Spatiotemporal filtering using principal component analysis and Karhunen‐Loeve expansion approaches for regional GPS network analysis

TLDR

Spatial filtering improves GPS coordinate precision by reducing common mode errors, but the usual assumption of spatially uniform errors fails for large networks, so PCA and KLE provide a framework to decompose time series into spatially varying modes for spatiotemporal filtering. The study aims to develop a filtering method that lets the data reveal the spatial distribution of common mode errors without assuming uniformity. The authors applied PCA and KLE to daily SCIGN coordinate time series from 2000 to 2004. The analysis shows that spatially and temporally correlated common mode errors dominate daily GPS solutions, exhibit near‑uniform spatial patterns indicating a very long‑wavelength source, and display temporally nonrandom behavior.

Abstract

Spatial filtering is an effective way to improve the precision of coordinate time series for regional GPS networks by reducing so‐called common mode errors, thereby providing better resolution for detecting weak or transient deformation signals. The commonly used approach to regional filtering assumes that the common mode error is spatially uniform, which is a good approximation for networks of hundreds of kilometers extent, but breaks down as the spatial extent increases. A more rigorous approach should remove the assumption of spatially uniform distribution and let the data themselves reveal the spatial distribution of the common mode error. The principal component analysis (PCA) and the Karhunen‐Loeve expansion (KLE) both decompose network time series into a set of temporally varying modes and their spatial responses. Therefore they provide a mathematical framework to perform spatiotemporal filtering. We apply the combination of PCA and KLE to daily station coordinate time series of the Southern California Integrated GPS Network (SCIGN) for the period 2000 to 2004. We demonstrate that spatially and temporally correlated common mode errors are the dominant error source in daily GPS solutions. The spatial characteristics of the common mode errors are close to uniform for all east, north, and vertical components, which implies a very long wavelength source for the common mode errors, compared to the spatial extent of the GPS network in southern California. Furthermore, the common mode errors exhibit temporally nonrandom patterns.