Cramer–Rao Lower Bound Analysis of Vegetation Height Estimation With Random Volume Over Ground Model and Polarimetric SAR Interferometry

Abstract

The random volume over ground model, which is based on a simple description of the electromagnetic wave interaction with a vegetated media, allows one to define techniques to estimate the vegetation height from the polarimetric interferometric synthetic aperture radar observations. We discuss this issue with the Cramer-Rao lower bound (CRLB) which provides a minimal bound of the variance independently of the estimation if it is unbiased. The usefulness of this approach is illustrated on three different examples. The first example deals with the influence of a priori knowledge of some physical parameters. We show that reducing the number of unknown physical parameters does not necessarily improve the CRLB. The second example focus on the efficiency of the Cloude et al. height estimator. On the considered data, this estimator reaches the CRLB when the standard deviation equals approximately one meter. In the third example we optimize the radar baseline.