Availability of two overlapping frequencies L1/E1 and L5/E5a of the signals transmitted by GPS and Galileo systems offers the possibility of tightly combining observations from both systems in a single observational model. A tightly combined observational model assumes a single reference satellite for all observations from both Galileo and GPS systems. However, when inter-system double-differenced observations are created, receiver inter-system bias is introduced. This study presents the results and the methodology for estimation and accounting for phase and code GPS-Galileo inter-system bias in precise relative positioning. The research investigates the size and temporal stability of the estimated bias for different receiver pairs as well as examines the influence of accounting for the inter-system bias on the user position solution. The obtained numerical results are based on four experiments carried out at different locations and time periods using both real and simulated GNSS data.

It has been acknowledged that smartphone GNSS observations suffer not only from high measurement noise and multipath but also from anomalies such as duty cycling and gradual accumulation of phase errors. These phenomena importantly constrain the application of smartphone phase measurement to high-precision techniques such as RTK or PPP. Hence, we aim at a comprehensive characterization of smartphone signal quality, including carrier-to-noise density ratio, measurement noise and anomalies present in observables with the focus on the impact of duty-cycling mode. The analysis confirms the abnormal properties of smartphone measurements related to the divergence between code and phase data and poor quality of the latter. To address these limitations, the second objective is to assess the smartphone medium- to long-range code-based relative positioning. This task includes the validation of the weighting scheme suited for handling the low quality of smartphone observations. The results show that it is feasible to use a sparse countrywide GNSS network as reference stations for code-based relative positioning. Even with the baselines over 100 km, we can significantly enhance the positioning with respect to a stand-alone solution and reach the submeter level of horizontal coordinate accuracy. We have also noticed a discernible benefit from the C/N0-dependent weighting scheme, which is superior to the satellite elevation one.

This paper provides the methodology and performance assessment of multi-GNSS signal processing for the detection of small-scale high-rate dynamic displacements. For this purpose, we used methods of relative (RTK) and absolute positioning (PPP), and a novel direct signal processing approach. The first two methods are recognized as providing accurate information on position in many navigation and surveying applications. The latter is an innovative method for dynamic displacement determination with the use of GNSS phase signal processing. This method is based on the developed functional model with parametrized epoch-wise topocentric relative coordinates derived from filtered GNSS observations. Current regular kinematic PPP positioning, as well as medium/long range RTK, may not offer coordinate estimates with subcentimeter precision. Thus, extended processing strategies of absolute and relative GNSS positioning have been developed and applied for displacement detection. The study also aimed to comparatively analyze the developed methods as well as to analyze the impact of combined GPS and BDS processing and the dependence of the results of the relative methods on the baseline length. All the methods were implemented with in-house developed software allowing for high-rate precise GNSS positioning and signal processing. The phase and pseudorange observations collected with a rate of 50 Hz during the field test served as the experiment’s data set. The displacements at the rover station were triggered in the horizontal plane using a device which was designed and constructed to ensure a periodic motion of GNSS antenna with an amplitude of ~3 cm and a frequency of ~4.5 Hz. Finally, a medium range RTK, PPP, and direct phase observation processing method demonstrated the capability of providing reliable and consistent results with the precision of the determined dynamic displacements at the millimeter level. Specifically, the research shows that the standard deviation of the displacement residuals obtained as the difference between a benchmark-ultra-short baseline RTK solution and selected scenarios ranged between 1.1 and 3.4 mm. At the same time, the differences in the mean amplitude of the oscillations derived from the established scenarios did not exceed 1.3 mm, whereas the frequency of the motion detected with the use of Fourier transformation was the same.

Several processing strategies that use dual-frequency GPS-only solution, multi-frequency Galileo-only solution, and finally tightly combined dual-frequency GPS + Galileo solution were tested and analyzed for their applicability to single-epoch long-range precise positioning. In particular, a multi-system GPS + Galileo solution was compared to GPS double-frequency solution as well as to Galileo double-, triple-, and quadruple-frequency solutions. Also, the performance of the strategies was analyzed under clear-sky and obstructed satellite visibility in both single-baseline and multi-baseline modes. The results indicate that tightly combined GPS + Galileo instantaneous positioning has a clear advantage over single-system solutions and provides an accurate and reliable solution. It was also confirmed that application of multi-frequency observations in case of Galileo system has an advantage over a dual-frequency solution.