The Consideration of Formal Errors in Spatiotemporal Filtering Using Principal Component Analysis for Regional GNSS Position Time Series

In the daily operation of regional GNSS (Global Navigation Satellite System) networks, the formal errors of all stations' coordinate components are calculated. However, spatiotemporal filtering based on traditional Principal Component Analysis (PCA) for regional GNSS position time series does not take these formal errors into account. This paper developed a PCA-based approach to extract Common Mode Error (CME) from the position time series of a regional GNSS station network, where formal errors were applied to construct a weight factor. Because coordinate components with larger errors have smaller weight factors in extracting CME, the performance of our proposed approach was anticipated to be better than the traditional PCA approach. The position time series of 25 stations in the Yunnan Province, China, were analyzed using our approach, as well as the traditional PCA approach. The average errors of the residual time series after removing the CMEs with our approach were 1.30 mm, 1.72 mm, and 4.62 mm for North, East and Up components, and the reductions with respect to those of the original time series were 18.23%, 15.42%, and 18.25%, respectively. If CMEs were removed from the traditional PCA approach, the corresponding average errors were 1.34 mm, 1.81 mm, and 4.84 mm, with reductions of 15.84%, 10.86%, and 14.32%, respectively. Compared to the traditional PCA approach, the average errors of our approach were reduced by about 2.39%, 4.56%, and 3.93% in the North, East and Up components, respectively. Analysis of CME indicated that it mainly contained white and flicker noise. In the synthetic position time series with 500 repeated simulations, the CME extracted by our approach was closer to the true simulated values than those extracted by the traditional PCA approach, regardless of whether local effects were considered or not. Specifically, the mean root mean square (RMS) reduction of our approach, relative to PCA, ranged from 1.35% to 3.93%. Our simulations illustrated that the RMS reductions depended not only on the magnitude, but also the variation of the formal error series, which further highlights the necessity of considering formal errors in spatiotemporal filtering.