Statistically-Based Trend Analysis of MTInSAR Displacement Time Series

Current multi-temporal interferometric Synthetic Aperture Radar (MTInSAR) datasets cover long time periods with regular temporal sampling. This allows high-rate and non-linear trends to be observed, which typically characterize pre-failure warning signals. In order to fully exploit the content of MTInSAR products, methods are needed for the automatic identification of relevant changes along displacement time series and the classification of the targets on the ground according to their kinematic regime. This work reviews some of the classical procedures for model ranking, based on statistical indices, which are applied to the characterization of MTInSAR displacement time series, and introduces a new quality index based on the Fisher distribution. Then, we propose a procedure to recognize automatically the minimum number of parameters needed to model a given time series reliably within a predefined confidence level. The method, though general, is explored here for polynomial models, which can be used in particular to approximate satisfactorily and with computational efficiency the piecewise linear trends that are generally used to model warning signals preceding the failure of natural and artificial structures. The algorithm performance is evaluated under simulated scenarios. Finally, the proposed procedure is also demonstrated on displacement time series derived by the processing of Sentinel-1 data.