Pseudorange Multipath Research Articles

Performance evaluation of BDS-3 new B1C/B2a and legacy B1I/B3I signals: Observational quality, POD and PPP

In addition to the BeiDou regional navigation satellite system (BDS-2) backward compatible B1I and B3I signals, the BeiDou global navigation satellite system (BDS-3) also broadcast the B1C and B2a signals for compatibility with other Global Navigation Satellite System (GNSS), and providing satellite-based augmentation service for the International Civil Aviation Organization. Considering that the majority of the existing researches on the BDS-3 precise orbit determination (POD) and precise point positioning (PPP) are based on the B1I/B3I signals, the special attention that systematically comparing the data quality, POD accuracy and PPP performance through B1I/B3I and B1C/B2a signals is aroused in this paper. Signal characteristics of different receivers and antennas for the aforesaid four various signals were analyzed in terms of the carrier-to-noise density ratio (C/N0), pseudorange multipath and observation noise. The B1C signal exhibits the minimum C/N0 values, and the B3I and B2a signals have the smaller pseudorange multipath errors. The smallest pseudorange noise can be observed form the B2a signal, while the root mean squares (RMSs) for carrier phase noise show tiny differences among the four signals. The BDS-3 POD results indicate that the orbit overlapping arc error in three-dimensional (3D) direction is 0.069 and 0.076 m for the B1C/B2a and B1I/B3I, and the standard deviation of the satellite laser ranging validation is 0.041 m for both the two schemes. The clock offset products were evaluated with respect to the precise clock products from Deutsches GeoForschungsZentrum (GFZ), and the standard deviations (STDs) are 0.166 and 0.176 ns for the B1C/B2a and B1I/B3I. Finally, there is no apparent difference in the RMSs for B1C/B2a and B1I/B3I static PPP, while the convergence time that shortened by 31.4 % can be achieved for B1C/B2a. For kinematic PPP, the 3D RMS is 0.043 m and the convergence time is 31.1 min for the B1C/B2a, which is reduced by 14.0 % and 35.2 %, respectively, compared to B1I/B3I.

Research on Soil Moisture Estimation of Multiple-Track-GNSS Dual-Frequency Combination Observations Considering the Detection and Correction of Phase Outliers.

Soil moisture (SM), as one of the crucial environmental factors, has traditionally been estimated using global navigation satellite system interferometric reflectometry (GNSS-IR) microwave remote sensing technology. This approach relies on the signal-to-noise ratio (SNR) reflection component, and its accuracy hinges on the successful separation of the reflection component from the direct component. In contrast, the presence of carrier phase and pseudorange multipath errors enables soil moisture retrieval without the requirement for separating the direct component of the signal. To acquire high-quality combined multipath errors and diversify GNSS-IR data sources, this study establishes the dual-frequency pseudorange combination (DFPC) and dual-frequency carrier phase combination (L4) that exclude geometrical factors, ionospheric delay, and tropospheric delay. Simultaneously, we propose two methods for estimating soil moisture: the DFPC method and the L4 method. Initially, the equal-weight least squares method is employed to calculate the initial delay phase. Subsequently, anomalous delay phases are detected and corrected through a combination of the minimum covariance determinant robust estimation (MCD) and the moving average filter (MAF). Finally, we utilize the multivariate linear regression (MLR) and extreme learning machine (ELM) to construct multi-satellite linear regression models (MSLRs) and multi-satellite nonlinear regression models (MSNRs) for soil moisture prediction, and compare the accuracy of each model. To validate the feasibility of these methods, data from site P031 of the Plate Boundary Observatory (PBO) H2O project are utilized. Experimental results demonstrate that combining MCD and MAF can effectively detect and correct outliers, yielding single-satellite delay phase sequences with a high quality. This improvement contributes to varying degrees of enhanced correlation between the single-satellite delay phase and soil moisture. When fusing the corrected delay phases from multiple satellite orbits using the DFPC method for soil moisture estimation, the correlations between the true soil moisture values and the predicted values obtained through MLR and ELM reach 0.81 and 0.88, respectively, while the correlations of the L4 method can reach 0.84 and 0.90, respectively. These findings indicate a substantial achievement in high-precision soil moisture estimation within a small satellite-elevation angle range.

The Extraction and Characterization of Pseudorange Multipath Based on BDS-3 Multi-Frequency Observations.

Global Navigation Satellite System (GNSS) observations are subject to various errors during their propagation process. A reasonable correction of these errors can improve the positioning, navigation, and timing (PNT) service capability. The impact of multipaths on pseudorange observations can reach a decimeters or even meters level. However, their mechanism is complex and there is currently no universally accepted high-precision correction model. The correlation between the pseudorange multipaths (MP) of BDS-2 satellites and satellite elevation has been confirmed, while there have been fewer analyses of the MP characteristics for different frequencies of BDS-3 satellites. The broadcasting of multi-frequency observations in BDS-3 should theoretically make the extracted MP more accurate compared to traditional methods. Based on this, in this contribution, a multi-frequency MP extraction algorithm based on the least squares principle is proposed, which can simultaneously eliminate the influence of higher-order ionospheric delay. The analytical expression for only eliminating first-order ionospheric delay is successfully derived. Subsequently, the characteristics of the MPs extracted from different frequency combinations and the impact of combination noise on the extraction accuracy are discussed. The influence of second-order ionospheric delay on the MPs for each frequency under different combination noises, as well as the periodic behavior exhibited in long-term observations of the BDS-3 medium earth orbit (MEO) and inclined geosynchronous orbit (IGSO) satellites, are also analyzed. Finally, the correlations between the MPs of each frequency of BDS satellite and elevation are quantitatively analyzed based on observations from 35 stations. Overall, this work has positive implications for the study of the MP characteristics of BDS-3 and subsequent modeling efforts.

A Data Quality Assessment Approach for High-Precision GNSS Continuously Operating Reference Stations (CORS) with Case Studies in Hong Kong and Canada/USA

Centimeter-level or better positioning accuracy is needed in engineering surveying applications. When employing the Global Navigation Satellite System (GNSS) in engineering surveying, the high-precision real-time kinematic (RTK) positioning method must be used to achieve such positioning accuracy. Currently, precise point positioning (PPP) cannot reliably achieve the positioning accuracy needed for engineering surveying in real time. The high-precision RTK positioning method needs carrier-phase measurements and a reference station/network. Surveyors may not need a GNSS receiver in their organizations/companies to act as the reference station. Continuously Operating Reference Stations (CORS), run by international/national organizations/agencies or private companies such as GNSS receiver manufacturers, let users freely access the raw GNSS measurements or corrections for real-time and post-processing applications. The positioning accuracy of the GNSS rover is affected by the data quality of the reference stations, including virtual reference stations (VRS). The International GNSS Service (IGS) currently provides the number of cycle slips and the L1 and L2 average pseudorange multipath errors per station daily. The US National Geodetic Survey (NGS) provides daily station coordinate residuals. Carrier-phase data quality of the CORS stations is not provided by their organizations/agencies. Nowadays, many CORS stations track multi-GNSS satellites. This paper proposes a multi-GNSS and multi-frequency data quality assessment approach for CORS stations with a focus on carrier-phase data quality. The proposed approach is demonstrated with case studies on IGS/CORS networks in Hong Kong and Canada/USA. In other words, a strategy to obtain non-linear combined carrier-phase multipath errors and noise is proposed in this work. The data quality of a CORS station depends on the site environment, monument type and height, and GNSS receiver/antenna. An account of the data quality at some selected stations is given; the main focus of the paper is on the proposed data quality assessment approach.

Precise orbit determination for TH02-02 satellites based on BDS3 and GPS observations

The Tianhui-2 02 (TH02-02) satellite formation, as a supplement to the microwave mapping satellite system Tianhui-2 01 (TH02-01), is the first Interferometric Synthetic Aperture Radar (InSAR) satellite formation-flying system that supports the tracking of BeiDou global navigation Satellite system (BDS3) new B1C and B2a signals. Meanwhile, the twin TH02-02 satellites also support the tracking of Global Positioning System (GPS) L1&L2 and BDS B1I&B3I signals. As the spaceborne receiver employs two independent boards to track the Global Navigation Satellite System (GNSS) satellites, we design an orbit determination strategy by estimating independent receiver clock offsets epoch by epoch for each GNSS to realize the multi-GNSS data fusion from different boards. The performance of the spaceborne receiver is evaluated and the contribution of BDS3 to the kinematic and reduced-dynamic Precise Orbit Determination (POD) of TH02-02 satellites is investigated. The tracking data onboard shows that the average number of available BDS3 and GPS satellites are 8.7 and 9.1, respectively. The carrier-to-noise ratio and carrier phase noise of BDS3 B1C and B2a signals are comparable to those of GPS. However, strong azimuth-related systematic biases are recognized in the pseudorange multipath errors of B1C and B3I. The pseudorange noise of BDS3 signals is better than that of GPS after eliminating the multipath errors from specific signals. Taking the GPS-based reduced-dynamic orbit with single-receiver ambiguity fixing technique as a reference, the results of BDS3-only and BDS3 + GPS combined POD are assessed. The Root Mean Square (RMS) of orbit comparison of BDS3-based kinematic and reduced-dynamic POD with reference orbit are better than 7 cm and 3 cm in three-Dimensional direction (3D). The POD performance based on B1C&B2a data is comparable to that based on B1I&B3I. The precision of BDS3 + GPS combined kinematic orbit can reach up to 3 cm (3D RMS), which has a more than 25% improvement relative to the GPS-only solution. In addition, the consistency between the BDS3 + GPS combined reduced-dynamic orbit and the GPS-based ambiguity-fixed orbit is better than 1.5 cm (3D RMS).

Smartphone Pseudorange Multipath Extraction Based on Variational Mode Decomposition and Wavelet Transform

Smartphone Pseudorange Multipath Extraction Based on Variational Mode Decomposition and Wavelet Transform

Analysis of Precise Orbit Determination of BDS-3 MEO and IGSO Satellites Based on Several Dual-Frequency Measurement Combinations

The Chinese BeiDou-3 navigation satellite system (BDS-3) is capable of transmitting both old B1I, B3I signals and new B1C, B2a, B2b signals. Current BDS-3 precise orbits are generally calculated using a B1I/B3I combination considering overlap with the BeiDou-2 navigation satellite system (BDS-2). In this contribution, the observation quality of BDS-3 medium earth orbit (MEO) satellites and inclined geosynchronous orbit (IGSO) satellites are analyzed based on three aspects, i.e., carrier to noise ratio (C/N0), pseudo-range noise and pseudo-range multipath (MP). The C/N0 of the MEO satellite is 2~3 dB higher than that of the IGSO satellite at the same elevation angle. Meanwhile, the order of the Root Mean Square (RMS) values of both pseudo-range noise and MP is B1I < B1C < B3I < B2a ≈ B2b. Three kinds of combinations, i.e., B1CB2a, B1CB2b and B1IB3I, are selected for the BDS-3 precise orbit determination (POD) experiment. Orbits are assessed by the orbit-only signal-in-space range error (SISRE) computed between pairs of the three kinds of combinations in this contribution, CODE and GFZ final orbits. Orbit-only SISRE assessment shows that B1CB2a/CODE, B1CB2b/CODE, B1CB2a/GFZ and B1CB2b/GFZ are at the same level with CODE/GFZ, and the orbit-only SISRE is at the level of 5 cm for MEOs and 9 cm for IGSOs, respectively. Meanwhile, B1IB3I/CODE and B1IB3I/GFZ are about 1–2 cm worse. Inter-solution comparison between B1CB2a, B1CB2b and B1IB3I also indicate that B1CB2a and B1CB2b have good consistency, while B1IB3I shows poor performance. Satellite laser ranging (SLR) residuals indicate that the mean RMS is 3–4 cm for the four BDS-3 MEOs for CODE final orbit, GFZ final orbit, B1CB2a and B1CB2b combinations, while the mean RMS value for B1IB3I combination is a few millimeters worse, at approximately 4–5 cm.

Theory and Experiment Analysis on the Influence of Floods on a GNSS Pseudo-Range Multipath and CNR Signal Based on Two Cases Study in China

The surrounding environment of a GNSS observation station is changed during a flood, and this results in a more serious multipath than in a normal environment. Considering that the multipath error is largely related to the pseudo-range multipath and CNR (Carrier-to-noise ratio) of the GNSS signal, the influence of floods on a pseudo-range multipath and CNR is analyzed in theory and through experiment. To ensure the accuracy of the analysis results, the ground track repeat period of GPS, GLONASS, and BDS satellites is investigated from the perspective of theory and skyplots. Two real cases study collected in Zhengzhou and Xinxiang, China, in 2021, are used to demonstrate the influence of floods on a pseudo-range multipath and CNR in detail. Experimental results show that the pseudo-range multipath of a GPS satellite performs more seriously during a flood. The maximum RMS increase rate is approximately 17.85%, and the average of all other satellites with a whole arc is approximately 6.55%. In addition, the CNR of three GNSS systems performs a decrease during a flood. For GPS and GLONASS satellites, the decrease performs more seriously at a high elevation angle than that at a low elevation angle. The maximum decrease is approximately 5 dB-Hz for the GPS satellite and approximately 7 dB-Hz for the GLONASS satellite. In terms of the BDS system, the CNR of all three orbital type satellites decreases during a flood. The average decrease is approximately 2 dB-Hz for BDS MEO and GEO satellites, and about 1 dB-Hz for the BDS IGSO satellite.

Pseudorange multipath at Zomba geodynamics Continuously Operating Reference Station (CORS) in Malawi

Multipath effects are mostly regarded as a nuisance in Global Navigation Satellite System (GNSS) receiver measurements and it is of utmost relevance to expose the magnitude this error has on observations. The impact of multipath is characterized in the context of a given environment and application. In Malawi, Zomba geodynamics Continuously Operating Reference Station (CORS) is in a multipath prone environment. The GNSS observations for this station have been used in geodynamics studies in Malawi without an understanding of multipath affecting the positioning accuracy. Taking this as an advantage, this paper evaluated pseudorange multipath (MP) and signal noise ratio (SNR) on both L1 (MP1 and SNR1) and L2 (MP2 and SNR2) for the station. This was specifically addressed by computing the elevation mask with minimum and maximum multipath effects. In addition, the number of satellite vehicles (SVs) and their associated Geometric Dilution of Precision (GDOP) are also determined to define their relationship with respect to elevation angles. One week GNSS observations spanning a twenty-four hour interval for DOY 001 to DOY 007 in January 2018 were analysed in Translation Editing and Quality Check (TEQC) software at four (10º, 15º, 20º and 25º) cut-off angles. Results indicate high multipath effects for both MP1 and MP2 at 10º elevation mask among the four elevation masks. The least MP1 and MP2 multipath effects were detected at an elevation angle of 25º. In addition, MP1 multipath was worse than MP2 all the angles. Moreover, statistical results demonstrated an increase in both SNR1 and SNR2 with respect to elevation angle. For these days, L2 signal was more affected by noise than L1. Further to this, an assessment of SVs and GDOP for the CORS show that at least ten (10) satellites were observed in each day at 10º and 15º elevation cut-off. The number of satellites dropped to five (5) at the elevation angle of 25º resulting into a larger GDOP value of 4.5 (a decrease by about 38% from 1.7 at 10º and 15º elevation cut-off angles). Therefore, to increase both the number of satellites and precision, Zomba CORS may be upgraded to a multi-constellation CORS by including other navigation systems such as GLONASS, Galileo and BeiDou. While it is possible to reject GNSS satellite observations below the horizon, it is recommended that post-processing of GNSS data for Zomba geodynamics CORS be done at elevation masks above 15º. Considering that multipath repeats itself every sidereal day, it is thus recommended to model or remove multipath affecting Zomba geodynamics CORS. In addition, the study also recommends that trees very close to Zomba CORS antenna be removed to reduce signal scattering.

Research on Linear Combination Models of BDS Multi-Frequency Observations and Their Characteristics

The linear combination of multi-frequency carrier-phase and pseudorange observations can form the combined observations with special properties. The type and number of combined frequencies will directly affect the characteristics of the combined observations. BDS-2 and BDS-3 broadcast three and five signals, respectively, and the study of their linear combination is of great significance for precision positioning. In this contribution, the linear combination form of multi-frequency carrier-phase observations in cycles and meters is sorted out. Seven frequency combination modes are formed, and some special combinations for positioning are searched. Then, based on the principle of minimum combined noise, a simpler search method for the optimal real coefficients of ionosphere-free (IF) combination based on the least squares (LS) principle is proposed. The general analytical expressions of optimal real coefficients for multi-frequency geometry-based and ionosphere-free (GBIF), geometry-free and ionosphere-free (GFIF), and pseudorange multipath (PMP) combinations with the first-order ionosphere delay taken into account are derived. And the expression derivation process is given when both the first-order and second-order ionospheric delays are eliminated. Based on this, the characteristics of the optimal real coefficient combination in various modes are compared and discussed. The various combinations reflect that the accuracy of the combined observations from dual-frequency (DF) to five-frequency (FF) is gradually improving. The combination coefficient becomes significantly larger after taking the second-order ionospheric delay into account. In addition, the combined accuracy of BDS-3 is better than that of BDS-2. When only the first-order ionosphere is considered, the combination attribute of (B1C, B1I, B2a) is the best among the triple-frequency (TF) combinations of BDS-3. When both the first-order and second-order ionospheric delays are considered, the (B1C, B3I, B2a) combination is recommended.

Performance of Multi-GNSS in the Asia-Pacific Region: Signal Quality, Broadcast Ephemeris and Precise Point Positioning (PPP)

Since BeiDou Navigation Satellite System (BDS) and Japan’s Quasi-Zenith Satellite System (QZSS) have more visible satellites in the Asia-Pacific region, and navigation satellites of Global Positioning System (GPS), Galileo satellite navigation system (Galileo), and GLONASS satellite navigation system (GLONASS) are uniformly distributed globally, the service level of multi-mode Global Navigation Satellite System (GNSS) in the Asia-Pacific region should represent the best service capability. Based on the observation data of 10 Multi-GNSS Experiment (MGEX) stations, broadcast ephemeris and precision ephemeris from 13 to 19 October 2021, this paper comprehensively evaluated the service capability of multi-GNSS in the Asia-Pacific region from three aspects of observation data quality, broadcast ephemeris performance, and precision positioning level. The results show that: (1) the carrier-to-noise-density ratio (C/N0) quality of the GPS and Galileo is the best, followed by BDS and GLONASS, and QZSS is the worst. GPS, BDS-2, GLONASS, and QZSS pseudorange multipath values range from 0 to 0.6 m, while Galileo system and BDS-3 pseudorange multipath values range from 0 to 0.8 m. (2) In terms of broadcast ephemeris accuracy, BDS-3 broadcast ephemeris has the best orbit, and the three-dimensional (3D) Root Mean Square (RMS) is 0.21 m; BDS-2 was the worst, with a 3D RMS of 1.99 m. The broadcast ephemeris orbits of GPS, Galileo, QZSS, and GLONASS have 3D RMS of 0.60 m, 0.62 m, 0.83 m, and 1.27 m, respectively. For broadcast ephemeris clock offset: Galileo has the best performance, 0.61 ns, GLONASS is the worst, standard deviation (STD) is 3.10 ns, GPS, QZSS, BDS-3 and BDS-2 are 0.65 ns, 0.75 ns, and 1.72 ns, respectively. For signal-in-space ranging errors (SISRE), the SISRE results of GPS and Galileo systems are the best, fluctuating in the range of 0 m–2 m, followed by QZSS, BDS-3, Galileo, and BDS-2. (3) GPS, BDS, GLONASS, Galileo, GPS/QZSS, and BDS/QZSS were used for positioning experiments. In static PPP, the convergence time and positioning accuracy of GPS show the best performance. The positioning accuracy of GPS/QZSS and BDS/QZSS is improved compared with that of GPS and BDS. In terms of kinematic PPP, the convergence time and positioning accuracy of GPS/QZSS and BDS/QZSS are improved compared with that of GPS and BDS. In addition to GLONASS and Galileo systems, the other combinations outperformed 3 cm, 3 cm, and 5 cm in the east, north, and up directions.

Correction Model of BDS-3 Satellite Pseudorange Multipath Delays and Its Impact on Single-Frequency Precise Point Positioning

Precise point positioning (PPP) is used in many fields. However, pseudorange multipath delay is an important error that restricts its accuracy. Pseudorange multipath delay can be considered as the combination of effective information and observation noise; it can be modeled after removing the observation noise. In this work, elastic nets (EN) regularization denoising method is proposed and compared with L2-norm regularization denoising method. Then, quadratic polynomial (QP) model plus autoregressive (AR) model (QP + AR) are used to model the denoised pseudorange multipath delays. Finally, the modeling results are corrected to the observations to verify the improvement of BDS-3 single-frequency PPP accuracy. Three single-frequency PPP schemes are designed to verify the effectiveness of denoising method and QP + AR model. The experimental results show that the accuracy improvement of B3I and B2a is more obvious than that of B1I and B1C when the modeling values are corrected to the pseudorange observations. The improvement of B3I and B2a in the east (E) and up (U) directions can reach 10.6%∼34.4% and 5.9%∼65.7%, and the improvement of the north (N) direction is mostly less than 10.0%. The accuracy of B1I and B1C in E and U directions can be improved by 0%∼30.7% and 0.4%∼28.6%, respectively, while the accuracy of N direction can be improved slightly or even decreased. Using EN regularization denoising and QP + AR model correction, single-frequency PPP performs better at B3I and B2a, while L2-norm regularization denoising and QP + AR model correction perform better at B1I and B1C. The accuracy improvement of B2a and B3I is more obvious than that of B1I and B1C. The convergence time after MP correction of each frequency is slightly shorter. Overall, the proposed pseudorange multipath delays processing strategy is beneficial in improving the single-frequency PPP of BDS-3 satellite.

Estimation of Inter-System Biases between BDS-3/GPS/Galileo and Its Application in RTK Positioning

For the development of a global navigation satellite system (GNSS), the third generation of BeiDou Navigation Satellite System (BDS-3) achieved full constellation for worldwide service on 23 June 2020. The new signals, B1C and B2a of BDS-3, further enhance the compatibility and interoperability between different GNSSs. In this study, we first assessed the quality of all the signals in BDS-3/GPS/Galileo. Then, to achieve the interoperability among BDS-3/GPS/Galileo, the inter-system bias (ISB), which appears if an inter-system difference exists between two GNSSs, was estimated at overlapping frequencies. Finally, we used the estimated ISBs in real-time kinematic (RTK) positioning. The results show the higher quality of the overlapping frequency B2a/L5/E5a than B1C/L1/E1 in terms of pseudo range multipath. The ISBs are stable both in the short term for one day and in the long term for over a year, which fit a zero-mean normal distribution well when the identical type of receiver is applied. Thus, it is reasonable to ignore the ISBs in the inter-system differences. With the estimated ISBs, the inter-system double-difference RTK can be achieved, which is called a tightly combined model (TCM) RTK. Compared with the traditional intra-system double-difference RTK, which is called a loosely combined model (LCM) RTK, the TCM RTK can achieve a higher success rate (SR) in terms of ambiguity resolution and higher positioning accuracy. In addition, the higher the cutoff elevation angle set, the greater the promotion can be obtained in SR. Even with a cutoff elevation angle of 50°, the SR of TCM is over 80%. Thus, it is important to apply TCM RTK when the observation conditions are limited, such as in dense jungles or the urban canyons.

Algorithm for Real-Time Cycle Slip Detection and Repair for Low Elevation GPS Undifferenced Data in Different Environments

Real-time cycle slip detection and repair is one of the key issues in global positioning system (GPS) high precision data processing and application. In particular, when GPS stations are in special environments, such as strong ionospheric disturbance, sea, and high-voltage transmission line interference, cycle slip detection and repair in low elevation GPS observation data are more complicated than those in normal environments. For low elevation GPS undifferenced carrier phase data in different environments, a combined cycle slip detection algorithm is proposed. This method uses the first-order Gauss–Markov stochastic process to model the pseudorange multipath in the wide-lane phase minus narrow-lane pseudorange observation equation, and establishes the state equation of the wide-lane ambiguity with the pseudorange multipath as a parameter, and it uses the Kalman filter for real-time estimation and detects cycle slips based on statistical hypothesis testing with a predicted residual sequence. Meanwhile, considering there are certain correlations among low elevation, observation epoch interval, and ionospheric delay error, a second-order difference geometry-free combination cycle slip test is constructed that takes into account the elevation. By combining the two methods, real-time cycle slip detection for GPS low elevation satellite undifferenced data is achieved. A cycle slip repair method based on spatial search and objective function minimization criterion is further proposed to determine the correct solution of the cycle slips after they are detected. The whole algorithm is experimentally verified using the static and kinematic measured data of low elevation satellites under four different environments: normal condition, high-voltage transmission lines, dynamic condition in the sea, and ionospheric disturbances. The experimental results show that the algorithm can detect and repair cycle slips accurately for low elevation GPS undifferenced data, the difference between the float solution and the true value for the cycle slip does not exceed 0.5 cycle, and the differences obey the normal distribution overall. At the same time, the wide-lane ambiguity and second-order difference GF combination sequence calculated by the algorithm is smoother, which give further evidence that the algorithm for cycle slip detection and repair is feasible and effective, and has the advantage of being immune to the special observation environments.

Optimization Technique for Pseudorange Multipath Mitigation Using Different Signal Selection Methods

Abstract Nowadays, the use of multi-Global Navigation Satellite System (GNSS) has improved positioning accuracy in autonomous driving, navigation and tracking systems utilized by general users. However, signal quality in urban areas is degraded by poor satellite geometry and severe multipath errors, which may disturb up to a hundred-meter-ranging error as a consequence. In this study, the performance of several satellite selection methods in multipath mitigation was evaluated, based on the concept that better quality signals and more accurate solutions will be obtained, the more multipath signals can be excluded. Three methods were performed and compared: 1) azimuth-dependent elevation mask based on fisheye image technique, 2) receiver autonomous integrity monitoring (RAIM), and 3) signal-to-noise ratio (SNR) mask in the SPP method. To examine the effect of the satellite selection methods on multipath error, the static test (single-point positioning (SPP) in real-time 1 Hz test) was performed in a multipath environment. The preliminary results showed a possible impact on improving the horizontal positioning accuracy of SPP. Among the three techniques assessed in this study, the results indicated that the SNR mask set at 36 dB-Hz in every elevation showed the most promising result. The SNR mask method could improve positioning accuracy by up to 46.80% compared to the SPP method.

Spectral analysis of multi-year GNSS code multipath time-series

In the presented study multi-year time series of changes in the L1 pseudo-range multipath are analysed. Data from 8 stations of the EUREF Permanent Network (EPN) were used in the study. Periodic components present in the signal and their stability over time were analysed. Also, the type of background noise was determined, based on the spectral index. In some cases, the presence of weak components with a 1/2 and 1/3 of the Chandler period has also been found. Time-frequency analysis shows that periodic signals are not stationary in most of the examined cases, and particular signal components occur only temporarily. The analysed signals were characterised by pink noise in the lower frequency range and by white noise for higher frequencies, which is also characteristic for time series of coordinates obtained from GNSS measurements.

Assessing the quality of ionospheric models through GNSS positioning error: methodology and results

Single-frequency users of the global navigation satellite system (GNSS) must correct for the ionospheric delay. These corrections are available from global ionospheric models (GIMs). Therefore, the accuracy of the GIM is important because the unmodeled or incorrectly part of ionospheric delay contributes to the positioning error of GNSS-based positioning. However, the positioning error of receivers located at known coordinates can be used to infer the accuracy of GIMs in a simple manner. This is why assessment of GIMs by means of the position domain is often used as an alternative to assessments in the ionospheric delay domain. The latter method requires accurate reference ionospheric values obtained from a network solution and complex geodetic modeling. However, evaluations using the positioning error method present several difficulties, as evidenced in recent works, that can lead to inconsistent results compared to the tests using the ionospheric delay domain. We analyze the reasons why such inconsistencies occur, applying both methodologies. We have computed the position of 34 permanent stations for the entire year of 2014 within the last Solar Maximum. The positioning tests have been done using code pseudoranges and carrier-phase leveled (CCL) measurements. We identify the error sources that make it difficult to distinguish the part of the positioning error that is attributable to the ionospheric correction: the measurement noise, pseudorange multipath, evaluation metric, and outliers. Once these error sources are considered, we obtain equivalent results to those found in the ionospheric delay domain assessments. Accurate GIMs can provide single-frequency navigation positioning at the decimeter level using CCL measurements and better positions than those obtained using the dual-frequency ionospheric-free combination of pseudoranges. Finally, some recommendations are provided for further studies of ionospheric models using the position domain method.

Differential Inter-System Biases Estimation and Initial Assessment of Instantaneous Tightly Combined RTK with BDS-3, GPS, and Galileo

In this contribution, we assess, for the first time, the tightly combined real-time kinematic (RTK) with GPS, Galileo, and BDS-3 operational satellites using observations from their overlapping L1-E1-B1C/L5-E5a-B2a frequencies. First, the characteristics of B1C/B2a signals from BDS-3 operational satellites is evaluated compared to GPS/Galileo L1-E1/L5-E5a signals in terms of observed carrier-to-noise density ratio, pseudorange multipath and noise, as well as double-differenced carrier phase and code residuals using data collected with scientific geodetic iGMAS and commercial M300Pro receivers. It’s demonstrated that the observational quality of B1C/B2a signals from BDS-3 operational satellites is comparable to that of GPS/Galileo L1-E1/L5-E5a signals. Then, we investigate the size and stability of phase and code differential inter-system bias (ISB) between BDS-3/GPS/Galileo B1C-L1-E1/B2a-L5-E5a signals using short baseline data collected with both identical and different receiver types. It is verified that the BDS-3/GPS/Galileo ISBs are indeed close to zero when identical type of receivers are used at both ends of a baseline. Moreover, they are generally present and stable in the time domain for baselines with different receiver types, which can be easily calibrated and corrected in advance. Finally, we present initial assessment of single-epoch tightly combined BDS-3/GPS/Galileo RTK with single-frequency and dual-frequency observations using a formal and empirical analysis, consisting of ambiguity dilution of precision (ADOP), ratio values, the empirical ambiguity resolution success rate, and the positioning accuracy. Experimental results demonstrate that the tightly combined model can deliver much lower ADOP and higher ratio values with respect to the classical loosely combined model whether for GPS/BDS-3 or GPS/Galileo/BDS-3 solutions. The positioning accuracy and the empirical ambiguity resolution success rate are remarkably improved as well, which could reach up to approximately 10%∼60% under poor observational conditions.

Early analysis of precise orbit and clock offset determination for the satellites of the global BeiDou-3 system

Eight new-generation BeiDou satellites (BeiDou-3) have been launched into Medium Earth Orbit (MEO), allowing for global coverage since March 2018, and they are equipped with new hydrogen atomic clocks and updated rubidium clocks. Firstly, we analyzed the signals for the carrier-to-noise-density ratio (C/N0) and pseudorange multipath (MP) by using international GNSS (Global Navigation Satellite System) Monitoring and Assessment System (iGMAS) station data, and found that B1C has a lower C/N0, and B2a has the same level of C/N0 as the B1I and B3I signals. For pseudorange multipath, compared with the BeiDou-2 satellites, the obvious systematic variation of MP scatters related to the elevation angle is greatly improved for the BeiDou-3 and BeiDou-3e satellites signals. For the signals of the BeiDou-3 satellites, the order of the Root Mean Square (RMS) values of multipath and noise is B3I < B1I < B2a < B1C. Then, the comparison of the precise orbit determination and clock offset determination for the BeiDou-2, BeiDou-3, and BeiDou-3 experimental (BeiDou-3e) satellites was done by using 10 stations from iGMAS. The 3D precision of the 24 h orbit overlap is 24.55, 25.61, and 23.35 cm for the BeiDou-3, BeiDou-3e, and BeiDou-2 satellites, respectively. BeiDou-3 satellite has a comparable precision to that of the BeiDou-2 satellite. For the precision of clock offset estimation, the Standard Deviation (STD) of the BeiDou-3 MEO satellite is 0.350 ns, which is an improvement of 0.042 ns over that of the BeiDou-2 MEO satellite. The stabilities of the BeiDou-3 and BeiDou-3e onboard clocks are better than those of BeiDou-2 by factors of 2.84 and 1.61 at an averaging time of 1000 and 10,000 s, respectively.

Effects of Site-Dependent Errors on the Accuracy of C/A Code DGPS Positioning

Several differential GPS processing techniques can be used; for instance, single differencing and double differencing, which are popular in practice. Irrespective of the DGPS processing technique used, the ultimate accuracy of the user-location depends on the existence of non-common or site-dependent errors, which occur at the points of observation and the reference. Of these, the most common and dominant site-dependent error is the multipath. Therefore, this research evaluates the effects of site-dependent errors on C/A code differential GPS correction accuracies by providing special emphasis on the multipath error. For the analyses, four segments of about 24-hour continuous static C/A code based DGPS observations were conducted at three precisely known ground stations and four different multipath environments were introduced by placing three different types of artificial signal reflectors at one of the observation stations. By using the known GPS receiver-reflector configuration, pseudo-range multipath was precisely calculated for each observation segment. C/A code DGPS positioning accuracies before and after multipath mitigation were presented by evaluating the effect of the most dominant site-dependent error, i.e., multipath, on C/A code DGPS correction accuracies.