This thesis delves into the realm of Multi-Temporal Interferometric Synthetic Aperture Radar (MT-InSAR) techniques, particularly Phase Linking algorithm, for precise displacement measurements while mitigating signal decorrelation. Following the unprecedented volume of free-access SAR data, the demand for an algorithm with low computational load has raised, enabling the analysis of a longer time series over larger coverage. Moreover, recent missions offer high resolution data source and necessitate algorithms that can ensure the estimation accuracy while retaining the spatial resolution. Hence, in response to these challenges, our objectives are twofolds: i) to formulate and develop a mathematical framework where Phase Linking is reformulated into a covariance fitting optimization problem; ii) to introduce a robust estimation framework based on Phase Linking. The performances of the proposed algorithms are analysed through simulations and a real data case study encompassing the Mexico City.