LEO satellite clock analysis and prediction for positioning applications

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.

KEYWORDS:

• LEO
• clock prediction
• USO
• OCXO
• relativistic effects

Acknowledgments

The authors appreciate the discussions about the LEO clock behaviours with the GRACE team of the Jet Propulsion Laboratory (JPL) and the Copernicus Precise Orbit Determination (POD) Service.

Data availability statement

The data of GRACE FO-1 were obtained from the JPL via https://podaac-tools.jpl.nasa.gov/drive/files/allData/gracefo. The data of SENTINEL-3B were obtained from the ESA via https://scihub.copernicus.eu/gnss/#/home. The real-time products of the National Centre for Space Studies (CNES) were obtained from http://www.ppp-wizard.net/products/REAL_TIME/. The final products of the Center for Orbit Determination in Europe (CODE) were obtained from ftp://ftp.aiub.unibe.ch/CODE/. The products of the International GNSS Service (IGS) real-time service (RTS) and the IGS final products were obtained from the Crustal Dynamics Data Information System (CDDIS) https://cddis.nasa.gov/archive/gnss/products/. The products of the Multi-GNSS Advanced Demonstration of Orbit and Clock Analysis (MADOCA) service were obtained from the Japan Aerospace Research and Development Agency (JAXA) ftp://mgmds01.tksc.jaxa.jp/mdc1/.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is funded by the Australian Research Council [Project number DP 190102444] Tracking Formation-Flying of Nanosatellites Using Inter-Satellite Links.

Notes on contributors

Kan Wang

Kan Wang is a research fellow in the School of Earth and Planetary Sciences, Curtin University. She obtained her doctoral degree in GNSS advanced modeling from ETH Zurich in 2016. Her research interest includes high-accuracy GNSS positioning, clock modeling, LEO POD, integrity monitoring, SBAS, and PPP-RTK processing.

Ahmed El-Mowafy

Ahmed El-Mowafy is Assoc. Professor of Positioning and Navigation and Director of Graduate Research, School of Earth and Planetary Sciences, Curtin University, Australia. He obtained his Ph.D. from the University of Calgary, Canada. He has extensive publications in precise positioning and navigation using GNSS, quality control, integrity monitoring and estimation theory.