Abstract: The total electron content (TEC) maps can be used to estimate the signal delay of GPS due to the ionospheric electron content between a receiver and a satellite. This delay can result in a GPS positioning error. Thus, it is important to monitor and forecast the TEC maps. However, the observed TEC maps have big patches of missingness in the ocean and scattered small areas on the land. Thus, precise imputation and prediction of the TEC maps are crucial in space weather forecasting.

In this talk, I first present several extensions of existing matrix completion algorithms to achieve TEC map reconstruction, accounting for spatial smoothness and temporal consistency while preserving essential structures of the TEC maps. We show that our proposed method achieves better reconstructed TEC maps as compared to existing methods in the literature. I will also briefly describe the use of our large-scale complete TEC database. Then, I present a new model for forecasting time series data distributed on a matrix-shaped spatial grid, using the historical spatiotemporal data and auxiliary vector-valued time series data. Large sample asymptotics of the estimators for both finite and high dimensional settings are established, and performances of the model are validated with extensive simulation studies and an application to forecast the global TEC distributions.

https://yangchenfunstatistics.github.io/yangchen.github.io/