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 satellite. This delay can result in GPS positioning error. Thus, it is important to monitor the TEC maps. The observed TEC maps have big patches of missingness in the ocean and scattered small areas of missingness on the land. In this paper we propose several extensions of existing matrix completion algorithms to achieve TEC map reconstruction, accounting for spatial smoothness and temporal consistency while preserving important structures of the TEC maps. We call the proposed method video imputation with softImpute, temporal smoothing and auxiliary data (VISTA). Numerical simulations that mimic patterns of real data are given. We show that our proposed method achieves better reconstructed TEC maps, as compared to existing methods in literature. Our proposed computational algorithm is general and can be readily applied for other problems besides TEC map reconstruction.
Funding Statement
This work (SZ, YC, and JR) is supported by NASA DRIVE Center at the University of Michigan under grant NASA 80NSSC20K0600. SZ acknowledges NASA award 80NSSC20K1313 and 80NSSC20K0190. YC acknowledges support from NSF DMS Award 1811083 and 2113397. SZ and YC also acknowledges NSF PHY Award 2027555.
Citation
Hu Sun. Zhijun Hua. Jiaen Ren. Shasha Zou. Yuekai Sun. Yang Chen. "Matrix completion methods for the total electron content video reconstruction." Ann. Appl. Stat. 16 (3) 1333 - 1358, September 2022. https://doi.org/10.1214/21-AOAS1541
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