Missing Data Imputation in GNSS Monitoring Time Series Using Temporal and Spatial Hankel Matrix Factorization

GNSS time series for static reference stations record the deformation of monitored targets. However, missing data are very common in GNSS monitoring time series because of receiver crashes, power failures, etc. In this paper, we propose a Temporal and Spatial Hankel Matrix Factorization (TSHMF) method that can simultaneously consider the temporal correlation of a single time series and the spatial correlation among different stations. Moreover, the method is verified using real-world regional 10-year period monitoring GNSS coordinate time series. The Mean Absolute Error (MAE) and Root-Mean-Square Error (RMSE) are calculated to compare the performance of TSHMF with benchmark methods, which include the time-mean, station-mean, K-nearest neighbor, and singular value decomposition methods. The results show that the TSHMF method can reduce the MAE range from 32.03% to 12.98% and the RMSE range from 21.58% to 10.36%, proving the effectiveness of the proposed method.

Automated summary

This paper proposes a method called TSHMF that considers both temporal and spatial correlation in monitoring GNSS time series, effectively addressing the issue of missing data. The method outperforms benchmark methods according to the experimental results.