Single Point Positioning with Sequential Least-Squares Filter and Estimated Real-Time Stochastic Model

To obtain higher accurate position estimates, the stochastic model is estimated by using residual of observations, hence, the stochastic model describes the noise and bias in measurements more realistically. By using GPS data and broadcast ephemeris, the numerical results indicating the accurate position estimates at sub-meter level are obtainable.

Preliminary assessment of the navigation and positioning performance of BeiDou regional navigation satellite system

BeiDou regional navigation satellite system （BDS） also called BeiDou-2 has been in full operation since December 27, 2012. It consists of 14 satellites, including 5 satellites in Geostationary Orbit （GEO）, 5 satellites in Inclined Geosynchronous Orbit （IGSO）, and 4 satellites in Medium Earth Orbit （MEO）. In this paper, its basic navigation and positioning performance are evaluated preliminarily by the real data collected in Beijing, including satellite visibility, Position Dilution of Precision （PDOP） value, the precision of code and carrier phase measurements, the accuracy of single point positioning and differential position- ing and ambiguity resolution （AR） performance, which are also compared with those of GPS. It is shown that the precision of BDS code and carrier phase measurements are about 33 cm and 2 mm, respectively, which are comparable to those of GPS, and the accuracy of BDS single point positioning has satisfied the design requirement. The real-time kinematic positioning is also feasible by BDS alolae in the opening condition, since its fixed rate and reliability of single-epoch dual-frequency AR is comparable to those of GPS. The accuracy of BDS carrier phase differential positioning is better than 1 cm for a very short baseline of 4.2 m and 3 cm for a short baseline of 8.2 km, which is on the same level with that of GPS. For the combined BDS and GPS, the fixed rate and reliability of single-epoch AR and the positioning accuracy are improved significantly. The accu- racy of BDS/GPS carrier phase differential positioning is about 35 and 20 % better than that of GPS for two short baseline tests in this study. The accuracy of BDS code differential positioning is better than 2.5 m. However it is worse than that of GPS, which may result from large code multipath errors of BDS GEO satellite measurements.

Analysis of Galileo signal-in-space range error and positioning performance during 2015-2018

A long-term analysis of signal-in-space range error (SISRE) is presented for all healthy Galileo satellites, and the first pair of full operational capability satellites in wrong elliptical orbits. Both orbit and clock errors for Galileo show an obvious convergence trend over time. The annual statistical analyses show that the average root mean squares (RMSs) of SISRE for the Galileo constellation are 0.58 m (2015), 0.29 m (2016), 0.23 m (2017), and 0.22 m (2018). Currently, the accuracy of the Galileo signal-in-space is superior to that of the global positioning system (GPS) Block IIF (0.35 m). In addition, the orbit error accounts for the majority of Galileo SISRE, while the clock error accounts for approximately one-third of SISRE due to the high stability of the onboard atomic clock. Single point positioning results show that Galileo achieves an accuracy of 2-3 m, which is comparable to that of GPS despite the smaller number of satellites and worse geometry. Interestingly, the vertical accuracy of Galileo, which uses the NeQuick ionospheric model, is higher than that of GPS. Positioning with single frequency E1 and E5 show a higher precision than E5a and E5b signals. Regarding precise point positioning (PPP), the results indicate that a comparable positioning accuracy can be achieved among different stations with the current Galileo constellation. For static PPP, the RMS values of Galileo-only solutions are within 1 cm horizontally, and the vertical RMSs are mostly within 2 cm horizontally. For kinematic PPP, the RMSs of Galileo-only solutions are mostly within 4 cm horizontally and 6 cm vertically.