Transformer Deep Learning for Accurate Orbit Corrections in Real-Time

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

Abstract: Fixing receiver positions from Global Navigation Satellite System (GNSS) satellites requires the accurate estimate of the orbit position of the satellites at the time the satellites transmit their ranging signal. The satellite orbit estimates are calculated from broadcasted ephemeris parameters obtained from navigation data. However, the broadcasted orbits may have errors up to 3 m or more. Because there are disturbances from both internal and external factors, such as internal satellite inertial, solar radiation pressures and gravity effects influencing the satellite’s dynamic. With these errors, a precise positioning with up to few cm accuracies is difficult to obtain. To reduce the errors, the estimated orbits need to be compensated. The common way to correct broadcasted satellite orbit is to leverage the high-accuracy final product of international GNSS service (IGS). However, the IGS final products for orbit estimation are available after more than ten days so that real-time corrections cannot be calculated. In addition, an internet connection is required to access the product so that stand-alone receiver operation cannot be performed. In this paper, the development of transformer deep neural model for real-time and accurate satellite orbit correction prediction up to two-hour ahead of time horizon is presented. The proposed transformer model has approximately 8.6 million parameters with 34 MB of size. The corrections data to train the model are calculated from the difference between broadcasted orbits and IGS final product. The training data are up to three years period with 30s data interval. The selection of the transformer model is the results from experimental comparisons among other models, including ARIMA as baseline and other neural network models (deep multi-layer perceptron (MLP) and long short-term memory (LSTM) network). Results show that the transformer model gives the best prediction accuracy for up to 0.4m. The transformer model predictions are compared with IGS Rapid and CODE-MGEX product as well as among different GPS satellite blocks and satellite clock types (Rubidium and caesium). From the comparisons, the transformer model can perform prediction for up to 50% higher accuracy than the IGS rapid product and CODE-MGEX product. The orbit prediction accuracy of the transformer model is < 2 m. The prediction model can be integrated into various types of GNSS receiver without changing their infrastructure.
Published in: Proceedings of the 36th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2023)
September 11 - 15, 2023
Hyatt Regency Denver
Denver, Colorado
Pages: 159 - 174
Cite this article: Syam, Wahyudin P., Priyadarshi, Shishir, Roqué, Andrés Abelardo García, Conesa, Alejandro Pérez, Buscarlet, Guillaume, Orso, Mickael Dall’, "Transformer Deep Learning for Accurate Orbit Corrections in Real-Time," Proceedings of the 36th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2023), Denver, Colorado, September 2023, pp. 159-174.
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