Filling missing values of multi-station GNSS coordinate time series based on matrix completion

•Realizing the interpolation of multi-station time series in a simultaneous way.•The method is non-parametric and keep the user intervention at minimum.•The patterns in both time and space domains are explored.•Different noise type is considered in the simulation experiment.•Numerical simulation is used to verify the performance of the proposed method. Global Navigation Satellite System (GNSS) coordinate time series inevitably suffer from random and even continuous missing data. However, many processing methods of GNSS time series analysis require continuous data, namely without any gaps. Therefore, interpolating data or filling the gaps is an important preprocessing step. Conventional methods including piecewise linear, cubic spline, cubic polynomial do this work station by station, implying that they often focus on single point time series. It is proposed in this work to use a technique called matrix completion, which is based on singular value thresholding algorithm. This is a spatio-temporal method as it can realize the interpolation of multi-station time series in a simultaneous way. Due to this spatio-temporal nature, the patterns in both time and space domains are explored and hence better interpolation performance can be expected. This method is non-parametric and highly automatic, keeping the user intervention at minimum. Both the simulation data and real-data in the experiment, through calculating the root mean square errors (RMSE) between artificial gaps and interpolation results, the proposed method shows the satisfactory performance.