Decomposition of geodetic time series: A combined simulated annealing algorithm and Kalman filter approach

Abstract In this paper we propose a network-based Kalman filter combined generalized simulated annealing algorithm approach to decompose a group of GPS position time series into secular trend, annual and semi-annual signals as well as noise components. This approach treats east, north and vertical components of the whole network separately and estimates network-average process-noise parameters to constrain the time variability of the seasonal signals and noise components. Each coordinate component for each station is modeled in state-space model (SSM) individually. The noise components are described as the combination of flicker noise (FN), random walk noise (RWN) and observation white noise (WN). Each component, except for the trend, is allowed to variate over the time, and their amplitudes are estimated by maximization of likelihood function using a generalized simulated annealing (GSA) algorithm. The proposed approach is applied to 10 reprocessed GPS position time series from the Tectonic and Environmental Observation Network of Mainland China (CMONOC II), and its output is compared with that of ordinary maximum likelihood estimation (MLE). The results show that the proposed approach is an effective tool for the decomposition of GPS position time series. Finally, the advantages and limitations of the proposed approach are also discussed.