Pseudorange Bias Research Articles

Evaluation of the Galileo high-accuracy service SSR product quality and PPP performance

The Galileo navigation satellite system (Galileo) High-Accuracy Service (HAS) is a global navigation satellite system (GNSS) augmentation service proposed by the European Union that providing free of charge orbit, clock and pseudo-range biases corrections to users around the world through E6 signals and by terrestrial means (Internet). However, there has been limited research on the performance of the HAS State Space Representation (SSR) products broadcast by the Galileo Service Centre (GSC). However, there has been limited research on the performance of the HAS SSR products broadcast by the GSC. This study uses BNC software to receive HAS SSR products and compares them with SSR products from three analysis centers with relatively high accuracy: Wuhan University (WHU), the Chinese Academy of Sciences (CAS), and Centre National d’Etudes Spatiales (CNES), and analyzes them in terms of orbit, clock error, and positioning performance. In addition, Galileo HAS as a satellite-based augmentation service, this study chooses BDS PPP B2b, which is also a satellite-based augmentation service, as a comparison to analyze the performance of the HAS augmentation service. The results indicate that the signal-in-space ranging error (SISRE) values for Global Positioning System (GPS) and Galileo corrected by HAS are 7.26 cm and 5.79 cm, respectively. The average convergence times for the GPS + Galileo combination in the static and kinematic modes are 9.4 min and 14.1 min, respectively. Moreover, in kinematic mode, single-system positioning achieved an accuracy of better than 12 cm in the E direction and better than 17 cm in the U direction. In comparison with BeiDou navigation satellite system (BDS) PPP-B2b, the average convergence time of HAS under static mode is 16 min, while that of B2b requires 19 min. Meanwhile, the positioning accuracy of B2b products in the three directions is improved by more than 1 cm compared with that of HAS. The convergence time of HAS in kinematic mode is 12 min shorter than that of B2b.

Improving PPP timing and time transfer based on signal distortion biases calibration

Abstract Precise point positioning (PPP) technology has been widely used for more than a decade in timing and time transfer. Pseudorange bias caused by signal distortion will reach up ±3 ns, which cannot be neglected in sub-nanosecond level PPP timing and time transfer. We propose to improve the performance of PPP timing and time transfer by considering signal distortion bias (SDB). In principle, SDB will affect PPP timing and time transfer by influencing the initial clock offset. Then, it is verified by theoretical and experimental analyses. The theoretical results show that the impact of SDB on PPP timing can reach up 1.8 ns in different regions. Also, the impact of SDB on time transfer can reach up 0.8 ns in different regions even if the baseline length and receiver types are the same. For experimental results, the accuracy of PPP timing and time transfer improves with SDB correction. For time transfer, the RMSs are reduced by 54.8%, 61.1% and 17.6% for GPS, BDS3 and Galileo in all links, respectively. The clock frequency consistency obtained from different systems has been improved. And the frequency stability of time link with Hydrogen clocks is improved by 53.0% at 10000s interval with SDB correction.

Calibration of Receiver-Dependent Pseudorange Bias and Its Impact on BDS Augmentation Positioning Accuracy

Pseudorange bias refers to the receiver-dependent and satellite-dependent constant bias in the pseudorange resulting from the nonideal characteristics of a signal. The impact of pseudorange bias on high-precision satellite navigation services has long been ignored. This paper proposes a pseudorange bias calibration method for two collocated receivers. Then, we calibrate pseudorange biases for two types of collocated receivers at a monitoring station within China and evaluate their impact on two high-precision services: BeiDou Navigation Satellite System 3 (BDS-3) dual-frequency pseudorange augmentation and precise point precision (PPP). Theoretical analysis reveals that the calibrated pseudorange biases contribute 17.2% and 7.7% to the user equivalent ranging error (UERE) of BDS-3 and Global Positioning System (GPS) dual-frequency pseudorange augmentation, respectively, and that the convergence time of the GPS static and kinematic PPP increases from 6 min and 26 min to 19 min and 58 min, respectively. The experimental results indicate that the calibrated pseudorange biases are consistent as the receiver location and time vary. The spatial distribution consistency is generally better than 0.1 m, and the temporal consistency is better than 0.15 m. The pseudorange biases for BDS-3 B1C and B2a are approximately 0.7 m and 0.1 m, respectively, whereas those for GPS L1C/A and L2P are both approximately 0.25 m. Furthermore, The results show that after correction of the pseudorange biases, the average convergence time for BDS-3/GPS static PPP decreases from 48.83/24.03 min to 38.54/21.12 min, respectively, a decrease of approximately 21%/12%. For BDS-3/GPS/BDS-3 + GPS kinematic PPP, the average convergence time decreases from 109.53/45.10/39.15 min to 62.99/40.83/22.94 min, respectively, a decrease of approximately 42%/41%/9%. Similarly, the three-dimensional positioning accuracy for BDS-3/GPS/BDS-3 + GPS dual-frequency pseudorange augmentation improves from 3.25/3.94/2.49 m to 2.65/3.69/2.16 m, respectively, increasing by approximately 6.3%, 18.5%, and 13.3%, respectively. The above analysis and experiments demonstrate that pseudorange bias is an important error source affecting both dual-frequency pseudorange augmentation and PPP services.

A Post-Processing Multipath/NLoS Bias Estimation Method Based on DBSCAN.

Positioning based on Global Navigation Satellite Systems (GNSSs) in urban environments always suffers from multipath and Non-Line-of-Sight (NLoS) effects. In such conditions, the GNSS pseudorange measurements can be affected by biases disrupting the GNSS-based applications. Many efforts have been devoted to detecting and mitigating the effects of multipath/NLoS, but the identification and classification of such events are still challenging. This research proposes a method for the post-processing estimation of pseudorange biases resulting from multipath/NLoS effects. Providing estimated pseudorange biases due to multipath/NLoS effects serves two main purposes. Firstly, machine learning-based techniques can leverage accurately estimated pseudorange biases as training data to detect and mitigate multipath/NLoS effects. Secondly, these accurately estimated pseudorange biases can serve as a benchmark for evaluating the effectiveness of the methods proposed to detect multipath/NLoS effects. The estimation is achieved by extracting the multipath/NLoS biases from pseudoranges using a clustering algorithm named Density-Based Spatial Clustering of Applications with Noise (DBSCAN). The performance is demonstrated using two real-world data collections in multipath/NLoS scenarios for both static and dynamic conditions. Since there is no ground truth for the pseudorange biases due to the multipath/NLoS scenarios, the proposed method is validated based on the positioning performance. Positioning solutions are computed by subtracting the estimated biases from the raw pseudoranges and comparing them to the ground truth.

Inconsistent pseudorange biases in time links and their effect on BDS and GPS PPP frequency transfer

Precise point positioning (PPP) using the Global Navigation Satellite System (GNSS) phase and code measurements has become the primary technique for time and frequency comparisons. Several scholars have studied multi-GNSS PPP clock comparisons; however, the inconsistent pseudorange bias from receivers with different correlator spaces and front-end designs in pseudorange observations has not been considered. In this study, we analyze the characteristics of the inconsistent biases of the Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS) and their effects on PPP frequency transfer. The biases are confirmed to exist in receivers from Septentrio, Trimble, Leica and differ by manufacturer. To explicitly investigate the pseudorange bias effects of GPS and BDS on the PPP time and frequency comparisons, nine stations with receivers from three different manufacturers that could track the BDS-2 and BDS-3 signals were selected. Regarding PPP frequency transfer with inhomogeneous receivers, the Modified Allan Deviations (MDEVs) of the GPS and BDS PPP frequency stabilities were significantly optimized after using bias corrections. According to the receiver type classification strategy, the overall improvements in frequency transfer with Trimble-Septentrio and Trimble-Leica can be reached up to 31%, 29%, and 39%, and 38%, 29%, and 31% for GPS, BDS-2, and BDS-3, respectively. Moreover, the convergence time of the clock comparisons was shortened after bias corrections were applied. For GOPE-BRUX and GOPE-MATE links, the corrected cases yielded average clock difference stability improvements of 38%, 35%, and 53% and 35%, 35%, and 23% for GPS, BDS-2, and BDS-3, respectively. The results show that bias corrections are vital and allow for more stable time links for PPP frequency transfer.

Pseudorange bias from inter-signal interference: the QZSS L5-L5S case

Pseudorange bias from inter-signal interference: the QZSS L5-L5S case

Research on performance improvement method of BDSBAS multi-GNSS service with DFMC protocol

BDSBAS refers to the DFMC protocol to broadcast long-term corrections and integrity messages in real-time to meet the high integrity requirements of civil aviation users. Based on the measured data of the BDSBAS monitoring station, the long-term corrections and integrity messages of BDS/GPS/GAL are calculated, and from the user's perspective verifies the service capability of the above information which mainly including positioning accuracy, pseudorange bias and Protection Level (PL). The test results show that the accuracy of multi-GNSS long-term corrections is better than 0.14 m; when the user uses the long-term corrections, the positioning accuracy can be improved by 27% in the horizontal direction and 31% in the vertical direction compared with the level of the single BDS. In addition, the results show that the BDSBAS DFMC service can satisfy the LPV-200 availability contour in Mainland China except western China and satisfy the Cat-I availability contour only in the central region of China depend on only BDS constellation. When all the messages of BDSBAS DFMC service based on BDS/GPS/GAL constellations are used, it can reach the availability of 100% which satisfy the LPV-200 index in China and surrounding areas, and the availability of 99.4% which satisfy the Cat-I index in Mainland China. Finally, the effect of pseudorange bias errors on positioning accuracy of different types of receivers are analyzed. Results show that pesudorange bias of BDS and GPS is about 0.2 m ∼ 0.3 m, and for Galileo is about 0.05 m. With multi-GNSS corrections and integrity information, the level of service availability and coverage for LPV-200 and CAT-I of BDSBAS DFMC service could be effectively improved.

BDS pseudorange biases handling: Simultaneous estimation, daily magnitude and analytical comparison of the BDS PPP models

With the completed establishment of the Beidou global navigation satellite system (BDS-3), the BDS constellation is qualified for the global positioning, navigation and timing (PNT) services. The simultaneous observed B1I/B3I signals of the BDS-2 and BDS-3 satellites facilitate the BDS-2/BDS-3 joint precise point positioning (PPP) solution. For reasons related to the modulation modes, signal property, receiver front end design, precise satellite clock products arising from the different analysis centers and so on, BDS pseudorange biases are absorbed by the pseudorange measurements, including the pseudorange bias variation, signal distortion bias (SDB) and time delay bias (TDB). The large magnitude of the BDS pseudorange biases will degrade the BDS PPP performance. Herein, the simultaneous estimation of the BDS pseudorange biases are applied in BDS PPP and totally six pseudorange biases processing strategies are presented. The magnitudes of the existed BDS SDB and TDB are analyzed. The statistics showed that the BDS PPP performance in term of the convergence time and positioning accuracy can be remarkably improved by considering the BDS pseudorange biases. By comparing the BDS PPP performance in different scenarios, we recommend three processing schemes that are reducing weight of the BDS-2 pseudorange observations, estimating the BDS TDB as constant and neglecting the SDB, and estimating the BDS SDB as the constant per satellite. The analytical results can facilitate the optimal BDS PPP performance.

Nonparametric estimation-based five-layer neural network RAIM with improved availability

The monitoring performance of receiver autonomous integrity monitoring (RAIM) is restricted when visible satellites are limited in challenging environments. For that, artificial neural network-based RAIM methods have been investigated to improve the detection efficacy. Nevertheless, their corresponding fault exclusion and protection level algorithms are hardly provided for integrity assessments. In this regard, a nonparametric estimation-based RAIM method (NE-RAIM) is investigated to support fault detection, exclusion, and protection level calculation in this paper, boosting the declined monitoring capacity caused by the decrease of visible satellites. We propose a classification variable and a dynamic sampling method based on the variance inflation theory and then obtain the regression of the classification variable using nonparametric estimation. In this way, a five-layer NE-RAIM neural network is constructed to enhance the detection capability further. We also provide a NE-RAIM-based fault exclusion strategy by analyzing the detection result vector. Meanwhile, a protection level algorithm is proposed to enable direct integrity and availability evaluation based on searching the worst-case scenario where the missed detection risk is maximized. Results show that NE-RAIM requires a minimum pseudorange bias of 35 m to realize 100% detection rates under all single-faulty-satellite modes. Compared with least-square RAIM and advanced RAIM, NE-RAIM improves overall 24 h availability by 59.30% and 4.52%, respectively.

A Distortionless Anti-Jamming Method Based on STAP for GNSS Receiver

Global Navigation Satellite System (GNSS) receivers often realize anti-jamming capabilities by combining array antennas with space-time adaptive processing (STAP). Unfortunately, in suppressing the interference, basic STAP degrades the GNSS signal. For one thing, additional carrier phase errors and code phase errors to the GNSS signal are introduced; for another, the shape of the cross-correlation function (CCF) will be distorted by STAP, introducing tracking errors when the receiver is in tracking mode. Both of them will eventually cause additional Pseudo-Range (PR) bias, and these problems prevent STAP from being directly applied to high-precision satellite navigation receivers. The paper proposes a novel anti-jamming method based on STAP that solves the above problems. First, the proposed method constructs a symmetric STAP by constraining the STAP coefficients. Subsequently, with the information of the steering vector, a compensation FIR filter is cascaded after the symmetric STAP. This approach ensures that the proposed method introduces only a fixed offset to the code phase and carrier phase, and the order of the STAP completely determines the offset, which can be compensated during PR measurements. Meanwhile, the proposed method maintains the symmetry of the CCF, and the receiver can accurately track the carrier phase and code phase in tracking mode. The effectiveness of the proposed method is validated through simulations, which suggest that, in the worst case, our method does not increase carrier and code phase errors and tracking error at the expense of only a 2.86dB drop in interference suppression performance.

Variation of receiver code biases under the influence of the receiver type and antenna configuration in the IGS network

Receiver code biases (RCBs) are known to be time delays within the receiver caused by their hardware imperfections. To better understand the characteristics of RCBs, the un-combined (UC) and ionosphere-free (IF) precise point positioning functional models are adapted and re-parameterized to estimate the variation of RCBs as a time-variant parameter. In this study, we analytically studied the temporal variations of RCBs; although there exists a benchmark difference between the UC and IF models, their estimates are in accordance with each other. Additionally, this contribution assesses the inter-day stability of RCBs with weekly observations from 165 globally distributed international global navigation satellite system service stations equipped the receivers of three mainly types. The inter-day stability results of RCB revealed that the RCBs of POL2 and OUS2 have better stability over consecutive 7 d and the single differenced (SD) RCBs can reach 0.2 m in the best case. The results show that 74.83% of the stations are equipped with Trimble receivers under the condition that the mean SD RCB values are between −0.5 and 0.5 m, while 85.57% of the stations are equipped with Septentrio receivers and the stations equipped with Javad can reach 84.35% under this condition. The RCB estimates are also relatively stable for the case in which the receiver hardware device stays unchanged. The relationship between RCBs, receiver type, and antenna configuration is found using six groups of receivers. A strong correlation exists between RCBs, receiver type, and antenna configuration, which is more obvious among Septentrio receivers. The results show that the Pearson correlation coefficients were all higher than 0.9, and the standard deviation of between-receiver RCBs was smaller than 0.327 m when equipped with Septentrio receivers. We concluded that there is a strong relationship between the receiver-related pseudorange biases and the receiver and antenna setup.

A new blind anti‐jamming algorithm based on a novel antenna array design

The next-generation navigation tools are developed to enable precision and reliability. Military users are more likely to encounter jamming, so it is necessary to seek the technologies which can steadily provide high-precision positioning services in all-weather and harsh conditions. However, when users use an array antenna for interference suppression, it usually introduces pseudorange and carrier phase biases, which deteriorates the accuracy and integrity of positioning. To address this issue, the authors propose a blind anti-interference algorithm with biases suppression. Compared to the commonly used blind space–time adaptive anti-jamming algorithms, this algorithm can not only retain the advantages of the simple structure of the blind anti-jamming algorithm but also suppress pseudorange biases and carrier phase biases, both of which are crucial for users to obtain the availability of positioning. Moreover, the algorithm proposed can be applied easily and quickly to the actual high-precision positioning system with minor hardware changes in some cases. The relevant theoretical analysis and experiments have proved the effectiveness of the proposed algorithm: (1) code phase biases and carrier phase biases can almost be ignored and (2) it also can significantly improve the accuracy and integrity of positioning; the average positioning error is 1.6 mm, and it can keep the positioning accuracy better than 0.1 m for 97.5% of the time.

Evaluation and mitigation of the influence of pseudorange biases on GNSS satellite clock offset estimation

The pseudorange bias inconsistencies are notably originating primarily from the individual chip shape distortions in the ranging signals, these distortions cause different shifts of the correlator’s tracking point for receivers, as a result giving rise to a different pseudorange bias for each pseudorange observation. The different bias should be properly dealt with in the process of satellite clock offset estimation when receivers of mixed types are used. In this work, using observations from 140 international global navigation satellite system (GNSS) service stations, the pseudorange bias was calculated, and the effect of inconsistent biases on satellite clock offset estimation from different receiver networks was investigated. The inconsistencies between the GPS satellites were ranging from −6 ns to 4 ns. For GALILEO and BDS, the biases are significant, ranging from −20 ns to 40 ns and −60 ns to 40 ns, respectively. The biases of the individual satellites are receiver-related and statistically stable from day to day. The influence of pseudorange bias was strikingly noticeable, and can improve the accuracy of the estimated clock offset by several ps for GPS; and by more than 15 ps for GALILEO and BDS after considering bias inconsistencies. Furthermore, owing to the pseudorange bias correction, the convergence and positioning performance have improved significantly, with an improvement of more than 12 % for the static precise point position (PPP), and more than 10 % for the kinematic PPP.

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.

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.

Accounting for Signal Distortion Biases for Wide-Lane and Narrow-Lane Phase Bias Estimation with Inhomogeneous Networks

Due to different designs of receiver correlators and front ends, receiver-related pseudorange biases, called signal distortion biases (SDBs), exist. Ignoring SDBs that can reach up to 0.66 cycles and 10 ns in Melbourne-Wübbena (MW) and ionosphere-free (IF) combinations can negatively affect phase bias estimation. In this contribution, we investigate the SDBs and evaluate the impacts on wide-lane (WL) and narrow-lane (NL) phase bias estimations, and further propose an approach to eliminating these SDBs to improve phase bias estimation. Based on a large data set of 302 multi-global navigation satellite system (GNSS) experiment (MGEX) stations, including 5 receiver brands, we analyze the characteristics of these SDBs The SDB characteristics of different receiver types for different GNSS systems differ from each other. Compared to the global positioning system (GPS) and BeiDou navigation satellite system (BDS), SDBs of Galileo are not significant; those of BDS-3 are significantly superior to BDS-2; Septentrio (SEPT) receivers show the most excellent consistency among all receiver types. Then, we apply the corresponding corrections to phase bias estimation for GPS, Galileo and BDS. The experimental results reveal that the calibration can greatly improve the performance of phase bias estimation. For WL phase biases estimation, the consistencies of WL phase biases among different networks for GPS, Galileo, BDS-2 and BDS-3 improve by 89%, 77%, 76% and 78%, respectively. There are scarcely any improvements of the fixing rates for Galileo due to its significantly small SDBs, while for GPS, BDS-2 and BDS-3, the WL ambiguity fixing rates can improve greatly by 13%, 27% and 14% after SDB calibrations with improvements of WL ambiguity fixing rates, the corresponding NL ambiguity fixing rates can further increase greatly, which can reach approximately 16%, 27% and 22%, respectively. Additionally, after the calibration, both WL and NL phase bias series become more stable. The standard deviations (STDs) of WL phase bias series for GPS and BDS can improve by more than 46%, while those of NL phase bias series can yield improvements of more than 13%. Ultimately, the calibration can make more WL and NL ambiguity residuals concentrated in ranges within ±0.02 cycles. All these results demonstrate that SDBs for phase bias estimation cannot be ignored and must be considered when inhomogeneous receivers are used.

Pseudorange Bias Analysis and Preliminary Service Performance Evaluation of BDSBAS

To satisfy the demands of civil aviation organizations and other users of satellite navigation systems for high-precision and high-integrity service performance, many countries and regions have established satellite-based augmentation systems (SBAS) referring to the Radio Technical Commission for Aeronautics (RTCA) service standards and agreements. The BeiDou SBAS (BDSBAS) provides both single-frequency service, which augments Global Positioning System (GPS) L1 C/A signal, and dual-frequency multi-constellation (DFMC) service, which augments BeiDou Navigation Satellite System (BDS) B1C and B2a dual frequency signals presently, meeting the requirements of the RTCA DO-229D protocol and the SBAS L5 DFMC protocol requirements, respectively. As one of the main error sources, the pseudorange bias errors of BDSBAS monitoring receivers were estimated and their effect on the performance of the BDSBAS service was analyzed. Based on the user algorithms of SBAS differential corrections and integrity information, the service accuracy, integrity, and availability of the BDSBAS were evaluated using real observation data. The results show that the maximum of monitoring receiver pseudorange bias errors between L1P and L1P/L2P can reach 1.57 m, which become the most important errors affecting the performance of the BDSBAS service. In addition, the results show that the pseudorange bias of GPS BlockIII is the smallest, while that of GPS BlockIIR is the largest. Compared with the positioning accuracy of the open service of the core constellation, the positioning accuracy of the BDSBAS service can be improved by approximately 47% and 36% for the RTCA service and DFMC service, respectively. For RTCA services, the protection limit (PL) calculated with the integrity information can 100% envelop the positioning error (PE) and no integrity risk event is detected. The service availability of BDSBAS for APV-I approach is approximately 98.8%, which is mainly affected by the availability of ionospheric grid corrections in the service marginal area. For DFMC service, the integrity risk is not detected either. The service availability for CAT-I approach is 100%. Improving the availability of ionospheric grid corrections is one of the important factors to improve service performance of BDSBAS RTCA service.

Calibrating receiver-type-dependent wide-lane uncalibrated phase delay biases for PPP integer ambiguity resolution

Wide-lane (WL) uncalibrated phase delay (UPD) is usually derived from Melbourne–Wübbena (MW) linear combination and is a prerequisite in Global Navigation Satellite Systems (GNSS) precise point positioning (PPP) ambiguity resolution (AR). MW is a linear combination of pseudorange and phase, and the accuracy is limited by the larger pseudorange noise which is about one hundred times of the carrier phase noise. However, there exist inconsistent pseudorange biases which may have detrimental effect on the WL UPD estimation, and further degrade user-side ambiguity fixing. Currently, only the large part of pseudorange biases, e.g., the differential code bias (DCB), are available and corrected in PPP-AR, while the receiver-type-dependent biases have not yet been considered. Ignoring such kind of bias, which could be up to 20 cm, will cause the ambiguity fixing failure, or even worse, the incorrect ambiguity fixing. In this study, we demonstrate the receiver-type-dependent WL UPD biases and investigate their temporal and spatial stability, and further propose the method to precisely estimate these biases and apply the corrections to improve the user-side PPP-AR. Using a large data set of 1560 GNSS stations during a 30-day period, we demonstrate that the WL UPD deviations among different types of receivers can reach ± 0.3 cycles. It is also shown that such kind of deviations can be calibrated with a precision of about 0.03 cycles for all Global Positioning System (GPS) satellites. On the user side, ignoring the receiver-dependent UPD deviation can cause significant positioning error up to 10 cm. By correcting the deviations, the positioning performance can be improved by up to 50%, and the fixing rate can also be improved by 10%. This study demonstrates that for the precise and reliable PPP-AR, the receiver-dependent UPD deviations cannot be ignored and have to be handled.

Considering inter-receiver pseudorange biases for BDS-2 precise orbit determination

The inter-receiver pseudorange biases exist between receivers equipping with different front-end designs and correlator types. It is distinguishable from differential code biases and would affect Global Navigation Satellite System (GNSS) estimations if it is not taken into account in data processing. In this contribution, the effects of inter-receiver pseudorange biases on the regional BeiDou navigation satellite system (BDS-2) satellite precise orbit determination (POD) will be investigated. For validation purposes, 35 globally distributed Multi-GNSS Experiment ground stations for which the receivers are from three manufacturers were used to determine the precise orbits of BDS-2 satellites from day of year 154 to 163, 2017. The accuracy of orbit overlap and satellite laser ranging (SLR) residual validation comparisons show that by implementing inter-receiver pseudorange bias corrections, the POD accuracies of the BDS-2 satellites can be effectively improved. The root mean square errors of 24-h precise orbit determination overlap corresponding to the radial, cross-track, and along-track components are improved by 1.4%, 2.7%, and 12.7%, respectively, after correcting the inter-receiver pseudorange biases. The standard deviations of the SLR residuals of satellite C01, C13, and C11 are reduced from 30.7, 7.1, and 3.5 cm to 30.2, 6.8, and 2.9 cm, respectively. The results also showed that inter-receiver pseudorange biases will cause an along-track bias in Geostationary Earth Orbit (GEO) satellite orbit determination. The performances of GEO POD in along-track component can be improved by considering the inter-receiver pseudorange biases.

Model and implementation of pseudorange-bias-free linear channel

The nonideal characteristics of the entire channel of satellite navigation signals from generation, propagation to reception will cause signal distortions, resulting in pseudorange biases. Such kind of biases cannot be eliminated by differential technologies and has become a core error source in high-accuracy applications. We study the theoretical model and implementation method of a pseudorange-bias-free linear channel. The ideal channel transfer function equation under the unbiased pseudorange requirement is first derived from the equivalent baseband model. Based on two corresponding criteria and the simulation of the influence of different amplitude- and phase-frequency responses, a digital phase compensation method based on an all-pass filter is proposed to eliminate pseudorange biases. Then the significant effects of the two phase equalizers are validated by a simulation example of the BPSK(10) signal. Finally, the real BDS3 PRN32 and PRN33 satellite B1C signals collected by a 40-m high-gain dish antenna are utilized to invert the channel transfer characteristics and processed by our software receiver. The measurement results demonstrate that the phase equalizers constructed according to either the linear phase criterion or the linear phase plus even-symmetric phase criterion can effectively reduce the pseudorange bias. The model and method provide a reference for payload and receiver optimization and are suitable for various signal structures and applications.