Abstract
ABSTRACT The positioning service aided by low Earth orbit (LEO) mega-constellations has become a hot topic in recent years. To achieve precise positioning, accuracy of the LEO clocks is important for single-receiver users. To bridge the gap between the applicable time of the clock products and the time of positioning, the precise LEO clocks need to be predicted over a certain period depending on the sampling interval of the clock products. This study discusses the prediction errors for periods from 10 s to 1 h for two typical LEO clock types, i.e. the ultra-stable oscillator (USO) and the oven-controlled crystal oscillator (OCXO). The prediction is based on GNSS-determined precise clock estimates, where the clock stability is related to the GNSS estimation errors, the behaviors of the oscillators themselves, the systematic effects related to the environment and the relativistic effects, and the stability of the time reference. Based on real data analysis, LEO clocks of the two different types are simulated under different conditions, and a prediction model considering the systematic effects is proposed. Compared to a simple polynomial fitting model usually applied, the proposed model can significantly reduce the prediction errors, i.e. by about 40%-70% in simulations and about 5%-30% for real data containing different miss-modeled effects. For both clock types, short-term prediction of 1 min would result in a root mean square error (RMSE) of a few centimeters when using a very stable time reference. The RMSE amounts to about 0.1 m, when a typical real-time time reference of the national center for space studies (CNES) real-time clocks was used. For long-term prediction of 1 h, the RMSE could range from below 1 m to a few meters for the USOs, depending on the complexity of the miss-modeled effects. For OCXOs, the 1 h prediction could lead to larger errors with an RMSE of about 10 m.
Highlights
In recent years, thousands of low Earth orbit (LEO) satellites launched or planned to be launched by com panies like SpaceX, OneWeb, Iridium and Orbcomm are about to form a dense satellite network near the Earth, i.e. with an altitude from a few hundreds of kilometers to about 1500 km (Montenbruck and Gill 2000; Reid et al 2018)
The prediction is based on GNSSdetermined precise clock estimates, where the clock stability is related to the global naviga tion satellite systems (GNSSs) estimation errors, the behaviors of the oscillators themselves, the systematic effects related to the environment and the relativistic effects, and the stability of the time reference
Compared to a simple polynomial fitting model usually applied, the proposed model can significantly reduce the prediction errors, i.e. by about 40%-70% in simulations and about 5%-30% for real data containing different miss-modeled effects
Summary
Thousands of low Earth orbit (LEO) satellites launched or planned to be launched by com panies like SpaceX, OneWeb, Iridium and Orbcomm are about to form a dense satellite network near the Earth, i.e. with an altitude from a few hundreds of kilometers to about 1500 km (Montenbruck and Gill 2000; Reid et al 2018). Apart from the real-time high-precision GNSS products, another limitation for the on-board processing can be attributed in some satellites to the limited computational power, which leads to the usage of simplified dynamic models in the POD and reduced precision in both the orbits and the clocks (Montenbruck and Ramos-Bosch 2008). Considering this fact, in this contribution, the clock estimates are estimated with the kinematic POD without using any dynamic models. 10 s 5 degrees IF combination of GPS phase (L1, L2) and code (P1, P2) 24 h Gravity of the Earth: EGM2008, degree 120 (Pavlis et al 2008) Gravity of other planets: JPL DE405 (Planetary ephemeris) (Standish 1998) Tides of solid Earth and Pole: IERS Conventions 2010 (Petit and Luzum 2010) Ocean tides: FES2004 (Lyard et al 2006) Relativistic effects GNSS/LEO antenna offsets, PCOs, PCVs Geometric distance between the a p riori LEO orbits and the GPS orbits GPS satellite clocks and the a priori LEO satellite clocks Phase wind-up effects Relativistic effects in the GPS clocks Shapiro relativistic corrections between LEO and GPS satellites biases are assumed to be constant in this study (Wang et al 2018), and do not influence the clock prediction
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