The high-precision global navigation satellite system (GNSS) positioning technique on smartphones has been attracting increasing interest in recent years. However, the low-cost GNSS chip and linearly polarised antenna embedded inside smartphones result in data lack and quality degradation, which hinders the high-precision GNSS positioning on smartphones. In this study, a mixed single- and dual-frequency quad-constellation precise point positioning (MSDQ-PPP) model is proposed to improve the positioning performance on smartphones by taking advantage of all available GNSS observations. Static and kinematic tests were made using a Xiaomi Mi8 smartphone to fully assess the MSDQ-PPP performance with comparisons to single-frequency PPP (SF-PPP) and dual-frequency PPP (DF-PPP) models. The static test results show that the MSDQ-PPP can reach an accuracy level of 0⋅39 m and 0⋅50 m in the horizontal and vertical directions with a convergence time of less than 10 min in most sessions. The MSDQ-PPP improves the positioning accuracy by 53% and 31% over the DF-PPP in the horizontal and vertical directions, respectively. In contrast to the SF-PPP, the positioning accuracy and convergence time improvement can reach 62% and 90% in the horizontal direction, respectively. In the kinematic test, the MSDQ-PPP achieves an accuracy of 0⋅7 m and 1⋅5 m in the horizontal and vertical directions, respectively. The accuracy improvement rates reach 78% and 76% over the DF-PPP, and 13% and 38% over the SF-PPP, respectively. Both static and kinematic MSDQ-PPP tests indicate significantly enhanced positioning performance.

Following substantial progress achieved recently, the Galileo constellation provides a considerable satellite resource for the GNSS applications. In this regard, the performance assessment of real-time single-frequency precise positioning with Galileo satellites is the main objective of this research. For this purpose, several experimental tests were conducted in this study with two single-frequency positioning models, namely single-frequency code-based positioning and code-phase combination. The results show that Galileo presents an adequate number of visible satellites sufficient for single-frequency positioning. Also, the study demonstrates that, in comparison to GPS observations, Galileo observations have a significantly lower noise level. For the single-frequency code-based positioning, Galileo presents a better positioning accuracy than GPS by 25⋅8% on average. When compared with GPS, a 9⋅4% better positioning accuracy is acquired from Galileo for the single-frequency code-phase combination, with its average convergence time shorter than GPS by a ratio of 24⋅4%.

The single initial Global Positioning System (GPS) has been expanded into multiple global and regional navigation satellite systems (multi-GNSS/RNSS) as the Global Navigation Satellite System (GLONASS) is restored and the BeiDou Navigation Satellite System (BDS), Galileo Satellite Navigation System (Galileo) and Quasi-Zenith Satellite System (QZSS) evolve. Using the differences among these five systems, the paper constructs a consolidated multi-GNSS/RNSS precise point positioning (PPP) observation model. A large number of datasets from Multi-GNSS Experiment (MGEX) stations are employed to evaluate the PPP performance of multi-GNSS/RNSS. The paper draws three main conclusions based on the experimental results. (1) The combined GPS/GLONASS/Galileo/BDS/QZSS presents the PPP with the shortest mean convergence time of 11·5 min, followed by that of GPS/GLONASS/Galileo/BDS (12·4 min). (2) The combined GPS/GLONASS/BDS/Galileo/QZSS shows the optimal PPP performance when the cut-off elevation angle is basically the same because of the rich observation data due to a large number of satellites. To be specific, for combined GPS/GLONASS/BDS/Galileo/QZSS, the PPP convergence percentage is 80·9% higher relative to other combined systems under 35° cut-off elevation angle, and the percentages of the root mean square values of PPP within 0–5 cm are enhanced by 80·5%, 81·5% and 87·3% in the North, East and Up directions relative to GPS alone at 35° cut-off elevation angle. (3) GPS alone fails to conduct continuous positioning due to the insufficiency of visible satellites at 40° cut-off elevation angle, while the kinematic PPP of multi-GNSS/RNSS remains capable of obtaining positioning solutions with relatively high accuracy, especially in the horizontal direction.

Precise positioning with low-cost single-frequency global navigation satellite system (GNSS) receivers has great potential in a wide range of applications because of its low price and improved accuracy. However, challenges remain in achieving reliable and accurate solutions using low-cost receivers. For instance, the successful ambiguity fixing rate could be low for real-time kinematic (RTK) while large errors may occur in precise point positioning (PPP) in some scenarios (e.g., trees along the road). To solve the problems, this paper proposes a method with the aid of additional lane-level digital map information to improve the accuracy and reliability of RTK and PPP solutions. In the method, a digital camera will be applied for lane recognition and the positioning solution from a low-cost receiver will be projected to the digital map lane link. With the projected point position as a constraint, the RTK ambiguity fixing rate and PPP performance can be enhanced. A field kinematic test was conducted to verify the improvement of the RTK and PPP solutions with the aid of map matching. The results show that the RTK ambiguity fixing rate can be increased and the PPP positioning error can be reduced by map matching.

Seafloor geodetic studies such as Global Positioning System (GPS)-Acoustic experiments often require the measurement platform on the sea surface to be positioned accurately to within a few centimetres. In this paper, we test the utility of Precise Point Positioning (PPP) for this application with two experiments. The first fixed platform experiment is a comparison between three independent processing software packages: Positioning and Navigation Data Analyst (PANDA), Global Navigation Satellite System-Inferred Positioning System and Orbit Analysis Simulation Software (GIPSY-OASIS), and the Canadian Spatial Reference System (CSRS)) and a more accurate solution based on conventional differential processing of a remote GPS station in the Aleutian Islands. The second moving platform experiment is a comparison among the three PPP software packages using 40 hours of ship navigation data collected during the Roger Revelle RR1605 cruise 170 nautical miles southwest of Palau in May 2016. We found the PPP solutions were repeatable to 5·49 cm in the horizontal components and 12·4 cm in the vertical component. This demonstrates not only that PPP is a useful tool for positioning marine platforms in remote locations, but also that modern ship navigation instruments such as the Kongsberg Seapath 330 + are suitable for seafloor geodetic application.

Real-time Precise Point Positioning (PPP) has been evolved as a cost-effective technique for highly precise maritime positioning. For a long period, maritime PPP technology has mainly relied on the Global Positioning System (GPS). With the revitalisation of GLONASS and the emerging BeiDou navigation satellite system (BDS), it is now feasible to investigate real-time navigation performance of multi-constellation maritime PPP with GPS, BDS and GLONASS. In this contribution, we focus on maritime PPP performance using real world maritime kinematic data and real-time satellite correction products. The results show that BDS has lower position accuracy and slower convergence time than GPS. The BDS and GPS combination has the best performance among the dual-constellation configurations. Meanwhile, the integration of BDS, GLONASS and GPS significantly improves the position accuracy and the convergence time. Some outliers in the single constellation configuration can be mitigated when multi-constellation observations are utilised.

With the evolving Global Navigation Satellite System (GNSS) landscape, the International GNSS Service (IGS) has started the Multi-GNSS Experiment (MGEX) to produce precise products for new generation systems. Various analysis centres are working on the estimation of precise orbits, clocks and bias for Galileo, Beidou and Quasi-Zenith Satellite System (QZSS) satellites. However, at the moment these products can only be used for post-processing applications. Indeed, the IGS Real-Time service only broadcasts Global Positioning System (GPS) and Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS) corrections. In this research, a simulator of multi-GNSS observations and real-time precise products has been developed to analyse the performance of GPS-only, Galileo-only and GPS plus Galileo Precise Point Positioning (PPP). The error models in the simulated orbits and clocks were based on the difference between the GPS Real-Time and the Final products. Multiple scenarios were analysed, considering different signals combined in the Ionosphere Free linear combination. Results in a simulated open area environment show better performance of the Galileo-only case over the GPS-only case. Indeed, up 33% and 29% of improvement, respectively, in the accuracy level and convergence time can be observed when using the full Galileo constellation compared to GPS. The dual constellation case provides good improvements, in particular in the convergence time (47% faster than GPS). This paper will also consider the impact of different linear combinations of the Galileo signals, and the potential of the E5 Alternative Binary Offset Carrier (AltBOC) signal. Even though it is significantly more precise than E5a, the PPP performance obtained with the Galileo E1-E5a combination is either better or similar to the one with Galileo E1-E5. The reason for this inconsistency was found in the use of the ionosphere free combination with E1. Finally, alternative methods of ionosphere error mitigation are considered in order to ensure the best possible positioning performance from the Galileo E5 signal in multi-frequency PPP.

This paper considers the effect of the biases in Global Positioning System (GPS) observations on satellite clock offset estimation. GPS triple-frequency satellite clock and reference observations are discussed. When the reference observation is selected and the corresponding satellite clock offset is computed, satellite clock offsets for all observations are obtained based on the computed satellite clock offset and the biases between the reference observation and other observations. The characteristics of these biases are analysed, and a service strategy for the GPS triple-frequency satellite clock offset is presented. To evaluate the computed GPS satellite clock offset, the performance in single-point positioning is validated. The positioning results show that the average relative improvements are about 20%, 28% and 19% for north, east and vertical components, when the Differential Code Bias (DCB) (P1-P2), DCB (P1-P5) and modelled Inter-Frequency Clock Bias (IFCB) are corrected. The effect of DCB (P1-P2), DCB (P1-P5) and modelled IFCB on the altitude direction is more evident than on the horizontal directions.

The BeiDou navigation satellite system (BDS) has been providing a regional service in the Asia–Pacific area since 27 December 2012, and a new Inclined Geosynchronous Satellite Orbit (IGSO) satellite IGSO-6 joined the 14-satellite constellation in operation on 29 March 2016. In this paper, the signal and positioning performance of IGSO-6 are assessed. Compared with other IGSOs, the carrier-to-noise-density ratios of IGSO-6 show comparable performance for the B3 signal and a lower power level for the B2 signal, while the B1 signal is more powerful and has the lowest noise and multipath errors. The satellite-induced code bias of IGSO-6 was investigated and indicates that IGSO-6 has similar characteristics to other IGSOs. The different inter-frequency bias variations among IGSOs with daily periodicity are demonstrated. The BDS positioning performances with IGSO-6 were investigated in Single Point Positioning (SPP) and Precise Point Positioning (PPP) modes at the 95% confidence level. For SPP, there was an improvement of about 4·9% and 3·6% in the horizontal and vertical components, respectively. The convergence time was improved by about 18·3% and 17·8% in the horizontal and vertical components for positioning accuracy to be better than 50 cm, respectively.

To meet the requirements of different applications, the International Global Navigation Satellite System (GNSS) Service (IGS) has provided Global Positioning System (GPS) satellite ephemerides and clock products with different accuracy levels (final, rapid and ultra-rapid products). Comparison of Precise Point Positioning/Inertial Navigation System/Ultra Wideband (PPP/INS/UWB) tightly coupled positioning with different precise satellite ephemeris and clock products is made and corresponding data analysis is provided. Final, rapid and ultra-rapid products are applied in a PPP/INS/UWB integrated system. The field trajectories, position and velocity errors of the integrated system with different products are compared. The results indicate that PPP/INS/UWB tightly coupled positioning with final and rapid products achieves an accurate performance. Compared with the position resolution using final products, the position accuracy with the ultra-rapid products (observed half) is slightly reduced and the position accuracy with the ultra-rapid products (predicted half) has a 0·1–0·2 m reduction. The influence of precise satellite ephemeris and clock products is very minor for non-real-time positioning, relative to the accuracy of PPP/INS/UWB tightly coupled positioning.

After Global Navigation Satellite Systems (GNSS) were first used in the field of hydrography in 1980, developments in hydrographic surveying accelerated. Survey precision in hydrography has been improved for both horizontal and vertical positioning and seafloor acoustic measurement by means of these new developments. Differential Global Positioning System (DGPS), Real Time Kinematic (RTK) and Network RTK (NRTK) techniques are the satellite-based positioning techniques that are commonly used in shallow water surveys and shoreline measurements. In line with these developments, the newer Precise Point Positioning (PPP) has been introduced. Combining precise satellite positions and clocks with dual-frequency GNSS data, PPP can provide position solutions from the centimetre to decimetre level. In this study, the coordinates of control points were determined by using the Post-Process PPP (PP-PPP) technique. Seven test points, which are the points of the Continuously Operating Reference Station - Turkey (CORS-TR) network, are selected near the shorelines within Turkey. The 24-hour data was split from one to six hours by one hour periods. Automatic Point Positioning Service (APPS) was selected to process the data. The poisoning error of the test points were given and compared with International Hydrographic Organization (IHO) S44 hydrographic survey standards.

In view that most Global Navigation Satellite System (GNSS) users are still using single-frequency receivers due to the low costs, single-frequency Precise Point Positioning (PPP) has been attracting increasing attention in the GNSS community. For a long period, single-frequency PPP technology has mainly relied on the Global Positioning System (GPS). With the recent revitalisation of the Russian GLONASS constellation and two newly emerging constellations, BeiDou and Galileo, it is now feasible to investigate the performance of Four-Constellation integrated Single-Frequency PPP (FCSF-PPP) with GPS, GLONASS, BeiDou and Galileo measurements. In this study, a FCSF-PPP model is presented to simultaneously process observations from all four GNSS constellations. Datasets collected at 47 globally distributed four-system Multi-GNSS Experiment (MGEX) stations on seven consecutive days and a kinematic experimental dataset are employed to fully assess the performance of FCSF-PPP. The FCSF-PPP solutions are compared to GPS-only and combined GPS/GLONASS single-frequency PPP solutions. The results indicate that the positioning performance is significantly improved by integrating multi-constellation signals.

Precise Point Positioning (PPP) performance is improving under the ongoing Global Positioning System (GPS) modernisation program. The availability of the third frequency, L5, enables triple-frequency combinations. However, to utilise the modernised L5 signal along with the existing GPS signals, P1-C5 differential code bias must be determined. In this paper, the global network of Multi-Global Navigation Satellite System Experiment (MGEX) stations was used to estimate P1-C5 satellites differential code biases $(DCB_{P1 - C5}^S )$. Mathematical background for triple-frequency linear combinations was provided along with the resultant noise and ionosphere amplification factors. Nine triple-frequency linear combinations were chosen, based on different criteria, for processing the modernised L5 signal along with the legacy GPS signals. Finally, test results using real GPS data from ten MGEX stations were provided showing the benefits of the availability of the third frequency on PPP solution convergence time and the precision of the estimated parameters. It was shown that triple-frequency combinations could improve the PPP convergence time and the precision of the estimated parameters by about 10%. These results are considered promising for using the modernised GPS signals for precise positioning applications especially when the fully modernised GPS constellation is available.

The complementary advantages of high-rate Global Positioning System (GPS) and accelerometer observations for measuring seismic ground motion have been recognised in previous research. Here we propose an approach of tight integration of GPS and accelerometer measurements. The baseline shifts of the accelerometer are introduced as unknown parameters and estimated by a random walk process in the Precise Point Positioning (PPP) solution. To demonstrate the performance of the new strategy, we carried out several experiments using collocated GPS and accelerometer. The experimental results show that the baseline shifts of the accelerometer are automatically corrected, and high precision coseismic information of strong ground motion can be obtained in real-time. Additionally, the convergence and precision of the PPP is improved by the combined solution.

On 27 December 2012 it was announced officially that the Chinese Navigation Satellite System BeiDou (BDS) was able to provide operational services over the Asia-Pacific region. The quality of BDS observations was confirmed as comparable with those of GPS, and relative positioning in static and kinematic modes were also demonstrated to be very promising. As Precise Point Positioning (PPP) technology is widely recognized as a method of precise positioning service, especially in real-time, in this contribution we concentrate on the PPP performance using BDS data only. BDS PPP in static, kinematic and simulated real-time kinematic mode is carried out for a regional network with six stations equipped with GPS- and BDS-capable receivers, using precise satellite orbits and clocks estimated from a global BDS tracking network. To validate the derived positions and trajectories, they are compared to the daily PPP solution using GPS data. The assessment confirms that the performance of BDS PPP is very comparable with GPS in terms of both convergence time and accuracy.

Recent developments in GPS positioning show that a user with a standalone GPS receiver can obtain positioning accuracy comparable to that of carrier-phase-based differential positioning. Such technique is commonly known as Precise Point Positioning (PPP). A significant challenge of PPP, however, is that about 30 minutes or more is required to achieve centimetre to decimetre-level accuracy. This relatively long convergence time is a result of the un-modelled GPS residual errors. A major residual error component, which affects the convergence of PPP solution, is higher-order Ionospheric Delay (IONO). In this paper, we rigorously model the second-order IONO, which represents the bulk of higher-order IONO, for PPP applications. Firstly, raw GPS measurements from a global cluster of International GNSS Service (IGS) stations are corrected for the effect of second-order IONO. The corrected data sets are then used as input to the Bernese GPS software to estimate the precise orbit, satellite clock corrections, and Global Ionospheric Maps (GIMs). It is shown that the effect of second-order IONO on GPS satellite orbit ranges from 1·5 to 24·7 mm in radial, 2·7 to 18·6 mm in along-track, and 3·2 to 15·9 mm in cross-track directions, respectively. GPS satellite clock corrections, on the other hand, showed a difference of up to 0·067 ns. GIMs showed a difference up to 4·28 Total Electron Content Units (TECU) in the absolute sense and an improvement of about 11% in the Root Mean Square (RMS). The estimated precise orbit clock corrections have been used in all of our PPP trials. NRCan's GPSPace software was modified to accept the second-order ionospheric corrections. To examine the effect of the second-order IONO on the PPP solution, new data sets from several IGS stations were processed using the modified GPSPace software. It is shown that accounting for the second-order IONO improved the PPP solution convergence time by about 15% and improved the accuracy estimation by 3 mm.

GPS applications such as Precise Point Positioning (PPP) require the availability of precise ephemeris at high rate. To support these applications, several institutions such as the International GNSS Service (IGS) have developed precise orbital service. Unfortunately, however, the data rate of such precise orbits is usually limited to 15 minutes. To overcome this problem, a number of orbital interpolation methods are proposed. This paper examines the performance of four interpolation methods for IGS precise GPS orbits, namely Lagrange, Newton Divided Difference, Cubic Spline and Trigonometric interpolation. In addition, the paper discusses a new approach, which utilizes the residuals between the broadcast and precise ephemeris to generate a high density precise ephemeris. It is shown that the new approach produces better results than previously reported orbital interpolation accuracy.