A method for detecting transient signals in GPS position time-series: smoothing and principal component analysis

We test a method for detecting anomalous transient signals from Global Positioning System (GPS) data. The method enhances signal-to-noise ratios of GPS position time-series through smoothing based on Kalman filter formulations in the time domain and principal component analysis (PCA) in the space domain. The smoother reduces measurement white noise, accounts for correlated noise and interpolates missing data. A first-order Gauss-Markov (FOGM) process is used in the state vector to estimate transient signals and correlated noise. The parameters of the FOGM and white processes are determined by minimizing cost functions constructed with the innovations sequence from the forward Kalman filter. PCA decomposes the FOGM state estimates into principal components (PCs) for temporal variation and sample eigenvectors for spatial distribution. Uncertainties of the PCA estimates are approximated by propagating errors for PCs and by using asymptotic distributions with an effective sample size for sample eigenvectors. The uncertainties can help determine the significance of the temporal variations of the PCs and the spatial distribution of sample eigenvectors. When the FOGM noise process has a long correlation time, the high order PCs show oscillatory behaviour and we develop a method to remove these effects. We show two examples of the detection capability of the algorithm with applications to transients in the Los Angeles basin, California, from the distant Hector Mine Earthquake in 1999 and ground water changes in 2005.