Modeling and Compensation of Timing and Spatial Ephemeris Errors of Non-Cooperative LEO Satellites With Application to PNT

The modeling and compensation of timing and spatial ephemeris errors of low Earth orbit (LEO) satellites is considered. First, models are derived capturing the effect of temporal and spatial errors of publicly available uncertain LEO ephemerides on pseudorange, carrier phase, and Doppler measurements. Next, a scheme is developed to enable rapid compensation of timing and spatial ephemeris errors. The scheme utilizes a stationary receiver with a known position, extracting opportunistically pseudorange, carrier phase, or Doppler measurements from LEO downlink signals. An unscented Kalman filter-based LEO tracking framework is developed, which employs the derived spatial and temporal error models. A simulation study is presented to evaluate the developed scheme with multiconstellation LEO satellites: Starlink, OneWeb, Orbcomm, and Iridium NEXT. It is demonstrated that the proposed scheme reduces the satellite's initial position error from several kilometers to hundreds of meters. It is also demonstrated that the proposed scheme is more robust to initial satellite position error than direct LEO satellite tracking. Monte Carlo experimental results are presented to demonstrate the efficacy of the error compensation scheme to localize a stationary receiver with 1) carrier phase; and 2) Doppler measurements from three Starlink and two OneWeb noncooperative LEO satellites. Starting with an initial 3-D error of 11 316 m, it is shown that utilizing SGP4-propagated LEO ephemerides results in an error of 1) 1186 m; and 2) 1109 m, respectively; while the proposed refined ephemerides results in an error of 1) 3.18 m; and 2) 7.91 m, respectively.