Real-time Single-frequency Precise Point Positioning Research Articles

Analysis of spatial–temporal characteristics for BDS-3 broadcast ionospheric models (BDS Klobuchar and BDGIM) in multi-GNSS real-time single-frequency precise point positioning

With the full operation of BDS-3 broadcast ionospheric models, i.e., the BeiDou global ionospheric delay correction model (BDGIM) and the BDS Klobuchar model, its impact on the multi-GNSS real-time (RT) single-frequency (SF) precise point positioning (PPP) needs to be investigated for low-cost GNSS users. The GPS Klobuchar model as a reference is also considered in this study. Two types of SF-PPP models including the ionosphere-corrected (IC) and ionosphere-weighted (IW) strategies are adopted in the positioning domain. GPS + GLONASS + Galileo + BDS-3 observations from 40 multi-GNSS experiment (MGEX) stations distributed in different latitudes are selected for conducting RT SF-PPP during the ionospheric quiet and active periods. The experiment shows that the positioning accuracy of IC RT SF-PPP can be degraded with the increase of the ionospheric activity levels or the decrease of latitudes. Except for low-latitude regions during the ionospheric active period, the 3D positioning accuracy of the northern hemisphere can be improved by at least 15.2 % compared to the southern hemisphere in the IC model with the BDS Klobuchar. The BDGIM model has the best performance among all IC RT SF-PPP solutions, but its 3D positioning accuracy can reach the sub-meter level only in mid-latitude regions. With the adoption of ionospheric constraints, the convergence of the IW model is always superior to that of the group and phase ionospheric correction (GRAPHIC) model, and the improvement of convergence in mid-latitude regions is clearly better than that in low-latitude regions. Due to the quality limitation of the BDS Klobuchar model, it has the longest convergence time among all IW models regardless of ionospheric conditions or latitude regions. Compared to the GPS Klobuchar, the significant improvement of convergence for the BDGIM-constrained RT SF-PPP is mainly presented in low-latitude regions of the northern hemisphere. The horizontal positioning accuracy of the BDGIM-constrained model is always improved in comparison with the GRAPHIC model, but there is a degradation in the vertical component, and the improvement of 3D positioning accuracy is no more than 11.7 %. In summary, the BDGIM-constrained model has the best performance among all RT SF-PPP solutions, its 3D positioning accuracy has the ability to achieve 0.25 m at present.

Performance of BDS-2/3, GPS, and Galileo Time Transfer with Real-Time Single-Frequency Precise Point Positioning

Single-frequency (SF) receivers are much cheaper than that of dual-frequency (DF). Even though DF precise point positioning (PPP) is nowadays applied in the time community, the cost of equipment is one of the key considerations for time users. Furthermore, the hardware delay calibration of single-frequency devices is simpler than that of dual-frequency devices. In addition, there is no literature to study real-time SF PPP time transfer. In this contribution, the possibility of time transfer using SF PPP was studied. The Un-combined SF PPP was employed for time transfer with ionospheric-constraint using real-time precise products. In this case, 18 multi-GNSS experiment (MGEX) stations and one time lab station were used to study real-time SF PPP time transfer using GPS, Galileo and BDS-2/3 satellites with 20-day. The results suggested that real-time single-frequency PPP can meet time transfer. the standard deviation (STD) of the clock difference obtained from GPS-only, Galileo-only and BDS-2/3 single-frequency PPP are about (0.51, 0.54, 0.91) ns, respectively. The frequency stability of real-time single-frequency PPP can achieve (1E-12, 1E-13, 1E-13) level at short-term and (1E-13, 1E-13, 1E-14) level at long-term, respectively, for BDS-2/3, Galileo-only and GPS-only based.

An investigation into real-time GPS/GLONASS single-frequency precise point positioning and its atmospheric mitigation strategies

One of the challenges in the innovative application of global navigation satellite systems (GNSS) lies in real-time single-frequency precise point positioning (RT-SFPPP). The well-known problems associated with SFPPP are its slow convergence and lower positioning accuracy due to the effects of various errors inherited by the GNSS positioning, including the atmospheric error. In order to mitigate the two above-mentioned problems, several scenarios for the reduction of the atmospheric delays in RT-SFPPP, including the ionospheric constraint and tropospheric constraint, were investigated in this research. The performance of the RT-SFPPP utilizing the above-mentioned methods was evaluated using one-week observations from multi-GNSS experiment stations in a simulated kinematic mode. Results showed that the convergence time of the RT-SFPPP was significantly shortened when the slant ionospheric delays derived from the real-time ionospheric products provided by Centre National d’Études Spatiales were applied as the pseudo-observations. Results also showed that the convergence time of GPS + GLONASS RT-SFPPP can be reduced by modeling the frequency-dependent part of the GLONASS receiver uncalibrated code delay as a quadratic polynomial function of GLONASS frequency number. The a priori zenith wet delays (ZWDs) derived from forecast Vienna Mapping Functions 3 (VMF3_FC) were compared to the reference ZWDs from globally distributed radiosonde stations. The mean root mean square error of the a priori ZWDs resulting from VMF3_FC at 381 radiosonde stations in 2020 was 1.53 cm compared to the radiosonde-based ZWDs. When the ZWDs derived from VMF3_FC were used as pseudo-observations in the position estimation system, the convergence time for the vertical positioning reaching a 0.3 m accuracy was considerably shortened.

An SVM Based Weight Scheme for Improving Kinematic GNSS Positioning Accuracy with Low-Cost GNSS Receiver in Urban Environments.

High-precision positioning with low-cost global navigation satellite systems (GNSS) in urban environments remains a significant challenge due to the significant multipath effects, non-line-of-sight (NLOS) errors, as well as poor satellite visibility and geometry. A GNSS system is typically implemented with a least-square (LS) or a Kalman-filter (KF) estimator, and a proper weight scheme is vital for achieving reliable navigation solutions. The traditional weight schemes are based on the signal-in-space ranging errors (SISRE), elevation and C/N0 values, which would be less effective in urban environments since the observation quality cannot be fully manifested by those values. In this paper, we propose a new multi-feature support vector machine (SVM) signal classifier-based weight scheme for GNSS measurements to improve the kinematic GNSS positioning accuracy in urban environments. The proposed new weight scheme is based on the identification of important features in GNSS data in urban environments and intelligent classification of line-of-sight (LOS) and NLOS signals. To validate the performance of the newly proposed weight scheme, we have implemented it into a real-time single-frequency precise point positioning (SFPPP) system. The dynamic vehicle-based tests with a low-cost single-frequency u-blox M8T GNSS receiver demonstrate that the positioning accuracy using the new weight scheme outperforms the traditional C/N0 based weight model by 65.4% and 85.0% in the horizontal and up direction, and most position error spikes at overcrossing and short tunnels can be eliminated by the new weight scheme compared to the traditional method. It also surpasses the built-in satellite-based augmentation systems (SBAS) solutions of the u-blox M8T and is even better than the built-in real-time-kinematic (RTK) solutions of multi-frequency receivers like the u-blox F9P and Trimble BD982.

A Refinement Method of Real-Time Ionospheric Model for China

Ionospheric delay is a crucial error source and determines the source of single-frequency precise point positioning (SF-PPP) accuracy. To meet the demands of real-time SF-PPP (RT-SF-PPP), several international global navigation satellite systems (GNSS) service (IGS) analysis centers provide real-time global ionospheric vertical total electron content (VTEC) products. However, the accuracy distribution of VTEC products is nonuniform. Proposing a refinement method is a convenient means to obtain a more accuracy and consistent VTEC product. In this study, we proposed a refinement method of a real-time ionospheric VTEC model for China and carried out experiments to validate the model effectiveness. First, based on the refinement method and the Centre National d’Études Spatiales (CNES) VTEC products, three refined real-time global ionospheric models (RRTGIMs) with one, three, and six stations in China were built via GNSS observations. Second, the slant total electron content (STEC) and Jason-3 VTEC were used as references to evaluate VTEC accuracy. Third, RT-SF-PPP was used to evaluate the accuracy in the positioning domain. Results showed that even if using only one station to refine the global ionospheric model, the refined model achieved a better performance than CNES and the Center for Orbit Determination in Europe (CODE). The refinement model with six stations was found to be the best of the three refinement models.

Comparison of three widely used multi‐GNSS real‐time single‐frequency precise point positioning models using the International GNSS Service real‐time service

Real-time single-frequency precise point positioning (RT-SFPPP) of low-cost has been attracting increasing attention in numerous global navigation satellite system (GNSS) applications. Nowadays, three multi-GNSS RT-SFPPP models are widely applied, i.e. ionosphere-corrected (IC), ionospherefree (IF) and ionosphere-weighted (IW) models. A comprehensive evaluation of the three models using CLK93 products is performed in the aspect of observation residuals, positioning accuracy and convergence. Data sets with quad-system are collected from 16 multi-GNSS experiments (MGEX) stations and are analysed in the simulated kinematic precise point positioning (PPP). Besides, kinematic PPP for a 5-h shipborne data set is also conducted. Experimental results show that the positioning accuracy of IW model using MGEX data is better than that of both IC and IF models. Regarding the kinematic shipborne test, positioning accuracy of IF/IW model is of 0.27/0.26, 0.21/0.26 and 0.49/0.48 m for the N, E and U components, respectively, which is much better than that of IC model. As for average convergence time, IW model shows the best performance, which is at least 25% faster than the IF model. Different from both IF and IW models, the amplification of ionospheric errors has some impact on the positioning performance of the IC model at different frequencies.

Estimation and representation of regional atmospheric corrections for augmenting real-time single-frequency PPP

Real-time single-frequency precise point positioning (PPP) can be significantly augmented by applying high-quality atmospheric corrections. In previous work, the satellite-and-station-specific slant total electron content (STEC) ionospheric corrections, derived from a regional reference network, are commonly used to augment single-frequency PPP for improving positioning accuracy and faster convergence. However, since the users are required to interpolate STEC ionospheric corrections from nearby reference stations, either duplex communication links should be established or all corrections of the reference network must be retrieved, which makes it inefficient to provide augmentation services to many users. Moreover, the regional tropospheric corrections are generally neglected in augmenting real-time single-frequency PPP. In this study, we present a method to estimate and represent tropospheric and ionospheric corrections from a regional reference network, which can be efficiently disseminated to users through a simplex communication link. First, the uncombined dual-frequency PPP, with external ionospheric constraints derived from international GNSS service predicted global ionospheric map, is used for estimating atmospheric delays with observations from a regional GNSS reference network. Then, the atmospheric delays are properly represented to facilitate real-time transmission by applying a polynomial model for the representation of zenith wet tropospheric corrections, and satellite-specific STEC maps for representing the slant ionospheric corrections. The above results in only simple communication links required to retrieve the regional atmospheric corrections for real-time single-frequency PPP augmentation. Observations from a regional network of 30 GNSS reference stations with inter-station distances of about 70 km during a 1-week-long period, including both quiet and active geomagnetic conditions, are used for generating the regional atmospheric corrections. The results indicate that the average root-mean-square errors of the obtained regional tropospheric and ionospheric corrections are better than 0.01 and 0.05 m when compared with those derived from dual-frequency uncombined PPP, respectively. The positioning accuracy of the single-frequency PPP augmented with regional atmospheric corrections is at 0.141 m horizontally and 0.206 m vertically under a 95% confidence level, a significant improvement compared to single-frequency PPP without atmospheric augmentation. The convergence time is also significantly reduced with 70.4% of the positioning sessions achieving instantaneous 3D convergence.

Low-Cost Real-Time PPP/INS Integration for Automated Land Vehicles.

The last decade has witnessed a growing demand for precise positioning in many applications including car navigation. Navigating automated land vehicles requires at least sub-meter level positioning accuracy with the lowest possible cost. The Global Navigation Satellite System (GNSS) Single-Frequency Precise Point Positioning (SF-PPP) is capable of achieving sub-meter level accuracy in benign GNSS conditions using low-cost GNSS receivers. However, SF-PPP alone cannot be employed for land vehicles due to frequent signal degradation and blockage. In this paper, real-time SF-PPP is integrated with a low-cost consumer-grade Inertial Navigation System (INS) to provide a continuous and precise navigation solution. The PPP accuracy and the applied estimation algorithm contributed to reducing the effects of INS errors. The system was evaluated through two road tests which included open-sky, suburban, momentary outages, and complete GNSS outage conditions. The results showed that the developed PPP/INS system maintained horizontal sub-meter Root Mean Square (RMS) accuracy in open-sky and suburban environments. Moreover, the PPP/INS system could provide a continuous real-time positioning solution within the lane the vehicle is moving in. This lane-level accuracy was preserved even when passing under bridges and overpasses on the road. The developed PPP/INS system is expected to benefit low-cost precise land vehicle navigation applications including level 2 of vehicle automation which comprises services such as lane departure warning and lane-keeping assistance.

Performance evaluation of real-time global ionospheric maps provided by different IGS analysis centers

With the development of real-time precise clock and orbit products, high-precision real-time ionospheric products have become one of the most critical resources for real-time single-frequency precise point positioning. Fortunately, there are several international GNSS service (IGS) analysis centers, e.g., UPC, WHU, and CAS, that are providing real-time global ionospheric maps (RT-GIMs). We evaluate these maps in detail over 2 years for different aspects. First, the RT-GIMs and 1-day predicted ionospheric products (C1PG GIM) differenced with the IGS final GIMs (IGSG GIM) are performed. Second, ionospheric vertical total electron content from Jason-2/3 data is set as a reference to evaluate the quality of RT-GIMs over oceanic regions. Third, 22 stations, which are not used in the generation of RT-GIMs, C1PG GIM, and IGSG GIM, are selected and the difference of slant total electron content (dSTEC) method is used to assess the accuracy and consistency of RT-GIMs over continental regions. Finally, the performance of RT-GIMs in the position domain is demonstrated based on SF-PPP solutions. The results show that the accuracy of the RT-GIMs is slightly worse than that of C1PG GIM and IGSG GIM. All RT-GIMs and the C1PG GIM have a smaller mean difference compared to the IGSG GIM by (−0.97, − 0.90, − 0.77, − 0.80) TECU for (UPC RT-GIM, CAS RT-GIM, WHU RT-GIM, C1PG GIM). Over oceanic regions, the RT-GIMs perform nearly the same as the C1PG GIM, but a slightly worse than IGSG GIM. The STDs are (3.96, 3.05, 3.25, 3.12, 2.54) TECU relative to Jason-2 and (4.94, 3.24, 3.38, 3.24, 2.65) TECU relative to Jason-3 for (UPC RT-GIM, CAS RT-GIM, WHU RT-GIM, C1PG GIM, IGSG GIM), respectively. Comparing with dSTEC values observed from the selected ground stations over continental regions, the RMS is (4.02, 2.16, 2.29, 1.86, 1.49) TECU for (UPC RT-GIM, CAS RT-GIM, WHU RT-GIM, C1PG GIM, IGSG GIM). In the position domain, the positioning accuracy of SF-PPP solution corrected by the RT-GIMs and C1PG GIM can reach decimeter level in the horizontal direction and meter level in the vertical direction, which is worse than obtained by IGSG GIM. Meanwhile, the positioning accuracy of SF-PPP corrected by RT-GIMs is almost the same as that obtained using C1PG GIM. For RT-GIMs, the accuracy of the CAS RT-GIM is slightly better than that of the other two RT-GIMs.

Least‐squares collocation modelling of regional ionospheric TEC for accelerating real‐time single‐frequency PPP convergence

Modelling of the regional ionospheric total electron content (TEC) is an important means for mitigating the ionospheric delay errors in the single-frequency (SF) precise point positioning (PPP). Mostly, the existing regional ionospheric models (RIM) only takes the trend term of the ionospheric TEC variations into account and neglect their random variable part. As a result, the TEC's irregular variations cannot be well modelled. In this study, a regional ionospheric TEC model based on the least-squares collocation (LSC) approach is proposed to account for both the trend and random parts. The predicted TEC from the LSC RIM is then employed in the real-time (RT) SF PPP for speeding up convergence. Datasets collected in two different latitude regions are utilised to establish the LSC RIM with a comparison to the conventional polynomial model and the global ionosphere map (GIM)-predicted products. The results show that the LSC model can remove ionospheric delay errors of at least 92%, which is larger than the polynomial model and GIM products. Further, the GPS RT SF PPP after introducing the predicted TEC from the LSC RIM can significantly reduce the convergence time by at least 48%, 58%, and 5% in the east, north, and up directions.

Real-Time Global Ionospheric Map and Its Application in Single-Frequency Positioning

The prevalence of real-time, low-cost, single-frequency, decimeter-level positioning has increased with the development of global navigation satellite systems (GNSSs). Ionospheric delay accounts for most errors in real-time single-frequency GNSS positioning. To eliminate ionospheric interference in real-time single-frequency precise point positioning (RT-SF-PPP), global ionospheric vertical total electron content (VTEC) product is designed in the next stage of the International GNSS Service (IGS) real-time service (RTS). In this study, real-time generation of a global ionospheric map (GIM) based on IGS RTS is proposed and assessed. There are three crucial steps in the process of generating a real-time global ionospheric map (RTGIM): estimating station differential code bias (DCB) using the precise point positioning (PPP) method, deriving slant total electron content (STEC) from PPP with raw observations, and modeling global vertical total electron content (VTEC). Experiments were carried out to validate the algorithm’s effectiveness. First, one month’s data from 16 globally distributed IGS stations were used to validate the performance of DCB estimation with the PPP method. Second, 30 IGS stations were used to verify the accuracy of static PPP with raw observations. Third, the modeling of residuals was assessed in high and quiet ionospheric activity periods. Afterwards, the quality of RTGIM products was assessed from two aspects: (1) comparison with the Center for Orbit Determination in Europe (CODE) global ionospheric map (GIM) products and (2) determination of the performance of RT-SF-PPP with the RTGIM. Experimental results show that DCB estimation using the PPP method can realize an average accuracy of 0.2 ns; static PPP with raw observations can achieve an accuracy of 0.7, 1.2, and 2.1 cm in the north, east, and up components, respectively. The average standard deviations (STDs) of the model residuals are 2.07 and 2.17 TEC units (TECU) for moderate and high ionospheric activity periods. Moreover, the average root-mean-square (RMS) error of RTGIM products is 2.4 TECU for the one-month moderate ionospheric period. Nevertheless, for the high ionospheric period, the RMS is greater than the RMS in the moderate period. A sub-meter-level horizontal accuracy and meter-level vertical accuracy can be achieved when the RTGIM is employed in RT-SF-PPP.

Quality assessment of CNES real-time ionospheric products

Real-time single-frequency precise point positioning (RT-SF-PPP) has become a desired positioning approach because it can achieve high positioning accuracy with a low-cost global navigation satelli...

Real-time single-frequency precise point positioning: accuracy assessment

The performance of real-time single-frequency precise point positioning is demonstrated in terms of position accuracy. This precise point positioning technique relies on predicted satellite orbits, predicted global ionospheric maps, and in particular on real-time satellite clock estimates. Results are presented using solely measurements from a user receiver on the L1-frequency (C1 and L1), for almost 3 months of data. The empirical standard deviations of the position errors in North and East directions are about 0.15 m, and in Up direction about 0.30 m. The 95% errors are about 0.30 m in the horizontal directions, and 0.65 m in the vertical. In addition, single-frequency results of six receivers located around the world are presented. This research reveals the current ultimate real-time single-frequency positioning performance. To put these results into perspective, a case study is performed, using a moderately priced receiver with a simple patch antenna.

Ionospheric Effect Mitigation for Real-Time Single-Frequency Precise Point Positioning

ABSTRACT: Precise Point Positioning (PPP) has received increased interest within the GPS community for a number of reasons: simplified field operation, cost-effectiveness, and no base station requirement. PPP with dual-frequency receivers and precise GPS products has demonstrated centimeter to decimeter positioning accuracy. Using real-time precise GPS products, this accuracy is also obtainable in a real-time mode. This paper investigates PPP using single-frequency GPS data which will be of interest to a broad range of applications because the majority of GPS users are using single-frequency GPS receivers. Since the ionospheric effect will be the biggest error source for single-frequency receiver based precise point positioning, different methods for ionospheric effect mitigation will be assessed and compared so that sub-meter positioning accuracy becomes obtainable.