On the Exploitation of Target Statistics for SAR Interferometry Applications A. Monti Guarnieri, S. Tebaldini Politecnico di Milano Abstract—This paper 1 focuses on multi-image Synthetic Aper- ture Radar Interferometry (InSAR) in presence of distributed scatterers, paying particular attention to the role of target decorrelation in the estimation process. This phenomenon is accounted for by splitting the analysis into two steps. In the first step we estimate the interferometric phases from the data, while in the second step we use these phases to retrieve the physical parameters of interest, such as Line of Sight (LOS) displacement and residual topography. In both steps we make the hypothesis that target statistics are at least approximately known. This approach is suited both to derive the performances of InSAR with different decorrelation models and for providing an actual estimate of LOS motion and DEM. Results achieved from Monte- Carlo simulations and a set of repeated pass ENVISAT images are shown. I. I NTRODUCTION The next generation of satellite-born SARs operating in P, L, C and X band, will provide new and undiscovered potentials for SAR interferometry (InSAR). Better orbital control and shorter revisiting times will allow to infer accurate information from repeated revisits over distributed targets, subjected to geometrical and temporal decorrelation. The lack of such systems in the past brought the literature to focus on the case of Permanent Scatterers (PS) that are, by definition, highly coherent and stable in the long term and for wide baseline spans [2], [3]. Several approaches have been presented in literature to per- form SAR interferometric analysis over scenes where the PS assumption may not be retained, such as forests, agricultural fields, soil or rock surfaces, or ice shelves. A number of these works share the idea to minimize the effect of target decorrelation by forming the interferograms from properly selected pairs, rather than with respect to a fixed reference image, as done in PS processing. Despite the good results achieved in the applications, however, there’s no clear and formal assessment of the criteria which should drive the selection of the image pairs to be used. As a result, the processing is heuristically based on the exploitation of a set of interferograms taken with the shortest temporal and/or spatial baselines possible [4], [5], [6]. A more sophisticated approach is the one exploiting the concept of Small Baseline Subsets (SBAS) [7], [8]. This technique accounts for spatial decorrelation phenomena by partitioning the data set into a number of subsets, each of which is constituted by images acquired from orbits close to each other. Then, the inversion of the parameters of interest 1 Part of this work was presented at IGARSS07, Barcelona [1]. is carried out on the basis of a minimum norm criterion exploiting the phases of all the available interferograms in each subset. With respect to these works, the aim of this paper is to propose an approach that formally accounts for the impact of target decorrelation, in such a way as to drive the interferogram selection and the estimation of the parameters of interest basing on statistical criteria. The basic idea is to split the estimation process into two steps 2 . In the first step, a maximum likelihood (ML) estimator is used that jointly exploits all the N × (N − 1)/2 interfer- ograms available with N acquisitions, in order to yield the best estimates of N − 1 phases, with one degree of freedom. Target decorrelation is accounted for by properly weighting each interferogram depending on the target statistics. In the following we will define the N − 1 estimated interferometric phases as Linked Phases (LPs), to remind that these terms are the result of the joint processing of all the N × (N − 1)/2 interferograms. Once the first estimation step has yielded the estimates of the interferometric phases, the second step is required to separate the contributions of the Atmospheric Phase Screen (APS) and the decorrelation noise from the parameters of interest, such as the Line of Sight Deformation Field (LDF) and the topography. It will be shown hereinafter that this two-step approach is consistent with the best estimate of LDF parameters provided by the Hybrid Cram´ er Rao bound (HCRB) [10]. A work naturally related to this paper is the one by Rocca [11]. In a sense, also in that paper a two step approach is proposed, in that first N ×(N −1)/2 interferograms are formed out of N acquisitions, and then the second order statistics of the interferograms are exploited to derive the optimal linear estimator of the parameters of interest, under the small phase approximation. The difference between the approach within this paper and the one by Rocca is that in this paper we deal with the problem of parameter estimation directly from the data, rather than from the interferograms, which constitutes a more rigorous treatment of the information carried by the data. Clearly, the two approaches converge asymptotically (i.e. large signal to noise ratio, large data space). The paper is organized as follows. Section II depicts the model of the SAR Single Look Complex (SLC) data to be exploited in the sections to follow. In section III the asymptotic 2 From the point of view of the estimation theory, the theoretical justification for splitting the estimation process into two steps may be proved by invoking the Extended Invariance Principle [9].