Unmodeled-error-corrected long-range ionosphere-free relative positioning with troposphere tomography and particle filter

Long-range Real-Time Kinematic (RTK) and Real-Time Differential (RTD) positioning systems face significant challenges from three main types of unmodeled errors: atmospheric delays, multipath effects, and others. This study proposes a comprehensive framework that systematically addresses each error type: first-order ionospheric delays are eliminated using the ionosphere-free combination model; tropospheric delays are corrected through high-resolution troposphere tomography while multipath and other residual unmodeled errors are mitigated using an advanced particle filter algorithm. Specifically, the tropospheric total refractivity field with high spatiotemporal resolutions are tomographically reconstructed with slant tropospheric delays (STDs) from a dense GNSS network. Then the STD for a light-of-sight signal is directly calculated from the tomographic refractivity field and used in the long-range RTK and RTD positioning. In addition, particle filter solves for non-Gaussian and non-stationary unmodeled errors by employing adaptive window dynamic adjustment for covariance and Halton sequence-based low-variance resampling. Experimental results across baselines ranging from 150 km to 600 km demonstrate the superiority of the proposed method, with reductions in root mean square error of up to around 75% in the vertical direction and significant improvements in the horizontal components. These findings highlight the efficacy of combining troposphere tomography and particle filtering to enhance GNSS positioning accuracy, offering a robust solution for high-precision applications in long baselines and even other challenging environments.