Elevation-cutoff-dependent convergence and steady-state performance of LEO-augmented multi-GNSS PPP time transfer
Abstract
Under restrictive elevation-cutoff conditions, Global Navigation Satellite System (GNSS) precise point positioning (PPP) time transfer can suffer delayed convergence because fewer satellites are available and the timing geometry degrades. However, it remains unclear whether low Earth orbit (LEO) geometric augmentation yields a consistent elevation-cutoff response for both convergence and steady-state performance. Using 5 days of Multi-GNSS Experiment (MGEX) GNSS observations and simulated Walker 288/24/1 LEO observations, we construct a GPS/BDS-3/Galileo (GCE) solution and a LEO-augmented solution (GCE + LEO), and compare the number of visible satellites, the time dilution of precision (TDOP), convergence time, steady-state standard deviation (STD) and modified Allan deviation (MDEV) at elevation cutoffs of 10°, 20°, 30° and 40°. As the cutoff increases from 10° to 40°, the mean number of visible satellites for GCE decreases from 26.06 to 11.42, while the mean TDOP increases from 0.547 to 3.482. Adding LEO observations increases satellite visibility by 17.2%–44.9% and reduces TDOP by 14.6%–27.6%. Across all four cutoffs, GCE + LEO shortens time-link convergence; the six-link median reductions are 16.4%, 25.0%, 22.2% and 31.6%, respectively, with a generally larger convergence benefit at higher cutoffs. The steady-state STD shows a different cutoff dependence: at 10°, all six links exhibit STD reductions, with a median link-wise relative reduction of 22.7%; at 20° and 30°, the median changes are both about −1.5%, and some links show slight increases of only a few percent; at 40°, the median change is only about 0.2%, indicating only a marginal difference between the two schemes. At an averaging time of τ = 3000 s, the six-link median MDEV reduction decreases from 48.9% at 10° to 2.1% at 40°. These results indicate that LEO augmentation of PPP time transfer is stage dependent: under restricted observing conditions it mainly accelerates the time link into a usable state, whereas under more favourable observing conditions it more clearly improves steady-state dispersion and medium-to-long-term frequency stability.