From network RTK to PPP-RTK, it is highly expected that high-precision positioning within a few minutes can be achieved with a sparse reference network. In this study, we investigate a rapid multi-frequency PPP convergence strategy based on Galileo E1/E5a/E6 and BeiDou-3 B1C/B2a/B3I signals, whose unambiguous wide-lane observables can efficiently assist in speeding up narrow-lane ambiguity resolution. Furthermore, frequency-specific biases existing on the third-frequency observables have been observed to slow down multi-frequency PPP-AR convergence. In this study, we partially mitigated their effects by estimating a second satellite clock for the third frequency of signals. We validated this approach with one month of data collected from 22 stations. On average, it took about 18 min for PPP wide-lane ambiguity resolution (PPP-WAR) to converge, while 32 min were required for ambiguity-float PPP. Compared with dual-frequency PPP-AR, which needed nearly 12 min to converge, multi-frequency PPP-AR required 6 min only. Once there were more than 10 satellites involved in PPP, the convergence could be achieved within 3 min on average. Meanwhile, 81% and 62% of multi-frequency PPP-AR solutions converged successfully within 5 and 1 min, respectively. Finally, we carried out a vehicle-borne experiment to validate this approach in a kinematic environment. Owing to frequent cycle slips during the movement of vehicle, it took 14 min for B1C/B2a/B3I and E1/E5a/E6 PPP-AR to obtain reliable positions, and 19 min for those using the other signal combinations B1C/B2a/B2b and E1/E5a/E5b, owning to higher noise. Overall, these results are promising for achieving high-precision PPP positioning globally within a few minutes if multi-frequency biases can be handled well in the data processing.

Rapid precise point positioning ambiguity resolution (PPP-AR) is of great importance to improving precise positioning efficiency. There is an expectation that Galileo multi-frequency (three or more frequencies) data processing will offer a promising way to accelerate PPP-AR. However, the performance of different combination observables out of raw Galileo multi-frequency data is still unclear, and the adverse impacts of missing receiver antenna phase center corrections have not been quantified in detail. We therefore studied uncombined Galileo PPP-AR by contrasting three typical triple-frequency combinations, which are E1/E5a/E5b, E1/E5a/E6, and E1/E5/E6 signals, using 30 days of data from 15 stations across Australia. We carried out triple-frequency PPP-AR by separately applying the official GPS receiver antenna phase centers, as currently employed in most relevant literatures, as well as the pilot Galileo receiver antenna phase centers preliminarily measured by the International GNSS Service. We found that, compared to dual-frequency (E1/E5a) PPP-AR, triple-frequency PPP-AR based on E1/E5a/E5b signals shortened the convergence time by only 7.6%, while those based on E1/E5a/E6 and E1/E5/E6 increased unexpectedly the convergence time by 17.6% and 12.7%, respectively, if the GPS receiver antenna corrections were presumed for Galileo signals. However, after using the pilot Galileo phase center corrections, triple-frequency PPP-AR based on E1/E5a/E5b, E1/E5a/E6, and E1/E5/E6 signals could speed up the convergence on average by about 16.2%, 30.3%, and 17.7%, respectively. Therefore, we demonstrate the critical impact of correct Galileo receiver antenna phase centers on multi-frequency PPP-AR convergences. Moreover, the triple-frequency signal combination E1/E5a/E6 is advantageous over others in achieving rapid triple-frequency Galileo PPP-AR.

Calving front location plays a crucial role in studying ice–ocean interaction, mapping glacier area change, and constraining ice dynamic models. However, relying solely on visual interpretation to extract annual changes in the calving front of ice shelves is a time-consuming process. In this study, a comparative analysis was conducted on the segmentation obtained from fully convolutional networks (FCN), U-Net, and U²-Net models, revealing that U²-Net exhibited the most effective classification. Notably, U²-Net outperformed the other two models by more than 30 percent in terms of the F1 parameter. Therefore, this paper introduces an automated approach that utilizes the U²-Net model to extract the calving front of ice shelves based on a Landsat image, achieving an extraction accuracy of 58 m. To assess the model’s performance on additional ice shelves in the polar region, the calving front of the Totten and Filchner ice shelves were also extracted for the past decade. The findings demonstrated that the ice velocity of the Filchner ice shelf exceeded that of the Totten ice shelf. Between February 2014 and March 2015, the majority of the calving fronts along the Filchner Ice Shelf showed an advancing trend, with the fastest-moving front measuring 3532 ± 58 m/yr.