Filtering GPS time-series using a vondrak filter and cross-validation

Multipath disturbance is one of the most important error sources in high-accuracy global positioning system (GPS) positioning and navigation. A new data filtering method, based on the Vondrak filter and the technique of cross-validation, is developed for separating signals from noise in data series, and applied to mitigate GPS multipath effects in applications such as deformation monitoring. Both simulated data series and real GPS observations are used to test the proposed method. It is shown that the method can be used to successfully separate signals from noise at different noise levels, and for varying signal frequencies as long as the noise level is lower than the magnitude of the signals. A multipath model can be derived, based on the current-day GPS observations, with the proposed method and used to remove multipath errors in subsequent days of GPS observations when taking advantage of the sidereal day-to-day repeating characteristics of GPS multipath signals. Tests have shown that the reduction in the root mean square (RMS) values of the GPS errors ranges from 20% to 40% when the method is applied.[PUBLICATION ABSTRACT]