Multifrequency InSAR height reconstruction through maximum likelihood estimation of local planes parameters

Abstract

In this paper, a technique that is able to reconstruct highly sloped and discontinuous terrain height profiles, starting from multifrequency wrapped phase acquired by interferometric synthetic aperture radar (SAR) systems, is presented. We propose an innovative unwrapping method, based on a maximum likelihood estimation technique, which uses multifrequency independent phase data, obtained by filtering the interferometric SAR raw data pair through nonoverlapping band-pass filters, and approximating the unknown surface by means of local planes. Since the method does not exploit the phase gradient, it assures the uniqueness of the solution, even in the case of highly sloped or piecewise continuous elevation patterns with strong discontinuities.

Methods and Performances for Multi-Pass SAR Interferometry

“…The equivalence between (23) and (48) shows that the two step procedure herein described is asymptotically consistent with the HCRB, and thus it may be regarded as an optimal solution at sufficiently large signal-to-noise ratios, or when the data space is large.…”

“…To give an intuitive idea of the conditions that must be met for the HCRB to represent a realistic bound, it is again useful to consider separately the roles of X −1 ε and R α in (23). Assume that the APS can be neglected with respect to the contribution coming from target decorrelation.…”

“…Assume that the APS can be neglected with respect to the contribution coming from target decorrelation. In this case, the bound for the variance of the LDF predicted by (23) defaults to the standard CRB, since it ignores the statistical component represented by the APSs. In formula:…”

“…This last section provides a simple and practical example of an application of the proposed bound (23). For simplicity's sake, the LDF is modeled as a LOS subsidence with constant velocity, v, even though an extension of this analysis to a larger set of unknowns is immediate.…”

“…where the covariance matrix of υ has been determined after (23), by zeroing the contribution of the APSs. Notice that the limit operation could be easily removed by considering a proper transformation of the linked phases in (42), as discussed in section 4.2.…”