Single-Frequency Precise Point Positioning Using Multi-Constellation GNSS: GPS, GLONASS, Galileo and BeiDou

The single-frequency precise point positioning (PPP) technique has attracted increasing attention due to its high accuracy and low cost. However, a very long convergence time, normally a few hours, is required in order to achieve a positioning accuracy level of a few centimeters. In this study, an approach is proposed to accelerate the single-frequency PPP convergence by combining quad-constellation global navigation satellite system (GNSS) and global ionospheric map (GIM) data. In this proposed approach, the GPS, GLONASS, BeiDou, and Galileo observations are directly used in an uncombined observation model and as a result the ionospheric and hardware delay (IHD) can be estimated together as a single unknown parameter. The IHD values acquired from the GIM product and the multi-GNSS differential code bias (DCB) product are then utilized as pseudo-observables of the IHD parameter in the observation model. A time varying weight scheme has also been proposed for the pseudo-observables to gradually decrease its contribution to the position solutions during the convergence period. To evaluate the proposed approach, datasets from twelve Multi-GNSS Experiment (MGEX) stations on seven consecutive days are processed and analyzed. The numerical results indicate that the single-frequency PPP with quad-constellation GNSS and GIM data are able to reduce the convergence time by 56%, 47%, 41% in the east, north, and up directions compared to the GPS-only single-frequency PPP.

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.

Investigating the contribution of BDS-3 observations to multi-GNSS single-frequency precise point positioning with different ionospheric models

Abstract. This paper introduces a newly developed model for both single and dual-frequency precise point positioning (PPP), which combines GPS and Galileo observables. As is well known, a drawback of a single GNSS system is the availability of sufficient number of visible satellites in urban areas. Combining GPS and Galileo systems offers more visible satellites to users, which is expected to enhance the satellite geometry and the overall positioning solution. However, combining GPS and Galileo observables introduces additional biases which require rigorous modelling, including the GPS to Galileo time offset (GGTO) and the inter-system bias. This research introduces a new ionosphere-free linear combination model for GPS/Galileo PPP, which accounts for the additional errors and biases. An additional unknown is introduced in the least-squares estimation model to account for the additional biases of the GPS/Galileo PPP solution. It is shown that a sub-decimeter level positioning accuracy and 20% reduction in the solution convergence time can be achieved with the newly developed GPS/Galileo PPP model.

Rapid convergence of precise point positioning (PPP) solutions to cm-level precision is a key factor for many applications. One means of accelerating this convergence is to exploit the benefit of information on the ionosphere. In order to preserve the integer nature of carrier-phase ambiguities in PPP, it is imperative that ionospheric corrections be provided with a set of compatible satellite phase biases. When using the decoupled-clock model, global ionospheric maps (GIMs) currently provided by the International GNSS Service are not directly applicable to PPP with ambiguity resolution. This paper describes a methodology for incorporating external ionospheric corrections into this model. It is shown that the use of both GIMs and ambiguity resolution can potentially reduce the convergence time of PPP to 10-cm horizontal accuracies from 30 to 4.5 minutes (68th percentile), while a regional network with inter-station spacing of 150 km can reach this threshold instantaneously under favorable ionospheric conditions. © 2014 Her Majesty the Queen in Right of Canada. NAVIGATION. © 2014 the Institute of Navigation.

The opening access of global navigation satellite system (GNSS) raw data in Android smart devices has led to numerous studies on precise point positioning on mobile phones, among which single-frequency precise point positioning (SF-PPP) has become popular because smartphone-based dual-frequency data still suffer from poor observational quality. As the ionospheric delay is a dominant factor in SF-PPP, we first evaluated two SF-PPP approaches with the MGEX (Multi-GNSS Experiment) stations, the Group and Phase Ionospheric Correction (GRAPHIC) approach and the uncombined approach, and then applied them to a Huawei P40 smartphone. For MGEX stations, both approaches achieved less than 0.1 m and 0.2 m accuracy in horizontal and vertical components, respectively. Uncombined SF-PPP manifested a significant decrease in the convergence time by 40.7%, 20.0%, and 13.8% in the east, north, and up components, respectively. For P40 data, the SF-PPP performance was analyzed using data collected with both a built-in antenna and an external geodetic antenna. The P40 data collected with the built-in antenna showed lower carrier-to-noise ratio (C/N0) values, and the pseudorange noise reached 0.67 m, which is about 67% larger than that with a geodetic antenna. Because the P40 pseudorange noise presented a strong correlation with C/N0, a C/N0-dependent weight model was constructed and used for the P40 data with the built-in antenna. The convergence of uncombined SF-PPP approach was faster than the GRAPHIC model for both the internal and external antenna datasets. The root mean square (RMS) errors for the uncombined SF-PPP solutions of P40 with an external antenna were 0.14 m, 0.15 m, and 0.33 m in the east, north, and up directions, respectively. In contrast, the P40 with an embedded antenna could only reach 0.72 m, 0.51 m, and 0.66 m, respectively, indicating severe positioning degradation due to antenna issues. The results indicate that the two SF-PPP models both can achieve sub-meter level positioning accuracy utilizing multi-GNSS single-frequency observations from mobile smartphones.

BDS (Beidou Navigation Satellite System) integrates the legacy PNT (Positioning, Navigation, Timing) service and the authorized SBAS (Satellite-Based Augmentation Services) service. To support the requirement of decimeter-level positioning, four types of differential corrections are developed in the BDS SBAS, including the State Space Representation (SSR)-based satellite orbit/clock corrections, the Observation Space Representation (OSR)-based ionospheric grid corrections, and the partition comprehensive corrections. In this study, we summarize the features of these differential corrections, including their definition and usages. The function model of precise point positioning (PPP) for dual- and single-frequency users using the four types of BDS SBAS corrections are proposed. Datasets are collected from 34 stations over one month in 2019, and PPP is performed for all the datasets. Results show that the root mean square (RMS) of the positioning errors for static/kinematic dual-frequency (DF) PPP are of 12 cm/16 cm in horizontal and 18 cm/20 cm in vertical component, while for single-frequency (SF) PPP are of 14 cm/32 cm and 22 cm/40 cm, respectively. With regard to the convergence performance, the horizontal and vertical positioning errors of kinematic DF-PPP can converge to 0.5 m in less than 15 min and 20 min, respectively. As for the kinematic SF-PPP, it could converge to 0.8 m in horizontal and 1.0 m in vertical within 30 min, where the ionosphere-constrained PPP performs better than the UofC PPP approach, owing to the contribution of the ionospheric grid corrections.

Temporal extrapolation of TEC using WNN during 2007–2018 and comparison against GIM, IRI2016 and Kriging

Precise point positioning (PPP) allows for centimeter- to decimeter-level positioning accuracy using a single global navigation satellite system (GNSS) receiver. However, the use of PPP is presently limited due to the time required for the solution to converge or re-converge to the expected accuracy, which typically requires about 30 minutes. This relatively long convergence time is essentially caused by the existing un-modeled GNSS residual errors. Additionally, in urban areas, the number of visible satellites is usually limited when a single satellite constellation is used, which in turn slows down the PPP solution convergence. This, however, can be overcome by combining the observations of two constellations, namely the GPS and Galileo systems. Unfortunately, combining the GPS and Galileo constellations, although enhances the satellite geometry, introduces additional biases that must be considered in the observation mathematical models. These include the GPS-to-Galileo time offset, and Galileo satellite and receiver hardware delays. In addition, the stochastic characteristics of the new Galileo E1 and E5a signals must be determined to a high degree of precision. This can be done by analyzing various sets of GPS and Galileo measurements collected at two stations with short separation. Several PPP models are developed in this dissertation, which combine GPS and Galileo observations in the un-differenced and between-satellite single-difference (BSSD) modes. These include the traditional un-differenced model, the decoupled clock model, the semi-decoupled clock model, and the between-satellite single-difference model. It is shown that the traditional un-differenced GPS/Galileo PPP model, the GPS decoupled clock model, and semi-decoupled clock GPS/Galileo PPP model improve the convergence time by about 25% in comparison with the un-differenced GPS-only PPP model. In addition, the semi-decoupled GPS/Galileo PPP model improves the solution precision by about 25% compared to the traditional un-differenced GPS/Galileo PPP model. Moreover, the BSSD GPS/Galileo PPP model improves the solution convergence time by about 50%, in comparison with the un-differenced GPS PPP model, regardless of the type of BSSD combination used. As well, the BSSD model improves the solution precision by about 50% and 25% when the BSSD loose and tight combinations are used, respectively, in comparison with the un-differenced GPS-only model.

<p>The vertical total electron content (VTEC) is one of the main quantities to describe the state of the ionosphere. To dispose this information is important to mass market Global Navigation Satellite System (GNSS) users to correct the ionospheric delay for positioning. The VTEC values and the corresponding standard deviations are routinely provided in the so-called Global Ionosphere Maps (GIM), with time intervals of 2, 1 and 0.25 hours on regular grids with 2.5º resolution in latitude and 5º resolution in longitude. To determine the ionospheric corrections from the GIMs for positioning applications, a quadratic interpolation is typically applied to the VTEC grid values which generally does not take into account the VTEC uncertainties. In this context, the impact of the use of the VTEC standard deviation is assessed in the positioning domain, considering the GIMs of two different analysis centers. The impact of the VTEC uncertainties is analyzed by means of single-frequency precise point positioning (PPP), applied to four Brazilian GNSS stations in different regions, considering four scenarios: geomagnetic storm, low solar flux and high solar flux (equinox and solstice). The use of the VTEC uncertainties values provided a significant improvement coinciding with high solar flux, especially for stations in regions under the most intense ionospheric effect, with mean rates of improvements up to 47%.</p>

The fast motion of low earth orbit (LEO) satellite contributes to the geometric diversity, allowing for rapid convergence of precise point positioning (PPP). In this contribution, we investigate the PPP performance of the LEO constellation-augmented full operational capability (FOC) multi-GNSS. We design six LEO constellations with different satellite numbers, orbit altitudes and orbit types, together with the FOC multi-GNSS constellations, and then simulate both the onboard LEO and ground-based observations. The multi-GNSS POD result shows much better orbit accuracy of 3.3, 2.7 and 2.6 cm in radial, along-track and cross-track components, respectively, compared with that of 10.3, 9.2 and 8.9 cm for GPS-only POD. Furthermore, the performance of LEO-augmented multi-GNSS PPP is evaluated. With the augmentation of 60-, 96-, 192- and 288-satellite LEO constellation, the multi-GNSS PPP convergence time can be shortened from 9.6 to 7.0, 3.2, 2.1 and 1.3 min, respectively, in midlatitude region. For LEO-augmented GPS- and BDS-only PPP, the improvement is more significant with the convergence time dramatically shortened by 90% from about 25 to within 3 min with 192- or 288-satellite constellation. The augmentation capability is also found to be associated with station latitude, and the higher latitude, the better performance. To enable about more than 70% significant reduction on convergence time, as well as considering the cost, the 192-satellite LEO constellation scheme is suggested. In terms of orbit altitude, the scheme of 1000 km presents better performance than that of 600 km. As for orbit type, the performances are comparable for polar and sun-synchronous orbits. Additionally, LEO-only PPP can be achieved with the convergence time of about 6.5 min.

The precise point positioning (PPP) is widely used as a typical representative of GNSS. But the main challenge of dual-frequency PPP is that it requires quite a long time to succeed in the ambiguity-fixed so it takes more than 30 min to obtain centimeter-level accuracy. A combination of GPS and low earth orbit (LEO) satellites can improve the diversity of available satellites' geometric distribution and reduce the correlation of observation data between epochs. Then the accuracy of float solution will be promoted and the ambiguity of GPS will take less time to get fixed. The purpose of this paper is to reduce the convergence time of PPP by the contribution of LEO satellites which have low earth orbit and move speedily. We adopt a free-ionosphere PPP model to combine GPS and LEO satellites. Numerous experimental results show that GPS/LEO PPP requires much less convergence time and gets higher positioning accuracy than that of PPP with GPS alone. In addition, an analysis is also made to compare GPS/LEO PPP and GPS/GLONASS PPP. The results indicate that GPS/LEO PPP also requires much less convergence time and gets higher positioning accuracy than that of GPS/GLONASS PPP when increasing the same number of available satellites. This proved that LEO satellites have more contribution to PPP performance than MEO.

Real-Time (RT) Precise Point Positioning (PPP) uses precise satellite orbits and clock corrections, and employs a separate receiver for positioning. With the growing demand, RT PPP is becoming an increasingly popular research topic. The ambiguity resolution (AR) can significantly improve the positioning accuracy and convergence time of PPP, so it is essential to study PPPAR in RT mode. In this paper, 37 MGEX stations from around the world are chosen, and the RT orbit, clock, and phase biases products broadcast by the Centre National d’Etudes Spatiales (CNES) are applied to PPPAR. Additionally, the residuals of the RT phase biases products, convergence time, and positioning accuracy are investigated. The results indicate that GPS products have the best quality of AR, with wide-lane (WL) and narrow-lane (NL) residuals of 98.9% and 95.3%, respectively, within ±0.25 cycles. Within ±0.25 cycles, the WL and NL residuals of the Galileo are 98.2% and 94.3%, respectively. Within ±0.25 cycles, the (Beidou Navigation Satellite System) BDS has a poor quality of AR, with WL and NL residuals of 97.3% and 73.1%, respectively. Due to the poor quality of the BDS AR, the convergence time of the BDS is not calculated in this paper. The convergence time of other systems is significantly reduced after AR processing, and the convergence time of the GPS/Galileo combination is the fastest, being 17.14 min in kinematic mode and only 11.85 min in static mode. The positioning accuracy of the GPS, Galileo, GPS/Galileo, and GPS/Galileo/BDS in the E and U directions is significantly improved after PPPAR.

Interplanetary coronal mass ejections (ICMEs) and the driven geomagnetic storms have a profound influence on the ionosphere, potentially leading to a degradation in positioning performance. In this study, we made a comprehensive analysis of the entire process of the impact of a typical ICME and its driven geomagnetic storm on the low-latitude ionosphere during March 13–14, 2022 (π-day storm) and the positioning performance of Global Navigation Satellite System (GNSS). During the passage of the ICME event, significant ionospheric scintillation, and TEC (total electron content) disturbances were observed in the low-latitude Hong Kong region. The ICME sheath region intensively compressed the magnetosphere via solar wind dynamic pressure enhancement and subsequently drove the storm main phase. It is found that both the magnetospheric compression that formed the storm initial phase and the storm main phase caused ionospheric scintillation. In comparison, the intensity of the ionospheric scintillation caused by the intense magnetospheric compression just before the storm main phase is even more pronounced. We also analyzed the impact of storms on standard point positioning (SPP), precise point positioning (PPP) and real-time kinematic (RTK) techniques. The positioning accuracies of single-frequency SPP and PPP experienced the most severe decline, and there was a noticeable increase in the initialization time for dual-frequency static PPP and RTK during the event. RTK demonstrated a shorter convergence time and higher accuracy during this event, but it was limited to short-baseline RTK (<30 km).

Performance assessment of real-time multi-GNSS integrated PPP with uncombined and ionospheric-free combined observables