GPS-Based Small Satellite Localization Using EKF Under Time-Varying Satellite Visibility Conditions

Accurate autonomous localization of Low Earth Orbit (LEO) small satellites relies heavily on Global Navigation Satellite Systems (GNSS). However, standard navigation filters often assume idealized, constant satellite visibility and uniform signal quality. In realistic orbital environments, the number of trackable GNSS satellites fluctuates rapidly due to Earth occultation, antenna field-of-view constraints, and variable signal strength. This paper presents a high-fidelity orbit propagator and an Extended Kalman Filter (EKF) designed to maintain robust state estimation under these time-varying GPS visibility conditions. The translational dynamics incorporate Earth's zonal harmonics, atmospheric drag, and third-body perturbations. To simulate a realistic operational environment, the GNSS measurement model generates synthetic observations with noise variances that scale dynamically based on geometric visibility and link-budget derived carrier-to-noise density. The EKF, operating with a fixed measurement noise model, handles the fluctuating number of observations via dynamic matrix resizing. Simulations conducted over a full LEO period demonstrate that despite severe Geometric Dilution of Precision (GDOP) spikes - where visibility drops to as few as five satellites - the filter successfully prevents divergence. The proposed framework achieves Root Mean Square (RMS) position errors of 0.86 m, 0.72 m, and 1.19 m in the X, Y, and Z axes, respectively, validating its reliability for highly dynamic spaceflight navigation.