Introducing precise atmosphere information into precise point positioning enables rapid ambiguity resolution and introduces a significant accuracy improvement. However, it can only be implemented in regions with dense networks and stable communication links. For larger areas, e.g., an intercontinental level, there is a conflict between the accuracy of corrections and the amount of atmosphere information to be disseminated. We develop a hierarchical augmentation mode to combine the advantages of the fitting model and region interpolation model to relieve the communication burden. Relying on the fitting model with fewer coefficients applied over large areas as the essential information, the unmodeled errors are calculated at each reference station, and further correction information is optional compensation depending on the magnitude of the unmodeled residuals. We perform the proposed models on 103 EUREF Permanent Network stations with 200-km station spacing and 84 stations as the external validation. The ionosphere and troposphere fitting models have an average accuracy of about 4.2 and 1.3 cm, respectively, under meteorologically calm conditions. The unmodeled error transmission determined by the magnitude of residuals can be reduced by 61% and 96% for the ionospheric and tropospheric delays, respectively, with respect to the legacy interpolation mode. Further compensation implemented, i.e., unmodeled residuals, can achieve instantaneous convergence for 83.6% of all solutions, and the overall initialization time is within 1.0 min. Thus, the proposed hierarchical positioning mode satisfies real-time positioning convergence requirements and significantly reduces massive corrections in communication.

Precise point positioning with ambiguity resolution (PPP-AR) is a powerful tool for geodetic and time-constrained applications that require high precision. The performance of PPP-AR highly depends on the reliability of the correct integer carrier-phase ambiguity estimation. In this study, the performance of narrow-lane ambiguity resolution of PPP using the Least-squares AMBiguity Decorrelation (LAMBDA) and bootstrapping methods is extensively investigated using real data from 55 IGS stations over one-month in 2020. Static PPP with 24-, 12-, 8-, 4-, 2-, 1- and ½-h sessions using two different cutoff angles (7° and 30°) was conducted with three PPP modes: i.e. ambiguity-float and two kinds of ambiguity-fixed PPP using the LAMBDA and bootstrapping methods for narrow-lane AR, respectively. The results show that the LAMBDA method can produce more reliable results for 2 hour and shorter observation sessions compared with the bootstrapping method using a 7° cutoff angle. For a 30° cutoff angle, the LAMBDA method outperforms the bootstrapping method for observation sessions of 4 h and less. For long observation times, the bootstrapping method produced much more accurate coordinates compared with the LAMBDA method without considering the wrong fixes cases. The results also show that occurrences of fixing the wrong integer ambiguities using the bootstrapping method are higher than that of the LAMBDA method.

The ubiquity of smartphones catalyzes myriad smartphone-based Internet of Things (IoT) applications, amongst which smartphone positioning which utilizes global navigation satellite system (GNSS) observations to provide spatial information plays a crucial role. However, noisy smartphone GNSS measurements prevent decimeter-level positioning performance in user environments. Recovering the integer property of GNSS carrier phase measurement ambiguities shows great potential in achieving high-accuracy positioning solutions. However, inaccurate ambiguity estimates and short signal wavelengths are the main barriers to successful ambiguity resolution (AR). Therefore, a partial AR with wide-lane (WL) ambiguities and an automatic ambiguity hold strategy is proposed. Simulated results show that, for single-epoch WL AR, even with one WL ambiguity correctly fixed, the positioning solution can be improved by 3 cm. With actual static and kinematic datasets, the proposed algorithm is evaluated and validated. Static results show an improvement of 83% in horizontal position when the WL AR approach is applied, and positioning accuracies can reach 6.8, 2.9, and 11.5 cm in the E, N, and U direction components, respectively. For kinematic data collected in highly variable realistic driving environments, the time series of positioning errors of WL AR solutions exhibit less variation than float solutions. And with fixed WL ambiguities, solutions can be improved to varying degrees, ranging from several centimeters to up to 8 dm depending on the environment. The largest improvement of 8 dm is observed for 95th percentile horizontal positioning errors under a suburban environment.