GPS + Galileo + BDS-3 medium to long-range single-baseline RTK: an alternative for network-based RTK?

Abstract

Thanks to the development of the real-time kinematic (RTK) algorithm and the emerging Global Navigation Satellite System (GNSS), especially for Galileo and BeiDou-3, reliable positioning accuracy for medium and long-baseline RTK became possible globally. Moreover, with the development of the GNSS receiver hardware, baseline length limitations due to radio-based communications are removed thanks to internet-based communication. In this work, single-baseline RTK, incorporated partial ambiguity resolution with troposphere and ionosphere weighting, using GPS (G), Galileo (E), BeiDou-3 (C3) and multi-GNSS (GE and GEC3), is conducted with real GNSS data of EUREF Permanent GNSS network under three different cutoff angles (10°, 20°, and 30°) for six different lengths of baselines (~50, ~150, ~250, ~350, ~450, and ~550 km). The results show that the multi-GNSS RTK solution significantly contributed to the positioning accuracy and convergence time of the single-system RTK solutions. Based on the results, non-available epoch-wise solutions for the high-degree cutoff angles are more obvious for the single-system RTK, whereas multi-GNSS solutions provide 100% solutions for each cutoff angle and baseline. The results indicate that instantaneous and a few epochs single-epoch ambiguity resolution is feasible for 50, 150, 250 and 350 km baseline lengths for multi-GNSS RTK. Based on the positioning results, horizontal–vertical positioning improvements of multi-GNSS RTK (GEC3) compared with the single-system GPS RTK are found as 50%–37%, 40%–35%, 55%–47%, 53%–54%, 57%–49% and 57%–49% for 50, 150, 250, 350, 450 and 550 km, respectively, under a 10° cutoff angle. For 20° and 30° cutoff angles, the accuracy improvements are much higher. The convergence time improvements (n/e/u) of multi-GNSS RTK (GEC3) compared with the single-system GPS RTK are found as 86/92/75%, 77/67/72%, 75/77/83%, 53/56/52%, 69/49/62%, and 52/45/39% for 50, 150, 250, 350, 450 and 550 km, respectively, under a 10° cutoff angle.

Anomalous Ambiguity Detection Between Reference Stations Based on Box-Cox Transformation of Tropospheric Residual Estimation

“…Consequently, the matrix form of the observation equation, as represented in Eq. ( 1), is obtained: (Ogutcu et al, 2023), where b and k denote two distinct reference stations, r represents the reference satellite, and n is the number of DD satellites; B is a column vector composed of wavelengths; N represents the float ambiguities; T is the DD w ZTD estimation corresponding to float ambiguities; and V represents the residuals of the float solution.…”