Legendre Polynomials for Nonlinear Modeling in InSAR Time Series

In the Interferometric Synthetic Aperture Radar Time Series (InSAR TS) analysis, Standard Polynomials (SP) are commonly employed to model ground deformation. However, these functions aim to be of low order, thus limiting the modelling of complex patterns and potentially overlooking actual phenomena due to temporal decorrelation. This paper proposes an alternative approach, leveraging Legendre Polynomials (LP) to model nonlinear deformations within the Small BAseline Subset (SBAS) algorithm, explicitly applied during stack inversion of unwrapped interferograms. We conducted numerical simulations with synthetic data to model distinct nonlinear deformation patterns, along with additional simulations based on real observation in the Yakustk region over Siberia. Our findings indicate that the LP approach not only effectively captures nonlinear trends but also exhibits greater robustness against temporal decorrelation compared to SP. Moreover, the LP achieves up to 20% higher correlation coefficients in low SNR conditions, while requiring only half of the parameters estimated by SP. The LP-based SBAS implementation can enhance InSAR TS analysis by adequately modelling and discriminating various ground deformations, without filtering out essential information.