Helmert Variance Component Estimation for Multi-GNSS Relative Positioning

The Multi-constellation Global Navigation Satellite System (Multi-GNSS) has become the standard implementation of high accuracy positioning and navigation applications. It is well known that the noise of code and phase measurements depend on GNSS constellation. Then, Helmert variance component estimation (HVCE) is usually used to adjust the contributions of di¿erent GNSS constellations by determining their individual variances of unit weight. However, HVCE requires a heavy computation load. In this study, the HVCE posterior weighting was employed to carry out a kinematic relative Multi-GNSS positioning experiment with six short-baselines from day of year (DoY) 171 to 200 in 2019. As a result, the HVCE posterior weighting strategy improved Multi-GNSS positioning accuracy by 20.5%, 15.7% and 13.2% ineast-north-up(ENU) components, compared to an elevation-dependent (ED) priori weighting strategy. We observed that the weight proportion of both code and phase observations for each GNSS constellation were consistent during the entire 30 days, which indicates that the weight proportions of both code and phase observations are stable over a long period of time. It was also found that the quality of a phase observation is almost equivalent in each baseline and GNSS constellation, whereas that of a code observation is different. In order to reduce the time consumption off the HVCE method without sacrificing positioning accuracy, the stable variances of unit weights of both phase and code observations obtained over 30 days were averaged and then frozen as a priori information in the positioning experiment. The result demonstrated similar ENU improvements of 20.0%, 14.1% and 11.1% with respect to the ED method but saving 88% of the computation time of the HCVE strategy. Our study concludes with the observations that the frozen variances of unit weight (FVUW) could be applied to the positioning experiment for the next 30 days, that is, from DoY 201 to 230 in 2019, improving the positioning ENU accuracy of the ED method by 18.1%, 13.2% and 10.6%, indicating the effectiveness of the FVUW.Peer ReviewedPostprint (published version

Spatiotemporal Evaluation of GNSS-R Based on Future Fully Operational Global Multi-GNSS and Eight-LEO Constellations

Spaceborne GNSS-R (global navigation satellite system reflectometry) is an innovative and powerful bistatic radar remote sensing technique that uses specialized GNSS-R instruments on LEO (low Earth orbit) satellites to receive GNSS L-band signals reflected by the Earth’s surface. Unlike monostatic radar, the illuminated areas are elliptical regions centered on specular reflection points. Evaluation of the spatiotemporal resolution of the reflections is necessary at the GNSS-R mission design stage for various applications. However, not all specular reflection signals can be received because the size and location of the GNSS-R antenna’s available reflecting ground coverage depends on parameters including the on-board receiver antenna gain, the signal frequency and power, the antenna face direction, and the LEO’s altitude. Additionally, the number of available reflections is strongly related to the number of GNSS-R LEO and GNSS satellites. By 2020, the Galileo and BeiDou Navigation Satellite System (BDS) constellations are scheduled to be fully operational at global scale and nearly 120 multi-GNSS satellites, including Global Positioning System (GPS) and Global Navigation Satellite System (GLONASS) satellites, will be available for use as illuminators. In this paper, to evaluate the future capacity for repetitive GNSS-R observations, we propose a GNSS satellite selection method and simulate the orbit of eight-satellite LEO and partial multi-GNSS constellations. We then analyze the spatiotemporal distribution characteristics of the reflections in two cases: (1) When only GPS satellites are available; (2) when multi-GNSS satellites are available separately. Simulation and analysis results show that the multi-GNSS-R system has major advantages in terms of available satellite numbers and revisit times over the GPS-R system. Additionally, the spatial density of the specular reflections on the Earth’s surface is related to the LEO inclination and constellation construction