This paper presents an investigation of the precise point positioning (PPP) performance of a combined solution from BDS-2 and BDS-3 satellites. To simultaneously process different BDS signal observations, i.e., B1/B1C, B2/B2a and B3C, undifferenced and uncombined observations with ionosphere delay constrained by the deterministic plus stochastic ionosphere model are used in the basic model. Special attention is paid to code bias and receiver clock parameters in the derivation of the observation model. The analysis is carried out using more than one-month data for BDS-2 and BDS-3 collected at the CANB, DWIN, KNDY and PETH stations in the Asia-Pacific region. The results suggest that compared with BDS-2 alone, the BDS-2 and BDS-3 solution provides significantly more accurate PPP, with increases of 28%, 21% and 5% in the up, north and east directions, respectively. In addition, the average root mean square error decreases to 0·21, 0·13 and 0·16 m for the three directions. Furthermore, the PPP convergence time for BDS-2 and BDS-3 is about 1·5 h and less than 1 h for the horizontal and vertical components, respectively, whereas that for BDS-2 alone is about 2·3 h for both directions.

Airborne-Pseudolite (A-PL) systems have been proposed to augment Global Navigation Satellite Systems (GNSSs) in difficult areas where GNSS-only navigation cannot be guaranteed due to signal blockages, signal jamming, etc. One of the challenges in realising such a system is to determine the coordinates of the A-PLs to a high accuracy. The GNSS Precise Point Positioning (PPP) technique is a possible alternative to differential GNSS techniques such as those that generate Real-Time Kinematic (RTK) solutions. To enhance the A-PL positioning performance in GNSS challenged areas, it is assumed that inter-PL range measurements are also used in addition to GNSS measurements. When processing these new measurements, cross-correlations among A-PL estimated states introduced during measurement updates need to be accounted for so as to obtain consistent estimated states. In this paper, a distributed algorithm based on a Split Covariance Intersection Filter (SCIF) is proposed. Three commonly used means of implementing the SCIF algorithm are analysed. Another challenge is that real-time GNSS PPP relies on the use of precise satellite orbit and clock information. One problem is that these real-time orbit and satellite clock error corrections may not be always available, especially for moving A-PLs in challenging environments when signal outages occur. To maintain A-PL positioning accuracy using GNSS PPP, it is necessary to predict these error corrections during outages. Different prediction models for orbit and clock error corrections are discussed. A test was conducted to evaluate the A-PL positioning based on GNSS PPP and inter-PL ranges, as well as the performance of error prediction modelling. It was found that GNSS PPP combined with inter-PL ranges could achieve better converged positioning accuracy and a reduction in convergence time of GNSS PPP. However, the performance of GNSS PPP with inter-PL ranges was degraded by observing A-PLs with limited positioning accuracy. Although the performance improvement achieved by the SCIF-based distributed algorithms was smaller than that by the centralised algorithm, greater robustness in dealing with deteriorated observed A-PLs' trajectory data was demonstrated by the distributed algorithms. In addition, short-term prediction models were analysed, and their performance was shown to reduce the effect of error correction outages on A-PL positioning accuracy.

Tropospheric delay is one of the main error sources in Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP). Zenith Hydrostatic Delay (ZHD) accounts for 90% of the total delay. This research focuses on the improvements of ZHD from tropospheric models and real meteorological data on the PPP solution. Multi-GNSS PPP experiments are conducted using the datasets collected at Multi-GNSS Experiments (MGEX) network stations. The results show that the positioning accuracy of different GNSS PPP solutions using the meteorological data for ZHD correction can achieve an accuracy level of several millimetres. The average convergence time of a PPP solution for the BeiDou System (BDS), the Global Positioning System (GPS), Global Navigation Satellite System of Russia (GLONASS), BDS+GPS, and BDS+GPS+GLONASS+Galileo are 55·89 min, 25·88 min, 33·30 min, 20·50 min and 15·71 min, respectively. The results also show that atmospheric parameters provided by real meteorological data have little effect on the horizontal components of positioning compared to the meteorological model, while in the vertical component, the positioning accuracy is improved by 90·6%, 33·0%, 22·2% and 19·8% compared with the standard atmospheric model, University of New Brunswick (UNB3m) model, Global Pressure and Temperature (GPT) model, and Global Pressure and Temperature-2 (GPT2) model and the convergence times are decreased 51·2%, 32·8%, 32·5%, and 32·3%, respectively.

Real-time Precise Point Positioning (PPP) relies on the use of accurate satellite orbit and clock corrections. If these corrections contain large errors or faults, either from the system or by meaconing, they will adversely affect positioning. Therefore, such faults have to be detected and excluded. In traditional PPP, measurements that have faulty corrections are typically excluded as they are merged together. In this contribution, a new PPP model that encompasses the orbit and clock corrections as quasi-observations is presented such that they undergo the fault detection and exclusion process separate from the observations. This enables the use of measurements that have faulty corrections along with predicted values of these corrections in place of the excluded ones. Moreover, the proposed approach allows for inclusion of the complete stochastic information of the corrections. To facilitate modelling of the orbit and clock corrections as quasi-observations, International Global Navigation Satellite System Service (IGS) real-time corrections were characterised over a six-month period. The proposed method is validated and its benefits are demonstrated at two sites using three days of data.

This paper presents the findings of a literature review on public private partnerships (PPPs) in two sectors – education and health – in Africa, Asia and Latin America. It highlights the heterogeneity of the category within and across sectors and shows that the key predictions of the PPP doctrine – cost-efficiency for improved social service delivery to the poor – are hardly fulfilled in practice. Moreover, PPPs – both as policy model and practical arrangements – are underpinned by a narrow conception of education and health, which denies their broader embeddedness within the economy and society. The paper identifies theoretical and methodological limitations of the existing scholarship. It underlines the scarcity of data on the corporate sector and, more broadly, about the economics of education and health PPPs. It also stresses the little attention paid to the beneficiaries. The paper finally calls for further research to open up the ‘black box’ of PPPs.

The integration of Precise Point Positioning (PPP) with Inertial Navigation Systems (INS) has been very intensively developed and widely applied in multiple areas. The integrated navigation system is able to provide high accuracy position and attitude with a single receiver. However, the cycle slip caused by high dynamics, signal lock and low satellite elevation will decrease accuracy and degrade the system performance. In this paper, an inertial aided cycle slip detection and repair method is applied in PPP/INS tightly coupled navigation to obtain higher accuracy navigation information. The inertial information is introduced to the wide-lane combination observation to avoid the noise and multipath from pseudorange. Detail error analysis is given to determine the critical value of INS position accuracy which makes inertial aided wide-lane combination have better performance and a new decision variable is constructed. The inertial aided cycle slip detection and repair scheme that replaces the ambiguity re-initialisation is applied in PPP. An experiment was performed to validate the new algorithm. The results indicate that the inertial aided decision variable has higher accuracy than the traditional Melbourne-Wübbena decision variable. The inertial aided scheme can efficiently detect and repair the small cycle slip (from 1 to 6) and large cycle slip (from 10 to 20). The inertial-aided cycle slip detection method introduced in PPP resolution will remove the error by ambiguity re-initialisation.

Recently, the International Global Navigation Satellite System (GNSS) Service (IGS) has launched the Real-Time Service (IGS-RTS). The RTS products enable real-time precise positioning applications. For single-frequency Real-Time Precise Point Positioning (RT-PPP), ionospheric delay mitigation is a major challenge. To overcome this challenge, we developed a Real-Time Regional Ionospheric Model (RT-RIM) over Europe using the RTS satellite orbits and clock products. The model has spatial and temporal resolution of 1° × 1° and 15 minutes, respectively. Global Positioning System (GPS) observations from 60 IGS and EUREF reference stations are processed using the Bernese 5·2 PPP module in order to extract the Real-Time Vertical Electron Content (RT-VTEC). The PPP convergence time and positioning accuracy using the RTS products is estimated and compared with dual frequency PPP and single-frequency PPP obtained through the combined rapid IGS Global Ionospheric Maps (IGS-GIM) over three consecutive days under high solar activity and one of them under active geomagnetic activity. The results show that the proposed model improves PPP accuracy and convergence time under the mid-latitude region about 40%, 55% and 40% for the horizontal, height and three-dimensional (3D) components respectively in comparison with the IGS-GIM.

This paper presents a new algorithm to accelerate Precise Point Positioning (PPP) convergence. The main idea is to consider the station tropospheric zenith total delay, which is obtained by a global zenith troposphere delay estimate model, as virtual observation and combine it with phase and pseudo-range observations to formulate observation equations. Without relying on any other external enhancement information, it only requires four satellites to quickly complete the positioning with centimetre-level accuracy. Compared with the conventional method, the new one brings about 15% improvement in convergence time.

This study investigates the accuracy of an online Precise Point Positioning (PPP) service operated by the Geodetic Survey Division of Natural Resources Canada (NRCan), Canadian Spatial Reference System (CSRS)-PPP, by using single/dual-frequency Global Positioning System (GPS) data collected by dual-frequency geodetic-grade and Original Equipment Manufacturer (OEM) board type single-frequency GPS receivers. In this work, a kinematic test was carried out in Halic Bay (Golden Horn), Istanbul, Turkey, to assess the performance of the PPP method in a dynamic environment. Based on this study, it can be concluded that the coordinates estimated from the online CSRS-PPP service have a potential of about metre-level accuracy by processing single frequency data collected by an OEM receiver and about a decimetre to a few centimetres level accuracy by processing dual frequency data collected by a geodetic-grade receiver. In general, results show that the PPP technique has become a significant alternative to the conventional relative (differential) positioning techniques (i.e., Differential GPS (DGPS), Real-time Kinematic (RTK)). The technique does not suffer from the drawbacks of the DGPS technique and has potential to provide the same position accuracy without the requirement for a reference station. Consequently, it has been concluded that the PPP technique may be effectively used in marine applications due to its ease of use and provision of high accuracy, as well as being able to offer reduced field operational costs.

The Precise Point Positioning (PPP) concept enables centimetre-level positioning accuracy by employing one Global Navigation Satellite System (GNSS) receiver. The main advantage of PPP over conventional Real Time Kinematic (cRTK) methods is that a local reference network infrastructure is not required. Only a global reference network with approximately 50 stations is needed because reference GNSS data is required for generating precise error correction products for PPP. However, the current implementation of PPP is not suitable for some applications due to the long time period (i.e. convergence time of up to 60 minutes) required to obtain an accurate position solution. This paper presents a new method to reduce the time required for initial integer ambiguity resolution and to improve position accuracy. It is based on combining GPS and GLONASS measurements to calculate the float ambiguity positioning solution initially, followed by the resolution of GPS integer ambiguities.

The results show that using the GPS/GLONASS float solution can, on average, reduce the time to initial GPS ambiguity resolution by approximately 5% compared to using the GPS float solution alone. In addition, average vertical and horizontal positioning errors at the initial ambiguity resolution epoch can be reduced by approximately 17% and 4%, respectively.

The determination of the correct integer number of carrier cycles (integer ambiguity) is the key to high accuracy positioning with carrier phase measurements from Global Navigation Satellite Systems (GNSS). There are a number of current methods for resolving ambiguities including the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method, which is a combination of least-squares and a transformation to reduce the search space. The current techniques to determine the level of confidence (integrity) of the resolved ambiguities (i.e. ambiguity validation), usually involve the construction of test statistics, characterisation of their distribution and definition of thresholds. Example tests applied include ratio, F-distribution, t-distribution and Chi-square distribution. However, the assumptions that underpin these tests have weaknesses. These include the application of a fixed threshold for all scenarios, and therefore, not always able to provide an acceptable integrity level in the computed ambiguities. A relatively recent technique referred to as Integer Aperture (IA) based on the ratio test with a large number of simulated samples of float ambiguities requires significant computational resources. This precludes the application of IA in real time.

This paper proposes and demonstrates the power of an integrity monitoring technique that is applied at the ambiguity resolution and positioning stages. The technique has the important benefit of facilitating early detection of any potential threat to the position solution, originating in the ambiguity space, while at the same time giving overall protection in the position domain based on the required navigation performance. The proposed method uses the conventional test statistic for ratio testing together with a doubly non-central F distribution to compute the level of confidence (integrity) of the ambiguities. Specifically, this is determined as a function of geometry and the ambiguity residuals from least squares based ambiguity resolution algorithms including LAMBDA. A numerical method is implemented to compute the level of confidence in real time.

The results for Precise Point Positioning (PPP) with simulated and real data demonstrate the power and efficiency of the proposed method in monitoring both the integrity of the ambiguity computation and position solution processes. Furthermore, due to the fact that the method only requires information from least squares based ambiguity resolution algorithms, it is easily transferable to conventional Real Time Kinematic (RTK) positioning.

This paper integrates a traditional Dornbusch overshooting model with a macro-economic model of hysteresis in foreign trade. We apply an approach which allows an aggregation of heterogeneous agents and which results in a continuous macroeconomic hysteresis-loop. In our model, short-run exchange rate overshooting generates a persistent current account effect, which feeds back into the exchange rate process and ultimately results in changes of the long-run equilibrium exchange rate. Monetary shocks can lead to hysteresis in both foreign trade and exchange rate processes, invalidating the long-run neutrality of money hypothesis and the purchasing power parity assumption of the conventional overshooting model.