Assessment of the performance of GPS/Galileo PPP-RTK convergence using ionospheric corrections from networks with different scales

Abstract

The rapid convergence of precise point positioning real-time kinematics (PPP-RTK) with centimeter-level accuracy is of utmost importance for many applications. One way of accelerating this convergence is to explore the use of ionospheric models and multiple global navigation satellite system (GNSS) observations, e.g., Global Positioning System (GPS) and Galileo Satellite Navigation System (Galileo) observations. Because the temporal and spatial variations of the ionosphere are significant, convergence analysis of PPP-RTK should be investigated in networks with different scales, especially networks with large differences in their scales. This study describes the convergence performance of PPP-RTK using GPS/Galileo observations derived from networks with different scales under medium ionospheric conditions. Slant ionospheric corrections were first estimated from the reference network and then imported as virtual observations to enhance the convergence performance of PPP-RTK at the user interface. The results show that for the 165-km reference site spacing, the portions of single-differenced (SD) ionospheric residuals within 0.3 total electron content units (TECU) were 85.2% and 81.7% for the GPS and Galileo observations, respectively. Considering the 90th percentile of horizontal position errors, the PPP-RTK convergence time within the network with 165-km spacing was shortened from 2.5 min for GPS-only observations to 2.0 min for integrated GPS + Galileo observations. For the network of about 50 km, the proportions of the SD ionospheric residuals of the GPS and Galileo constellation within 0.3 TECU were 95.9% and 82.8%, respectively. The PPP-RTK convergence time of the 90th percentile horizontal positioning errors based on GPS-only observations was 2.0 min but 1.5 min based on integrated GPS + Galileo observations. Using GPS and Galileo observations, the convergence time could be reduced by 25% for the network with 50-km spacing. Our results suggest that the convergence time of PPP-RTK depends on the scale of the reference network and becomes shorter as the scale of the network decreases. Compared with the GPS-only PPP-RTK, the GPS/Galileo PPP-RTK could shorten the convergence time further. Graphical Abstract

Improved PPP-RTK by Considering the Non-Homogeneous Uncertainty of the ionosphere with a Spatial Three-Direction Model

“…Therefore, we employed 8-min intervals to model the ionospheric delay error RMS. Without considering the variation in ionospheric delay precision in the three directions, the BLL model is constructed with a simple function of the baseline d and is widely used to model the precision of the ionospheric correction [23][24][25][26][27][28]. Th ficients of the SDC and BLL models are estimated separately using the RMS value ionospheric correction residuals every 8 min in each of the eight reference network the estimated coefficients, the precision of ionospheric delay interpolation is mod the BLL and the SDC models in each of eight different references.…”

“…This indica the fitting values of the SDC model are in excellent agreement with the actual prec the ionospheric corrections. Additionally, the mean values of the fitting errors of th model for G05/G02 in reference networks with different inter-station distances are 1 Without considering the variation in ionospheric delay precision in the three spatial directions, the BLL model is constructed with a simple function of the baseline distance and is widely used to model the precision of the ionospheric correction [23][24][25][26][27][28]. The coefficients of the SDC and BLL models are estimated separately using the RMS values of the ionospheric correction residuals every 8 min in each of the eight reference networks.…”

“…The results demonstrate that the standard deviation value grows as the inter-station distance of the reference network increases. Considering the effect of the reference network scale on ionospheric correction accuracy, empirical linear or exponential functions related to the baseline length (BLL) have been employed to calculate the standard deviation value of ionospheric correction [25][26][27]. These standard deviation values will change with the station spacing of the reference network, but it may experience an accuracy degradation due to the overlooking of the temporal variation in the ionospheric delay.…”

PPP-RTK with Rapid Convergence Based on SSR Corrections and Its Application in Transportation

“…(2) Utilizing external atmospheric products; it has been proven PPP-RTK reduces the convergence time by using global or regional ionospheric products [25,26]. In the presence of ionospheric delays, the convergence time could be shortened to 1.5 to 3 min [27,28]. Based on a small scale of GNSS networks, with interpolated accurate ionospheric and tropospheric delays, the convergence time was further reduced to 1 min [14], and a rapid reinitialization of less than 1 min was also achieved [29,30].…”