## 4 Minimum Acceleration Combination Technique: Rationale and Applications
A simplified version of the MinA algorithm, which only computes the time-series of E-W and U-D components and estimates the rate of deformation along the N-S direction is detailed in [32]. Notice that in the areas where the expected N-S deformation is almost negligible the algorithm can be further simplified by only considering as unknowns the E-W and U-D displacement signals. MinA algorithm can be simply complemented, as a post-processing phase, with additional data, such as GPS, PO-based and levelling measurements, with no drastic modifications of the original algorithm. The general scheme of the MinA algorithm is shown in Figure 19.  
An example, consisting of the application of the MinA algorithm to a data archive relevant to the Big Island of Hawaii (U.S.) was presented in [32]. Dataset was composed by 36 Stripmap and 13 ScanSAR images acquired on descending orbits (Track 200, Frame 3231) and 23 Stripmap and seven ScanSAR images collected on ascending orbits (Track 93, Frame 387) by the ASAR/ENVISAT satellite, spanning the overall time interval between 20 January 2003 and 22 September 2009. Figures 20-22 show the mean displacement velocity maps as well as a selection of E-W, U-D and N-S displacement time-series relevant to pixels located in areas with significant deformations. Let us finally discuss the accuracy of the 3-D displacement time-series retrieved by applying the MinA technique by comparing time-series with continuous GPS measurements available over the Big Island area. The deformation time-series for the E-W, U-D and N-S components are shown  
Figure 19: MinA diagram block. K independent sets of LOS measurements of the surface ground displacement, as obtained by processing data from K multi-angle/multi-sensor SAR systems, are combined (taking into account the associated quality reconstruction maps). The combination is based on the application of minimum-acceleration constraints on the achievable U-D, E-W and N-S time-series of deformation. (Adapted with permission from [32], IEEE, 2016). in Figures 20-22, where the combined time-series are represented with black triangles and the GPS measurement with red stars. Standard deviation values of the difference between DInSAR and GPS data are indicated in the presented plots. In this analysis, GPS measurements were assumed as a reference, thus neglecting any possible errors that may affect the data. As a result of the comparison, it was demonstrated that U-D and E-W time-series have an accuracy (on average) of about 8 and 9 mm, respectively. Conversely, N-S displacements estimates have accuracy of the order of 2.5 cm. Note that a simplified version of the MinA algorithm was applied in this case, allowing only the estimate of the N-S deformation rate. Accordingly, areas characterized by severe non-linear deformation signals (see for instance the deformation related to KTM GPS station) show worse accuracies (of about 8 cm in the case of KTM station). As expected, the N-S displacement time-series retrieval accuracy is on the order of a few centimetres, whereas for the E-W and U-D component it is on the order of some millimetres. Figure 20: U-D DinSAR results relevant to Big Island of Hawaii, U.S. (**a**) false colour mean displacement velocity map superimposed on a grey-scale SAR amplitude image of the area. (**b–g**) Plots of the U-D time-series (black triangles) compared to GPS-driven U-D time-series of displacement (red stars). GPS locations are highlighted in (**a**). (Adapted with permission from [32], IEEE, 2016). However, these values are better than ones expected by using Pixel-Offset [139] or Multiple-Aperture-Interferometry [147, 148] techniques, which are on the order of fractions of the image pixel dimension (on the order of 10 centimetres, or more). As an additional example, we also show in Figure 23 the results of another experiment performed by combining a set of COSMO-SkyMed and Sentinel-1A SAR data acquired over the coastal area of Shanghai.