Separation of continuous GPS transients using independent component analysis and low rank methods

Abstract:

We present our research on the de-noising and interpolation of missing continuous GPS data and the subsequent un-mixing of transients based on the assumption that there are relatively few signals of interest linearly mixed in the data, resulting in a low rank subspace. Continuous GPS measurements contain high levels of noise from a variety sources that can be treated as a combination of Gaussian white noise, spatially correlated noise, and flicker noise. The noise obscures various weak transient signals arising from either tectonic or seasonal hydrologic processes. Both noise and numerous gaps in the data recordings due to weather or station failure complicate identification of transient events. When continuous GPS network data is represented as matrix, we demonstrate that the transient signals of interest are low rank. Based on this assertion, we apply a set of rank penalized algorithms that interpolate and de-noise GPS data. Furthermore, to isolate the mixed transients, we apply Independent Component Analysis (ICA), a technique that separates signals based on statistical independence, and compares the performance to existing techniques that use Principle Component Analysis (PCA). We apply these techniques on both synthetic and real position time series from UNAVCO’s Plate Boundary Observatory in southern California.