how the combination of GPS (Global Positioning System) and GLONASS (GLObal NAvigation Satellite System) observations affect the estimation of DCB of satellites (SDCB) and receivers (RDCB) under the effects of geomagnetic storms and seasonal changes. The MATLAB-based software GR_DCB (GPS and GLONASS DCB estimation) was developed to estimate the SDCB and RDCB based on GPS and GLONASS observations. Theresults were tested using data from the International GNSS Service (IGS) network from nine stations and compared to previous studies to assess the effectiveness of the developed code. The findings are consistent with IGS products and more precise than previous studies that relied solely on GPS observations. An analysis of the effects of the geomagnetic storm on DCB variance is considered for June 22–23, 2015. During the geomagnetic storm, all GPS and GLONASS stations exhibited a fall in RDCB, led by a modest increase in some stations. The SDCB had no observed change on storm days compared with quiet days. The seasonal change affected GPS and GLONASS stations RDCB. Winter, which has the highest RDCB mean values, is also the season when a deviation in RDCB is the greatest. Autumn and Summer had the lowest dispersion in RDCB over the season and the lowest RDCB values.

Epoch-Wise Estimation and Analysis of GNSS Receiver DCB under High and Low Solar Activity Conditions

Differential code bias (DCB) is one of the main errors involved in ionospheric total electron content (TEC) retrieval using a global navigation satellite system (GNSS). It is typically assumed to be constant over time. However, this assumption is not always valid because receiver DCBs have long been known to exhibit apparent intraday variations. In this paper, a combined method is introduced to estimate the epoch-wise receiver DCB, which is divided into two parts: the receiver DCB at the initial epoch and its change with respect to the initial value. In the study, this method was proved feasible by subsequent experiments and was applied to analyze the possible reason for the intraday receiver DCB characteristics of 200 International GNSS Service (IGS) stations in 2014 (high solar activity) and 2017 (low solar activity). The results show that the proportion of intraday receiver DCB stability less than 1 ns increased from 72.5% in 2014 to 87% in 2017, mainly owing to the replacement of the receiver hardware in stations. Meanwhile, the intraday receiver DCB estimates in summer generally exhibited more instability than those in other seasons. Although more than 90% of the stations maintained an intraday receiver DCB stability within 2 ns, substantial variations with a peak-to-peak range of 5.78 ns were detected for certain stations, yielding an impact of almost 13.84 TECU on the TEC estimates. Moreover, the intraday variability of the receiver DCBs is related to the receiver environment temperature. Their correlation coefficient (greater than 0.5 in our analyzed case) increases with the temperature. By contrast, the receiver firmware version does not exert a great impact on the intraday variation characteristics of the receiver DCB in this case.

On low-cost GNSS observables under different grades of antennas: Receiver-related biases and RTK results

Low-cost receivers are becoming mainstream devices for providing positioning, navigation and timing (PNT) services that are accessible to the public. In contrast to existing advances, it is inappropriate for less-rigorous functional models and rough systemic error models, including the unknown characteristics of receiver-related biases (RRB) caused by internal hardware and the indefinite impact of an external antenna, to restrain the development of low-cost global navigation satellite system (GNSS) receivers. In this work, a comparative analysis was conducted to assess the respective effects of the internal hardware and an external antenna on low-cost receiver observables. We reparameterized a single-differenced geometry-based functional model and adopted a least squares filtering method to estimate RRB, including inter system biases (ISB), differential code biases (DCB), differential phase biases (DPB). First, an abnormal phenomenon was reported that the C099-F9P receiver showed better performance than the Trimble receiver on RRB when a U-blox ANN-MB antenna was used. Second, comparing the DCB and the DPB results, we found that the negative effect of the external antenna on the code observables is stronger than that on the phase observables. The standard deviation (STD) of the L1-L2 and E1-E5b DCB from the C099-F9P receiver reach 0.160 and 0.129 m, respectively, when the ANN-MB antenna is used. When connected to a higher-grade antenna, the low-cost receivers show DCB estimates stability similar to the Trimble receivers, where the L1-L2 and E1-E5b DCB STDs can reach 0.078 and 0.076 m, respectively. Third, it should be noted that the L1-L2 and E1-E5b DCB will change if a low-cost receiver restarts or is powered off. Fourth, of the DPB STDs of the low-cost and Trimble receivers connected to three different grades of antennas maintain agreement and reach 0.007 cycles or better. The phase observables can be free from the effect of the antenna in short-term case. Above all, the comparison results illustrate that low-cost GNSS receivers have the potential for high-precision applications and achieve an accuracy level and ability similar to high-grade receivers in mass applications when a survey-grade or higher-quality antenna is equipped.

Single station bias calculation using data from calibrated GNSS station for various baseline distances

Precise ionospheric TEC can be derived from dual-frequency GNSS carrier phase leveled pseudorange measurements. However, differential code biases (DCB) of satellite and receiver are the main errors that cannot be ignored for precise TEC calculation. We have proposed a method of calculating station DCB using calibrated STEC data from a baseline GNSS station. The method is simply based on the understanding that the ionosphere observed by two baseline GNSS stations at the same universal time (UT) can be considered similar and would pose similar delay to the signals propagating to the two stations. The method is tested for different baseline distances of 250–1000 km and in different latitudinal regions. For 500 km baseline, the average DCB calculation error for one year data is less than 0.22 ns, 0.11 ns, and 0.25 ns for low, mid and high latitude regions, respectively. The most consistent results were obtained from high latitudes where the standard deviation remains less than 0.22 ns. The least accurate were the low latitude results where the spread of error were between 0.29 to 0.50 ns. Results showed that the accuracy and consistency of the DCB estimation reduced with the increasing baseline distance between the two participating GNSS stations. This was specifically true for low latitude regions.

A Novel Method to Estimate Multi-GNSS Differential Code Bias without Using Ionospheric Function Model and Global Ionosphere Map

Global navigation satellite system (GNSS) differential code bias (DCB) is one of main errors in ionospheric modeling and applications. Accurate estimation of multiple types of GNSS DCBs is important for GNSS positioning, navigation, and timing, as well as ionospheric modeling. In this study, a novel method of multi-GNSS DCB estimation is proposed without using an ionospheric function model and global ionosphere map (GIM), namely independent GNSS DCB estimation (IGDE). Firstly, ionospheric observations are extracted based on the geometry-free combination of dual-frequency multi-GNSS code observations. Secondly, the VTEC of the station represented by the weighted mean VTEC value of the ionospheric pierce points (IPPs) at each epoch is estimated as a parameter together with the combined receiver and satellite DCBs (RSDCBs). Last, the estimated RSDCBs are used as new observations, whose weight is calculated from estimated covariances, and thus the satellite and receiver DCBs of multi-GNSS are estimated. Nineteen types of multi-GNSS satellite DCBs are estimated based on 200-day observations from more than 300 multi-GNSS experiment (MGEX) stations, and the performance of the proposed method is evaluated by comparing with MGEX products. The results show that the mean RMS value is 0.12, 0.23, 0.21, 0.13, and 0.11 ns for GPS, GLONASS, BDS, Galileo, and QZSS DCBs, respectively, with respect to MGEX products, and the stability of estimated GPS, GLONASS, BDS, Galileo, and QZSS DCBs is 0.07, 0.06, 0.13, 0.11, and 0.11 ns, respectively. The proposed method shows good performance of multi-GNSS DCB estimation in low-solar-activity periods.

Analysis and Empirical Modeling of Ionospheric Horizontal Gradients in the TEC Mapping Onboard LEO Satellites

The ionospheric mapping function (IMF) is fundamental in retrieving total electron content (TEC) from observations on board low earth orbiting (LEO) satellites, as well as the receiver differential code bias (DCB) estimation. Most IMFs apply the assumption that the electron density field is spherical symmetric, only dependent on the elevation angle of signal ray path without considering the azimuthal diversity. However, the ionospheric horizontal asymmetry may introduce large mapping errors in slant to vertical TEC conversion or vice versa especially at low elevation angles. This study investigates the variations of the horizontal gradients in the topside ionosphere and plasmasphere, and proposes a formalism for parametrizing the time, location, elevation and azimuth angle dependent horizontal gradients based on the Global Core Plasma Model (GCPM). Several parameters are estimated to represent the north-to-south, east-to-west asymmetric patterns of slant TEC and the horizontal mapping factor with varying elevation angle. Results show the empirical model of the horizontal gradients are well constructed and contribute positively to reducing the mapping error of vertical TEC. The root-mean-square error (RMS) at all elevation angles are decreased to 0.5 TECU and 1.0 TECU under low and high solar activity conditions respectively. This approach is potential to be used in the absolute GNSS/LEO TEC and DCB estimation and topside ionosphere/plasmasphere exploration.

A Station-Specific Ionospheric Modeling Method for the Estimation and Analysis of BeiDou-3 Differential Code Bias Parameters

<h3>Abstract</h3> A modified generalized trigonometric series (GTS) function is presented for the joint estimation of local ionospheric activities and differential code biases (DCBs) of the third-generation BeiDou navigation satellite system (BeiDou-3). Using observational data from the iGMAS and IGS-MGEX networks, DCBs between the pilot-, data- and I-components of BeiDou-3 signals are estimated and analyzed for January 2019. The stability of the modified GTS-based satellite DCB estimates an improvement of about 29.7% compared to the original GTS-based results. In comparison with transmitted T_GDB1Cp and T_GDB2ap parameters, the consistency between broadcast and post-processed biases reaches 0.33 and 0.50 ns. The estimated data-pilot biases are observed to be notably smaller than BeiDou-3 transmitted inter-signal correction (ISC) parameters. In the analysis of receiver B1I-B3I, DCBs generated from the independent BeiDou-2 and BeiDou-3 constellations, the receiver-type dependent biases are emphasized, which raises the consideration of using receiver-group specific bias concept in the future estimation of BeiDou DCBs.

Characterization and Performance Assessment of BeiDou-2 and BeiDou-3 Satellite Group Delays

<h3>Abstract</h3> Based on one year of data, a comprehensive assessment of broadcast group delays and differential code biases (DCBs) from network solutions is presented for all open BeiDou signals. Daily DCB estimates exhibit a precision of 0.1 ns, which also places a limit on long-term variations of the satellite group delays. On the other hand, the estimated DCBs show a notable dependence on the employed receivers, which causes inconsistencies at the few-nanosecond level between BeiDou-2 and BeiDou-3 satellites. Systematic satellite-specific offsets can likewise be identified in broadcast group delay values and clock offsets. These constitute the dominant contribution of the signal-in-space range error (SISRE) budget and are a limiting factor for single point positioning and timing. Use of the modernized B1C/B2a signals is therefore recommended instead of B1I/B3I. This offers a SISRE reduction from about 0.6 m to 0.45 m and also improves the consistency of precise clock and bias products derived from heterogeneous receiver networks.

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

Characteristics of receiver-related biases between BDS-3 and BDS-2 for five frequencies including inter-system biases, differential code biases, and differential phase biases

It is foreseeable that the BeiDou navigation satellite system with global coverage (BDS-3) and the BeiDou navigation satellite (regional) system (BDS-2) will coexist in the next decade. Care should be taken to minimize the adverse impact of the receiver-related biases, including inter-system biases (ISBs), differential code biases (DCB), and differential phase biases (DPB) on the positioning, navigation, and timing (PNT) provided by global navigation satellite systems (GNSS). Therefore, it is important to ascertain the intrinsic characteristics of receiver-related biases, especially in the context of the combination of BDS-3 and BDS-2, which have some differences in their signal level. We present a method that enables time-wise retrieval of between-receiver ISBs, DCB, and DPB from multi-frequency multi-GNSS observations. With this method, the time-wise estimates of the receiver-related biases between BDS-3 and BDS-2 are determined using all five frequencies available in different receiver pairs. Three major findings are suggested based on our test results. First, code ISBs are significant on the two overlapping frequencies B1II and B2b/B2I between BDS-3 and BDS-2 for a baseline with non-identical receiver pairs, which disrupts the compatibility of the two constellations. Second, epoch-wise DCB estimates of the same type in BDS-3 and BDS-2 can show noticeable differences. Thus, it is unreasonable to treat them as one constellation in PNT applications. Third, the DPB of BDS-3 and BDS-2 may have significant short-term variations, which can be attributed to, on the one hand, receivers composing baselines, and on the other hand, frequencies.

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.

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.

Analysis of differential code biases and inter-system biases for GPS and NavIC satellite constellations

&lt;abstract&gt; &lt;p&gt;Multi Global Navigation Satellite System (GNSS) plays an essential role in navigation and geodesy fields for positioning, Navigation, and Timing (PNT) services. The predominant challenge of multi-GNSS is hardware bias errors such as Differential code Bias (DCB) and Inter System Biases (ISB). The estimation of DCB and ISB are essential for analyzing the GNSS system performance to improve the positional accuracy. Navigation with the Indian Constellation (NavIC) system consists of the entire constellation of seven Geo-Stationary satellites to cater to Position Navigation Time (PNT) services over India and adjacent areas. In this paper, the relation between DCB and ISB of Global Positioning System (GPS) and NavIC systems is investigated using two ground-based NovAtel GPS and three Accords NavIC Receivers data (January to April 2019) at Koneru Lakshamaiah Education Foundation (K.L. Deemed to University), Guntur, India (16.47°N, 80.61°E). The correlation results indicate that NavIC GSO satellites are more stable than GEO satellites from DCB and ISB analysis due to low elevation angles and multipath effects. A systematic bias error is observed between NavIC and GPS satellite systems from ISB and DCB results. The current research work outcome would be beneficial for modeling GNSS ionospheric Total Electron Content (TEC) for high precision multi-constellation and multi-frequency GNSS systems.&lt;/p&gt; &lt;/abstract&gt;

Simultaneous estimation of GPS P1-P2 differential code biases using low earth orbit satellites data from two different orbit heights

Global navigation satellite system (GNSS) differential code bias (DCB) is a significant error source in ionosphere modeling that uses GNSS observation data. Given that the orbit altitudes of low earth orbit (LEO) satellites are above the F layer of ionosphere, ionized electrons come from the upper ionosphere or plasmasphere, so observations suffer from small signal delays. DCBs can be estimated using LEO data instead of that from ground stations. In most studies, LEO-based DCB estimation employs onboard data from either a single LEO or from two that are at the same orbit height. In our study, we applied four LEO satellites data from two different orbit heights to estimate GPS satellite DCBs, receiver DCBs and LEO-based vertical total electron content (VTEC) parameters simultaneously. Before DCB estimation, a data preprocessing strategy suitable for LEO onboard data was applied to obtain clear pseudorange data. We developed a processing method for the upper ionosphere using LEO onboard data from different orbit heights, by introducing LEO-based VTEC models in advance to remove its effects; two introduced VTEC models were derived from modeling results using paired data from the same orbital height, respectively. We draw some conclusions as follows. For the LEO satellites at different orbit heights, the more the number of LEO satellites involved, the more stable estimation results achieved. We also noted that the GPS satellite DCBs stability and accuracy with established LEO-based VTEC models, using multi-LEOs data from different orbit heights, were better than the achievable results using onboard data from the same orbital height or using single LEO satellite schemes. Compared with the estimation results of single LEO solutions, the monthly stabilities and accuracies for multi-LEOs solutions from different orbit heights are improved by 25–35% approximately. Among all the tested schemes, superior stability derived from simultaneous estimation using four LEO data at different orbit heights is 0.064 ns; the optimal accuracies for DCB estimation for different GPS satellites are the scheme GRACE-A and JASON-2 (two LEOs) of 0.146 ns, approximately, compared with Center of Orbit Determination of Europe products, respectively. The stability and accuracy of LEO-based DCB estimations were approximately similar to those achieved using ground solutions.

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.

Impact of flex power on GPS Block IIF differential code biases

GPS Block IIF satellites are able to redistribute the transmit power between the signal components. This ability is called flex power, and it has been developed as a remedy against jamming. Since it is operationally not possible to increase the transmit power for all signal components simultaneously, a redistribution between them is necessary under certain operational situations. Flex power has been active on Block IIF satellites since January 2017 over a specific regional area and has an impact on differential code bias estimation as well as the signal-to-noise density ratio. A network of the International GNSS Service stations containing only Septentrio PolaRx5 and PolaRx5TR receivers between August 1 and November 21, 2019 has been used for differential code bias estimation using GPS L1 C/A, L1 P(Y), L2 P(Y), and L2C signals with and without consideration of the flex power in the estimation process for Block IIF satellites. The estimation results are compared with the German Aerospace Center as well as the Chinese Academy of Sciences DCB products to validate the results.

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

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 triple-frequency 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.