Receiver Differential Code Biases Research Articles

Regional Real-Time between-Satellite Single-Differenced Ionospheric Model Establishing by Multi-GNSS Single-Frequency Observations: Performance Evaluation and PPP Augmentation

The multi-global navigation satellite system (GNSS) undifferenced and uncombined precise point positioning (UU-PPP), as a high-precision ionospheric observables extraction technology superior to the traditional carrier-to-code leveling (CCL) method, has received increasing attention. In previous research, only dual-frequency (DF) or multi-frequency (MF) observations are used to extract slant ionospheric delay with the UU-PPP. To reduce the cost of ionospheric modeling, the feasibility of extracting ionospheric observables from the multi-GNSS single-frequency (SF) UU-PPP was investigated in this study. Meanwhile, the between-satellite single-differenced (SD) method was applied to remove the effects of the receiver differential code bias (DCB) with short-term time-varying characteristics in regional ionospheric modeling. In the assessment of the regional real-time (RT) between-satellite SD ionospheric model, the internal accord accuracy of the SD ionospheric delay can be better than 0.5 TECU, and its external accord accuracy within 1.0 TECU is significantly superior to three global RT ionospheric models. With the introduction of the proposed SD ionospheric model into the multi-GNSS kinematic RT SF-PPP, the initialization speed of vertical positioning errors can be improved by 21.3% in comparison with the GRAPHIC (GRoup And PHase Ionospheric Correction) SF-PPP model. After reinitialization, both horizontal and vertical positioning errors of the SD ionospheric constrained (IC) SF-PPP can be maintained within 0.2 m. This proves that the proposed SDIC SF-PPP model can enhance the continuity and stability of kinematic positioning in the case of some GNSS signals missing or blocked. Compared with the GRAPHIC SF-PPP, the horizontal positioning accuracy of the SDIC SF-PPP in kinematic mode can be improved by 37.9%, but its vertical positioning accuracy may be decreased. Overall, the 3D positioning accuracy of the SD ionospheric-constrained RT SF-PPP can be better than 0.3 m.

Estimation and evaluation of hourly Meteorological Operational (MetOp) satellites' GPS receiver differential code biases (DCBs) with two different methods

Abstract. Differential code bias (DCB) is one of the Global Positioning System (GPS) errors, which typically affects the calculation of total electron content (TEC) and ionospheric modeling. In the past, DCB was normally estimated as a constant in 1 d, while DCB of a low Earth orbit (LEO) satellite GPS receiver may have large variations within 1 d due to complex space environments and highly dynamic orbit conditions. In this study, daily and hourly DCBs of Meteorological Operational (MetOp) satellites' GPS receivers are calculated and evaluated using the spherical harmonic function (SHF) and the local spherical symmetry (LSS) assumption. The results demonstrated that both approaches could obtain accurate and consistent DCB values. The estimated daily DCB standard deviation (SD) is within 0.1 ns in accordance with the LSS assumption, and it is numerically less than the standard deviation of the reference value provided by the Constellation Observing System for Meteorology Ionosphere and Climate (COSMIC) Data Analysis and Archive Center (CDAAC). The average error's absolute value is within 0.2 ns with respect to the provided DCB reference value. As for the SHF method, the DCB's standard deviation is within 0.1 ns, which is also less than the standard deviation of the CDAAC reference value. The average error of the absolute value is within 0.2 ns. The estimated hourly DCB with LSS assumptions suggested that calculated results of MetOpA, MetOpB, and MetOpC are, respectively, 0.5 to 3.1 ns, −1.1 to 1.5 ns, and −1.3 to 0.7 ns. The root mean square error (RMSE) is less than 1.2 ns, and the SD is under 0.6 ns. According to the SHF method, the results of MetOpA, MetOpB, and MetOpC are 1 to 2.7 ns, −1 to 1 ns, and −1.3 to 0.6 ns, respectively. The RMSE is under 1.3 ns and the SD is less than 0.5 ns. The SD for solar active days is less than 0.43, 0.49, and 0.44 ns, respectively, with the LSS assumption, and the appropriate fluctuation ranges are 2.0, 2.2, and 2.2 ns. The variation ranges for the SHF method are 1.5, 1.2, and 1.2 ns, respectively, while the SD is under 0.28, 0.35, and 0.29 ns.

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.

Analysis of differential code biases for GPS receivers over the Indian region

Abstract The GPS Aided Geo Augmented Navigation (GAGAN) system provides the navigational services for single-frequency GNSS user via broadcasting the differential corrections with GEO stationary satellites. The significant differential correction contribution comes from ionospheric time delays and is necessary to be determined precisely. Dual-frequency GPS receivers measure the ionospheric time delays using GPS code and carrier phase measurements. The determination of absolute ionospheric Total Electron Content (TEC) requires the calibration of GPS satellites and receiver hardware biases due to different frequency-dependent signals (L1 and L2) due to environmental changes (Temperature and Humidity). In this paper, A receiver-based Differential Code Biases (DCB) algorithm is implemented to derive a joint estimation of TEC and RDCB parameters using the weighted Least Square (WLS) method. The daily averaged DCBs data for 26 GPS receivers are obtained for 3 years (2014–2016) from 26 GPS reeivers over Indian region. The receiver DCB algorithmis validated with the Fitted Receiver Biases (FRB) method. The correlation (R) between VTEC and RDCB is conducted to investigate the RDCB stability. The results would be useful for the accurate determination of ionospheric differential corrections to GAGAN users.

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.

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.

Estimating GPS satellite and receiver differential code bias based on signal distortion bias calibration

Estimating GPS satellite and receiver differential code bias based on signal distortion bias calibration

Investigation of Displacement and Ionospheric Disturbance during an Earthquake Using Single-Frequency PPP

Currently, it is still challenging to detect earthquakes by using the measurements of Global Navigation Satellite System (GNSS), especially while only adopting single-frequency GNSS. To increase the accuracy of earthquake detection and warning, extra information and techniques are required that lead to high costs. Therefore, this work tries to find a low-cost method with high-accuracy performance. The contributions of our research are twofold: (1) an improved earthquake-displacement estimation approach by considering the relation between earthquake and ionospheric disturbance is presented. For this purpose, we propose an undifferenced uncombined Single-Frequency Precise Point Positioning (SF-PPP) approach, in which both the ionospheric delay of each observed satellite and receiver Differential Code Bias (DCB) are parameterized. When processing the 1 Hz GPS data collected during the 2013 Mw7.0 Lushan earthquake and the 2011 Mw9.0 Tohoku-Oki earthquake, the proposed SF-PPP method can provide coseismic deformation signals accurately. Compared to the results from GAMIT/TRACK, the accuracy of the proposed SF-PPP was not influenced by the common mode errors that exist in the GAMIT/TRACK solutions. (2) Vertical Total Electron Content (VTEC) anomalies before an earthquake are investigated by applying time-series analysis and spatial interpolation methods. Furthermore, on the long-term scale, it is revealed that significant positive/negative VTEC anomalies appeared around the earthquake epicenter on the day the earthquake occurred compared to about 4–5 days before the earthquake, whereas, on the short-term scale, positive/negative VTEC anomalies emerged several-hours before or after an earthquake.

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.

Accounting for biases between BDS-3 and BDS-2 overlapping B1I/B3I signals in BeiDou global ionospheric modeling and DCB determination

The receiver pseudo-range biases between BDS-2 and BDS-3 in global ionospheric modeling and differential code bias (DCB) determination are investigated by using the overlapping B1I/B3I signals. The BDS receiver DCB estimations from global ionospheric modeling and the results of single-differences of short-baselines reveal that the receiver pseudo-range bias differences between BDS-3 and BDS-2 B1I/B3I observations are related to receiver types, and the maximum of the bias differences can be up to 8.6 ns. It means that the receiver DCB differences between BDS-3 and BDS-2 B1I/B3I observations should be considered in BDS-3/BDS-2 ionospheric modeling and DCB determination. Compared with DCB products from Chinese Academy of Sciences (CAS), the RMS is better than 0.3 ns when the receiver pseudo-range bias differences between BDS-3 and BDS-2 are ignored, while the RMS is about 0.51 ns when the receiver pseudo-range bias differences are considered. Based on the analysis of the BDS-3 and BDS-2 receiver pseudo-range bias differences, it indicates there are significant deviations in existing CAS satellite DCB products for BDS B1I/B3I observations. In terms of the stability of BDS satellite DCB estimations, the monthly STDs of BDS-3 DCB estimations improves by 20.2% on average when the receiver pseudo-range bias differences between BDS-3 and BDS-2 are considered. Taking the final Global Ionospheric Maps (GIMs) from Centre for Orbit Determination in Europe (CODE) as references, the accuracy of BDS-only global ionospheric modeling is 2.4 total electron content unit (TECU) when the receiver DCB differences between BDS-3 and BDS-2 are considered, and improves by 9.3% compared with the results which ignores the receiver pseudo-range bias differences between BDS-3 and BDS-2.

Variation Characteristics of Multi-Channel Differential Code Biases from New BDS-3 Signal Observations

A multi-frequency Global Navigation Satellite System (GNSS) provides greater opportunities for positioning and navigation applications, particularly the BeiDou Global Navigation Satellite System (BDS-3) satellites. However, multi-frequency signals import more pseudorange channels, which introduce more multi-channel Differential Code Biases (DCBs). The satellite and receiver DCBs from the new BDS-3 signals are not clear. In this study, 9 DCB types of the new BDS-3 signals from 30-days Multi-GNSS Experiment (MGEX) observations are estimated and investigated. Compared with the DCB values provided by the Chinese Academy of Science (CAS) products, the mean bias and root mean squares (RMS) error of new BDS-3 satellite DCBs are within ±0.20 and 0.30 ns, respectively. The satellite DCBs are mostly within ±0.40 ns with respect to the product of the Deutsches Zentrum für Luft- und Raumfahrt (DLR). The four sets of constructed closure errors and their mean values are within ±0.30 ns and ±0.15 ns, respectively. The mean standard deviation (STD) of the estimated satellite DCBs is less than 0.10 ns. In particular, our estimated satellite DCBs are more stable than DCB products provided by CAS and DLR. Unlike satellite DCBs, the receiver DCBs have poor compliance and show an obvious relationship with the geographic latitude when compared to the CAS products. The STDs of our estimated receiver DCBs are less than 1.00 ns. According to different types of receiver DCBs, the distribution of STDs indicates that the coefficient of the ionospheric correction has an influence on the stability of the receiver DCBs under the ionosphere with the same accuracy level. In addition, the type of receiver shows no regular effects on the stability of receiver DCBs.

A Study on Pseudorange Biases in BDS B1I/B3I Signals and the Impacts on Beidou Wide Area Differential Services

Due to satellite signal deformations, there are different constant biases in the same satellite signal that are measured by different technical types of receivers and different satellite signals that are measured by the same type of receiver, which are named pseudorange biases. These biases cannot be transmitted to users with existing navigation parameters, such as satellite time group delay (TGD) and receiver differential code biases (DCB). With the improvement of the signal-in-space accuracy of the Global Navigation Satellite System (GNSS), the pseudorange bias has become one of the primary error sources affecting the accuracy of GNSS services. To ensure the accuracy for users under the wide area differential services (WADS), we extracted the pseudorange biases of Beidou Satellite Navigation System (BDS) B1I, B3I and B1I/B3I signals and analyzed the impact of those biases on users under the WADS. Finally, we tried to eliminate this influence. The results show that the pseudorange biases of the B3I signal are smaller than those of the B1I signal at the centimeter level, but the pseudorange biases of the B1I/B3I signal can reach the meter level. Due to the large pseudorange bias of the B1I/B3I signal, the average user equivalent ranging error (UERE) under the WADS is 1.19 m, which is no better than the average UERE under open services (OS). Influenced by the pseudorange biases, the average positioning accuracies of the B1I/B3I signal are 4.17 m and 4.24 m under the WADS and the OS. When the pseudorange biases are deducted, these accuracies are 3.03 m and 3.50 m, respectively.

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.

Processing and Validation of FORMOSAT‐7/COSMIC‐2 GPS Total Electron Content Observations

AbstractSlant absolute total electron content (TEC) is observed by the Formosa Satellite‐7/Constellation Observing System for Meteorology, Ionosphere, and Climate‐2 (FORMOSAT‐7/COSMIC‐2, F7/C2) Tri‐GNSS Radio Occultation System (TGRS) instrument. We present details of the data processing algorithms, validation, and error assessment for the F7/C2 global positioning system (GPS) absolute TEC observations. The data processing includes estimation and application of solar panel dependent pseudorange multipath maps, phase to pseudorange leveling, and estimation of separate L1C‐L2C and L1C‐L2P receiver differential code biases. We additionally perform a validation of the F7/C2 GPS absolute TEC observations through comparison with colocated, independent, TEC observations from the Swarm‐B satellite. Based on this comparison, we conclude that the accuracy of the F7/C2 GPS absolute TEC observations is less than 3.0 TEC units. Results are also presented that illustrate the suitability of the F7/C2 GPS absolute TEC observations for studying the climatology and variability of the topside ionosphere and plasmasphere (i.e., altitudes above the F7/C2 orbit of 550 km). These results demonstrate that F7/C2 provides high quality GPS absolute TEC observations that can be used for ionosphere‐thermosphere data assimilation as well as scientific studies of the topside ionosphere and plasmasphere.

Effects of ionospheric constraints in Precise Point Positioning processing of geodetic, low-cost and smartphone GNSS measurements

The proliferation of low-cost GNSS hardware smartphones providing multi-constellation, multi-frequency carrier-phase and pseudorange measurements for the Android platform offer an avenue for Precise Point Positioning (PPP) GNSS use in recent years. However, smartphone PPP is restricted due to high multipath effects and signal loss leading to metre-level accuracy and longer convergence time compared against professional-grade GNSS receivers. Proven by previous research, the combination of ionospheric constraints and receiver differential code bias (DCB) estimation is an efficient approach to improve PPP solution initialization. Therefore, this study analyzes the performance improvements by applying ionospheric constraints (IC) to PPP in comparison to conventional PPP solutions for different grades of GNSS receivers (geodetic, low-cost, and smartphone hardware) in open-sky and suburban environments. The results reveal that smartphone PPP enjoys more beneficial effects from ionospheric constraints (IC) than low-cost and geodetic hardware, as a significant 30% improvement in horizontal rms is observed in the first epoch of examined datasets, and a 57% improvement in the first 20 min of data collection. For low-cost and geodetic equipment, the first epoch improvement is only 21% and 18%, respectively. Furthermore, a 44% convergence time reduction for smartphone PPP-IC is observed to attain 1 m level of horizontal accuracy. Based on these investigations, PPP-IC can provide greater impact for those low-quality measurements before convergence, showing potential in achieving fast initialization and accurate positioning within a short time for autonomous vehicles, precision agriculture, and smartphone location-based services.

Estimation and analysis of GNSS receiver differential code bias in Southeast Asia using a new method

The receiver differential code bias (DCB) is one of the main errors in GNSS navigation and positioning as well as ionospheric monitoring. In this paper, we present a new method to estimate the receiver differential code bias (DCB) using Multi-GNSS observations in Southeast Asia. Different from the traditional method by using ionosphere modeling or Global ionospheric map (GIM), the total electron content (TEC) of station in the new method is estimated directly together with the receiver DCB. The data of one year with 34 stations were used to evaluate the performance of the presented method. The results show a good agreement between our estimated receiver DCBs and the MGEX DCB products and the RMS of eight types of GNSS receiver DCB are mostly less than 1ns with respect to the MGEX products. Finally, the stability of GNSS receiver DCB was analysed for eight stations located in Southeast Asia as examples. The result indicates that those stations were relatively stable with mostly less than 1ns of STD of receiver DCB. Moreover, no evidence of latitudinal and receiver type dependencies of the stability of receiver DCB for those selected stations was found.

Functional model modification of precise point positioning considering the time-varying code biases of a receiver

Precise Point Positioning (PPP), initially developed for the analysis of the Global Positing System (GPS) data from a large geodetic network, gradually becomes an effective tool for positioning, timing, remote sensing of atmospheric water vapor, and monitoring of Earth’s ionospheric Total Electron Content (TEC). The previous studies implicitly assumed that the receiver code biases stay constant over time in formulating the functional model of PPP. In this contribution, it is shown this assumption is not always valid and can lead to the degradation of PPP performance, especially for Slant TEC (STEC) retrieval and timing. For this reason, the PPP functional model is modified by taking into account the time-varying receiver code biases of the two frequencies. It is different from the Modified Carrier-to-Code Leveling (MCCL) method which can only obtain the variations of Receiver Differential Code Biases (RDCBs), i.e., the difference between the two frequencies’ code biases. In the Modified PPP (MPPP) model, the temporal variations of the receiver code biases become estimable and their adverse impacts on PPP parameters, such as ambiguity parameters, receiver clock offsets, and ionospheric delays, are mitigated. This is confirmed by undertaking numerical tests based on the real dual-frequency GPS data from a set of global continuously operating reference stations. The results imply that the variations of receiver code biases exhibit a correlation with the ambient temperature. With the modified functional model, an improvement by 42% to 96% is achieved in the Differences of STEC (DSTEC) compared to the original PPP model with regard to the reference values of those derived from the Geometry-Free (GF) carrier phase observations. The medium and long term (1 × 104 to 1.5 × 104 s) frequency stability of receiver clocks are also significantly improved.

A new method to estimate GPS satellite and receiver differential code biases using a network of LEO satellites

The differential code biases (DCBs) of the global positioning system (GPS) receiver onboard low-Earth orbit (LEO) satellites are commonly estimated by a local spherical symmetry assumption together with the known GPS satellite DCBs from ground-based observations. Nowadays, more and more LEO satellites are equipped with GPS receivers for precise orbit determination, which provides a unique chance to estimate both satellite and receiver DCBs without any ground data. A new method to estimate the GPS satellite and receiver DCBs using a network of LEO receivers is proposed. A multi-layer mapping function (MF) is used to combine multi-LEO satellite data at varying orbit heights. First, model simulations are conducted to compare the vertical total electron content (VTEC) derived from the multi-layer MF and the reference VTEC obtained from the empirical ionosphere model International Reference Ionosphere and Global Core Plasmasphere Model. Second, GPS data are collected from five LEO missions, including ten receivers used to estimate both the satellite and receiver DCBs simultaneously with the multi-layer MF. The results show that the GPS satellite DCB solutions obtained from space-based data are consistent with ground-based solutions provided by the Centre for Orbit Determination in Europe. The proposed normalization procedure combining topside observations from different LEO missions has the potential to improve the accuracies of satellite DCBs of Global Navigation Satellite Systems as well as the receiver DCBs onboard LEO satellites, although the number of LEO missions and spatial–temporal coverage of topside observations are limited.

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.

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.