LAUSR

Missing data are critical deficiency in the investigation of displacement measurement in urban Internet of Things system. In the insight of recovering missing displacement data, this article presents a data-driven and high-dimensional gap-imputation method, Tucker decomposition with L2 regularization. Results on the global navigation satellite system (GNSS) time series collected from an intelligent structural health monitoring system show that the recovery accuracy is improved compared with some popular benchmark methods. When the missing rate is 50%, compared with singular spectrum analysis, singular value decomposition, CP optimization algorithm, $k$ -nearest neighbors, and Tucker decomposition via alternating least squares, Tucker decomposition with L2 regularization can improve the average mean absolute error by about 4.74, 4.95, 5.82, 2.29, and 5.67 mm for all locations. It can be concluded that the consideration of multiple temporal correlations is necessary for missing data imputation. Compared with matrix decomposition, tensor decomposition can improve the ability for high-dimensional correlations in the GNSS time series.