GRU-Based Pseudorange Error Modeling for LEO Satellites

Low Earth Orbit (LEO) constellations can support resilient positioning, navigation, and timing (PNT). We propose a LEO-only pipeline that learns link-wise pseudorange residuals using a gated recurrent unit (GRU) and then applies standard least-squares (LS) estimation. Features include pseudoranges, satellite azimuth/elevation, and atmospheric corrections (ionospheric and tropospheric delays). From held-out data, we compute per-link user equivalent range errors (UERE) to weight LS and apply a geometry-quality gate. Time-in-Spec (TiS) is the fraction of epochs that satisfy a UERE-weighted threshold; only LS estimates within TiS are accepted. The method is trained on three suburban trajectories and evaluated on a distinct fourth trajectory that is route- and time-disjoint. Results show 48.91% TiS, with 3D root-mean-square error (RMSE) reduced from 6.12 m to 2.17 m (64.5%) and maximum error reduced from 23.32 m to 3.03 m (87.0%). Twenty-five Monte Carlo (MC) simulations confirm performance consistency. GRU-based range correction combined with UERE-weighted LS yields accurate and reliable LEO-only positioning.