On the Definition of an Independent Stochastic Model for InSAR Time Series

Abstract

Interferometry SAR (InSAR) enables the estimation of displacements of (objects on) the Earth’s surface. To provide reliable estimates, both an independent stochastic and functional model are required. However, the intrinsic problem of InSAR is that both are unknown. Here, we propose an independent definition of the stochastic model, via an approximation scheme for the variance–covariance matrix (VCM) for double-differenced phase observations for an arc, i.e., the phase difference between two points relative to a reference epoch. Detecting temporal partitions in the amplitude time series, we assign quality values to all phase observations within each partition. To reduce the impact of outliers, we introduce the normalized median absolute deviation (NMAD) of the vector of amplitudes to robustly estimate the variance of the phase observations. The method results in a scatterer-specific and time-variable stochastic model, which is independent of the phase observations itself and prior to parameter estimation. This differs from many conventional methods, where the quality is often determined a posteriori from the residuals between the model and the observations. This yields more realistic and reliable displacement estimates, as well as improved statements on the precision and reliability of the estimated parameters.