Fast and Reliable Forecasting for Satellite Clock Bias Correction with Transformer Deep Learning

Wahyudin P. Syam, Shishir Priyadarshi, Andrés Abelardo García Roqué, Alejandro Pérez Conesa, Guillaume Buscarlet, Mickael Dall’ Orso

Abstract:	Global Navigation Satellite System (GNSS) typically use ranging signals to provide a global-coverage solution for positioning, velocity and timing applications. An accurate and stable clock is required for pseudorange estimation and GNSS timeline. The very accurate and long-time stable on-board atomic clocks on each GNSS satellite (SV), without any corrections after a certain period, will deviate from GNSS time and cause the significant reduction of position accuracies. To correct the atomic clocks bias, GNSS main ground-control stations accurately estimate the bias, usually having a residual approximately between 1 ns and 10 ns (corresponding to pseudorange error up to 0.3 – 3 m) respectively and re-transmit the correction to the SV. For critical application that require precise positioning at decimetre-level accuracy, an accurate clock bias correction, in the order of 3 ns (< 1 m pseudorange error) is required. For Global Positioning System (GPS), the clock bias correction interval is few hours with potential drift can be up to > 12 ns, leading to > 4 m pseudorange error. International GNSS Service (IGS) provides accurate clock bias corrections that can be openly accessed. IGS final product provides clock bias correction ±75 ps accuracy with availability 12-18 days. Alternatively, IGS ultra-rapid product provides clock bias correction with accuracy of 3 ns - 5 ns (pseudorange error up to 1.5 m). Another drawback of using IGS product is that the receiver data processing unit should be connected to internet and to download IGS clock-bias. In this paper, the development and performance evaluation of a Machine Learning (ML) time-series model, based on a transformer deep neural network, for SV clock bias correction prediction tool are presented. The main purpose of the developed ML software tool is to provide fast and reliable forecasting of clock bias correction for stand-alone single-frequency receivers without changing the infrastructure of the receivers and with prediction accuracy of < 2 ns. From the training results, the target prediction accuracy, up to two-hour time horizon, of < 2ns can be achieved. Performance analysis and comparison of the developed transformer model prediction with respect to IGS rapid, CODE-MGEX clock-bias product and holdover method are performed. In addition, prediction comparison among difference SV block and clock-types are also presented. From all the comparisons, the ML predictions perform up to 50% better than the other clock-bias prediction methods.
Published in:	Proceedings of the 54th Annual Precise Time and Time Interval Systems and Applications Meeting January 23 - 26, 2023 Hyatt Regency Long Beach Long Beach, California
Pages:	76 - 96
Cite this article:	Syam, Wahyudin P., Priyadarshi, Shishir, Roqué, Andrés Abelardo García, Conesa, Alejandro Pérez, Buscarlet, Guillaume, Orso, Mickael Dall’, "Fast and Reliable Forecasting for Satellite Clock Bias Correction with Transformer Deep Learning," Proceedings of the 54th Annual Precise Time and Time Interval Systems and Applications Meeting, Long Beach, California, January 2023, pp. 76-96. https://doi.org/10.33012/2023.18702
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