Precise Positioning in Alpine Areas with Troposphere and Multipath Estimation

Abstract

Real-time kinematic (RTK) positioning with Global Navigation Satellite System (GNSS) signals is widely used, e.g., for surveying, agriculture, and potentially for autonomous vehicles and unmanned air vehicles in the future. In this paper, an extended RTK positioning for significant height differences between two low-cost GNSS receivers with patch antennas is presented. In this case, the classical model for double difference measurements needs to be extended, i.e., a differential tropospheric zenith delay and pseudorange multipath errors need to be estimated besides the baseline and carrier phase integer ambiguities. The increased number of unknowns results in an ill-conditioned system of observation equations and a substantial correlation between the state estimates. We introduce prior information on the differential tropospheric zenith delay based on the differential air pressure and exploit the temporal correlation of pseudorange multipath errors. Moreover, a criterion for the integer ambiguity candidate vector selection is provided, which is robust over phase multipath and unavoidable errors in the float ambiguity covariance matrix. The proposed method is validated with two low-cost GNSS modules that were placed at the Zugspitzplatt (2601 m a.s.l.) and Eibsee (1018 m a.s.l.). The obtained estimates for the baseline and differential tropospheric zenith delay show a high repeatability over several independent ambiguity fixings. The residuals of the fixed carrier phase measurements are within 2 cm for almost all satellites, which confirms both the measurement model and the ambiguity fixing.