## 3 Multi-Track/Multi-Satellite InSAR Methodologies
Although PO methods have mostly been devoted to studying single deformation events, some efforts have also been made for extending these techniques to the generation of 3-D displacement time series, by combining the information derived from both sequences of multi-temporal DInSAR interferograms and amplitude maps. In particular, this is the case of the Pixel-Offset SBAS (PO-SBAS) technique [139]. The algorithm analyses the amplitudes of selected image pairs to calculate the relative across-track (range) and along-track (azimuth) pixel-offsets and inverts them through an SVD method for the retrieval of the range and the azimuthal displacement time-series. Experiments carried out using ENVISAT images collected over Sierra Negra Caldera have proved the capability of the PO-SBAS technique to investigate the temporal evolution of large or rapidly varying surface deformation phenomena, guaranteeing accuracy values of the order of 10-12 cm. Very recently, a method for retrieving the 3-D components associated with massive deformation episodes, fully-based on the use of PO-SBAS measurements have been presented in [140]. The key idea of [140] is to combine the PO-SBAS time-series, which represent a direct measure of the deformation along the sensor-azimuthal direction (roughly parallel to N-S) and the LOS direction, taking into account the orbital flight parameters. To overcome the problem that orbitals are not coeval, the combination is performed by assuming that ascending and descending acquisitions are as close as possible in time (i.e., by considering them as acquired at the same time. A way to overcome this limitation has been studied in [136; 141; 142; 143; 132]. In particular, the Minimum Acceleration (MinA) combination algorithm has been developed in such a way to complement PO-SBAS, GPS and InSAR-based measurements in a single framework (see Section 4 for additional details). Very recently, innovative DInSAR-based combination approaches relying on the use of a Kalman filter have also been proposed [136]. More specifically, a method to combine overlapping segments of SAR images acquired at adjacent tracks to generate high spatiotemporal resolution maps of the (combined) LOS displacement field has been presented in [141]. Within this general context, in [142; 143], similar methods have been proposed for the combination of multi-track interferograms from various sensors and orbital positions; thus, obtaining time series of the U-D and E-W displacement. These approaches preserve the temporally variable components of the deformation field and, practically, assume the N-S deformation negligibility. In particular, the algorithm presented in [142], which is known in the literature to as Multiple-SBAS (MSBAS) consists of generating and simultaneously processing a considerable sequence of multiple-platform differential SAR interferograms. The latter are jointly inverted to recover (over the geocoded grid common to all available SAR data tracks) 2-D (U-D and E-W) surface deformation time-series by solving an underdetermined system of linear equations. This latter relates the LOS displacements relevant to all the available unwrapped interferograms to the (unknown) 2-D deformation components and it is inverted through the LS approach by searching for a minimum-norm (MN)-velocity solution based on the use of the Tikhonov regularization [143; 144].