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Global navigation satellite systems (GNSS) can attain centimeter level positioning accuracy, which is conventionally provided by real-time precise point positioning (PPP) and real-time kinematic (RTK) techniques. Corrections from the data center or the reference stations are required in these techniques to reduce various GNSS errors. The time-relative positioning approach differs from the traditional PPP and RTK in the sense that it does not require external real-time corrections. It computes the differences in positions of a single receiver at different epochs using phase observations. As the code observations are not used in this approach, its performance is not affected by the noise and multipath of code observations. High reliability is another advantage of time-relative precise positioning because the ambiguity resolution is not needed in this approach. Since the data link is not required in the method, this approach has been widely used in remote areas where wireless data link is not available. The main limitation of time-relative positioning is that its accuracy degrades over time between epochs because of the temporal variation of various errors. The application of the approach is usually limited to be within a time interval of less than 20 min. The purpose of this study was to increase the time interval of time-relative positioning and to extend the use of this method to applications with a longer time requirement, especially in remote areas without wireless communication. In this paper, the main error sources of the time-relative method are first analyzed in detail, and then the approach to improve the accumulated time relative positioning method is proposed. The performance of the proposed method is assessed using both static and dynamic observations with a duration as long as several hours. The experiments presented in this paper show that, among the four scenarios tested (i.e., GPS, GPS/Galileo, GPS/Galileo/BeiDou, and GPS/Galileo/BeiDou/GLONASS), GPS/Galileo/BeiDou performed best and GPS/Galileo/BeiDou/GLONASS performed worst. The maximum positioning errors were mostly within 0.5 m in the horizontal direction, even after three hours with GPS/Galileo/BeiDou. It is expected that the method could be used for positioning and navigation for as long as several hours with decimeter level horizontal accuracy in remote areas without wireless communication.

The high precision positioning can be easily achieved by using real-time kinematic (RTK) and precise point positioning (PPP) or their augmented techniques, such as network RTK (NRTK) and PPP-RTK, even if they also have their own shortfalls. A reference station and datalink are required for RTK or NRTK. Though the PPP technique can provide high accuracy position data, it needs an initialisation time of 10-30 min. The time-relative positioning method estimates the difference between positions at two epochs by means of a single receiver, which can overcome these issues within short period to some degree. The positioning error significantly increases for long-period precise positioning as consequence of the variation of various errors in GNSS (Global Navigation Satellite System) measurements over time. Furthermore, the accuracy of traditional time-relative positioning is very sensitive to the initial positioning error. In order to overcome these issues, an improved time-relative positioning algorithm is proposed in this paper. The improved time-relative positioning method employs PPP model to estimate the parameters of current epoch including position vector, float ionosphere-free (IF) ambiguities, so that these estimated float IF ambiguities are used as a constraint of the base epoch. Thus, the position of the base epoch can be estimated by means of a robust Kalman filter, so that the position of the current epoch with reference to the base epoch can be obtained by differencing the position vectors between the base epoch and the current one. The numerical results obtained during static and dynamic tests show that the proposed positioning algorithm can achieve a positioning accuracy of a few centimetres in one hour. As expected, the positioning accuracy is highly improved by combining GPS, BeiDou and Galileo as a consequence of a higher amount of used satellites and a more uniform geometrical distribution of the satellites themselves. Furthermore, the positioning accuracy achieved by using the positioning algorithm here described is not affected by the initial positioning error, because there is no approximation similar to that of the traditional time-relative positioning. The improved time-relative positioning method can be used to provide long-period high precision positioning by using a single dual-frequency (L1/L2) satellite receiver.

One's position has become an important piece of information for our everyday lives in a smart city. Currently, a position can be obtained easily using smartphones that is equipped with low-cost Global Navigation Satellite System (GNSS) chipsets with accuracy varying from 5 m to 10 m. Differential GNSS (DGNSS) is an efficient technology that removes the majority of GNSS errors with the aid of reference stations installed at known locations. The sub-meter accuracy can be achieved when applying the DGNSS technology on the advanced receivers. In 2016, Android has opened the accesses of raw GNSS measurements to developers. However, most of the mid and low-end smartphones only provide the data using the National Marine Electronics Association (NMEA) protocol. They do not provide the raw measurements, and thus do not support the DGNSS operation either. We proposed a DGNSS infrastructure that correct the standalone GNSS position of smartphones using the corrections from the reference station. In the infrastructure, the position correction is generated considering the GNSS satellite IDs that contribute to the standalone solution in smartphones, and the position obtained is equivalent to the solution of using the range-domain correction directly. To serve a large number of smartphone users, a Client/Server architecture is developed to cope with a mass of DGNSS positioning requests efficiently. The comparison of the proposed infrastructure against the ground truth, for all field tests in open areas, showed that the infrastructure achieves the horizontal positioning accuracy better than 2 m. The improvement in accuracy can reach more than 50% for the test in the afternoon. The infrastructure brings benefits to applications that require more accuracy without requiring any hardware modifications., Competing Interests: The authors declare no conflict of interest.

The Chinese BeiDou Navigation Satellite System (BDS) has been an important constitute of the Global Navigation Satellite System (GNSS), and the combination of GPS and BDS shows significant improvements when compared with single GPS system for real-time kinematic (RTK) positioning, and improves on availability and fixing rates, especially in the East Asian area. While network RTK might have different types of receivers, both for global and regional networks, different types of receiver may adopt different internal multipath mitigation methods and other techniques that result in different pseudorange characteristics, especially for a multipath. Then, the performance of wide-lane ambiguity resolution (WL AR) is affected. In this study, we first analyze and compare the characteristics of BDS dual-frequency observations for different types of receivers, including Trimble, Leica, Javad, and Septentrio, based on multipath (MP) observables, and then we assess their influence on double-differenced (DD) WL AR. The numerical results show that an obvious low-frequency component exists in MP observables of BDS geostationary earth-orbit satellites (GEOs) for Leica receivers, while its high-frequency measurement noise is very small. For geosynchronous orbit satellites (IGSOs) and medium earth-orbit satellites (MEOs), a slight fluctuation can also be observed that is similar to that of GPS satellites, except for the satellite-included code bias. In Trimble, Javad, and Septentrio receivers, the MP series are dominated by high-frequency measurement noise, both for GEOs and non-GEOs, except for satellite-included code bias. Furthermore, the characteristic of Leica receivers for BDS GEOs seriously affects WL AR and, even for a short baseline, it takes a long time for WL ambiguities to converge, or not converge for many GEO-related DD WL ambiguities, while Trimble, Javad, and Septentrio receivers perform well for short and medium baselines. Then, a time-difference method is proposed to mitigate the multipath of BDS GEOs for a Leica receiver. After applying the proposed method, WL ambiguity fixing rates of GEO-related satellite pairs are improved significantly and the convergence time is shortened from several hours to ten minutes.