The long convergence time required to achieve high-precision position solutions with integer ambiguity resolution-enabled precise point positioning (PPP-RTK) is driven by the presence of ionospheric delays. When precise real-time ionospheric information is available and properly applied, it can strengthen the underlying model and substantially reduce the time required to achieve centimeter-level accuracy. In this study, we present and analyze the real-time PPP-RTK user performance using ionospheric corrections from multi-scale regional networks during a day with medium ionospheric disturbance. It is the goal of this contribution to measure the impact the network dimension has on the ambiguity-resolved user position through the predicted ionospheric corrections. The user-specific undifferenced ionospheric corrections are computed at the network side, along with the satellite phase biases needed for single-receiver ambiguity resolution, using the best linear unbiased predictor. Such corrections necessitate the parameterization of an estimable user receiver code bias, on which emphasis is given in this study. To this end, we process GPS dual-frequency data from four four-station evenly distributed CORS networks in the United States with varying station spacings in order to evaluate if and to what extent the ionospheric corrections from multi-scale networks can improve the user convergence times. Based on a large number of samples, our experimental results showed that sub-10 cm horizontal accuracy can be achieved almost instantaneously in the ionosphere-weighted partially-ambiguity-fixed kinematic PPP-RTK solutions based on corrections from a network with 68 km spacing. Most of the solutions (90%) were shown to require less than 6.0 min, compared to the ionosphere-float PPP solutions that needed 68.5 min. In case of sparser networks with 115, 174 and 237 km spacing, 50% of the horizontal positioning errors are shown to become less than one decimeter after 1.5, 4.0 and 7.0 min, respectively, while 90% of them require 10.5, 16.5 and 20.0 min. We also numerically demonstrated that the user’s convergence times bear a linear relationship with the network density and get shorter as the density increases, for both full and partial ambiguity resolution.

This paper presents an analysis of the ionospheric corrections required to get a significant improvement in PPP-RTK performance. The main aim was to determine the improvement in the position precision and time-to-first-fix in the PPP-RTK user side using ionospheric corrections computed from a network. The study consists of two main steps. The first one includes an empirical investigation of the ionosphere model precision necessary to greatly improve the PPP-RTK performance in a simulated environment in terms of precision and convergence time. In the second one, an optimal ionosphere representation was developed to provide precise ionospheric corrections by parameterizing the ionospheric slant delays after the PPP-RTK network processing in terms of ionosphere model coefficients and differential code biases using real GNSS measurements. Experimental results demonstrate that the proposed methodology can be used for reliable regional ionosphere modeling and satellite code bias estimation, due to the consistency of the satellite code bias estimates with those provided from the International GNSS Service Analysis Centres, the high stability of the estimated receiver and satellite code biases and the low least-squares residuals of the network-based ionosphere modeling solution. Finally, it has been shown that the precision of ionospheric corrections at zenith needs to be better than 5 cm to enable faster PPP-RTK solutions.

The benefits of an increased number of global navigation satellite systems (GNSS) in space have been confirmed for the robustness and convergence time of standard precise point positioning (PPP) solutions, as well as improved accuracy when (most of) the ambiguities are fixed. Yet, it is still worthwhile to investigate fast and high-precision GNSS parameter estimation to meet user needs. This contribution focuses on integer ambiguity resolution-enabled Precise Point Positioning (PPP-RTK) in the use of the observations from four global navigation systems, i.e., GPS (Global Positioning System), Galileo (European Global Navigation Satellite System), BDS (Chinese BeiDou Navigation Satellite System), and GLONASS (Global’naya Navigatsionnaya Sputnikova Sistema). An undifferenced and uncombined PPP-RTK model is implemented for which the satellite clock and phase bias corrections are computed from the data processing of a group of stations in a network and then provided to users to help them achieve integer ambiguity resolution on a single receiver by calibrating the satellite phase biases. The dataset is recorded in a local area of the GNSS network of the Netherlands, in which 12 stations are regarded as the reference to generate the corresponding corrections and 21 as the users to assess the performance of the multi-GNSS PPP-RTK in both kinematic and static positioning mode. The results show that the root-mean-square (RMS) errors of the ambiguity float solutions can achieve the same accuracy level of the ambiguity fixed solutions after convergence. The combined GNSS cases, on the contrary, reduce the horizontal RMS of GPS alone with 2 cm level to GPS + Galileo/GPS + Galileo + BDS/GPS + Galileo + BDS + GLONASS with 1 cm level. The convergence time benefits from both multi-GNSS and fixing ambiguities, and the performances of the ambiguity fixed solution are comparable to those of the multi-GNSS ambiguity float solutions. For instance, the convergence time of GPS alone ambiguity fixed solutions to achieve 10 cm three-dimensional (3D) positioning accuracy is 39.5 min, while it is 37 min for GPS + Galileo ambiguity float solutions; moreover, with the same criterion, the convergence time of GE ambiguity fixed solutions is 19 min, which is better than GPS + Galileo + BDS + GLONASS ambiguity float solutions with 28.5 min. The experiments indicate that GPS alone occasionally suffers from a wrong fixing problem; however, this problem does not exist in the combined systems. Finally, integer ambiguity resolution is still necessary for multi-GNSS in the case of fast achieving very-high-accuracy positioning, e.g., sub-centimeter level.