Weighted empirical mode decomposition for processing GNSS position time series with the consideration of formal errors

Abstract

Empirical Mode Decomposition (EMD) is suitable to process the nonlinear and non-stationary time series for filtering noise out to extract the signals. The formal errors are provided along with Global Navigation Satellite System (GNSS) position time series, however, not being considered by the traditional EMD. In this contribution, we proposed a modified approach that called weighted Empirical Mode Decomposition (weighted EMD) to extract signals from GNSS position time series, by constructing the weight factors based on the formal errors. The position time series over the period from 2011 to 2018 of six permanent stations (SCBZ, SCJU, SCMN, HLFY, FJPT, SNXY) were analyzed by weighted EMD, as well as the traditional EMD. The results show that weighted EMD can extract more signals than traditional EMD from original GNSS position time series. Additionally, the fitting errors were reduced 14.52 %, 12.25 % and 8.06 % for North, East and Up components for weighted EMD relative to traditional EMD, respectively. Moreover, 100 simulations of four stations are further carried out to validate the performances of weighted EMD and traditional EMD. The mean Root Mean Squared Errors (RMSEs) are reduced from traditional EMD to weighted EMD with the reductions of 9.08 %, 9.63 % and 6.84 % for East, North and Up components, respectively, which highlights the necessity of considering the formal errors. Therefore, it reasonable to conclude that weighted EMD can extract the signals more than traditional EMD, which can be suggested to analyze GNSS position time series with formal errors.