Aurélien Arnaubec

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

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.

Vegetation Height Estimation Precision With Compact PolInSAR and Homogeneous Random Volume Over Ground Model

Analyzing the precision of vegetation height estimation with compact (i.e., single transmit instead of dual transmit) polarimetric interferometric synthetic aperture radar (PolInSAR) with the homogeneous random volume over ground model can help justify the use of this type of radar rather than using the full PolInSAR. However, since compact PolInSAR provides less information than full PolInSAR, a loss of precision in the vegetation height estimation is expected, which can depend on the single transmit polarization. The adaptation of the Cramer-Rao bound (CRB) derived for full PolInSAR in our earlier work to compact PolInSAR measurement provides a general methodology to characterize this loss of precision. Indeed, the CRB is a lower bound of the variance of unbiased estimators that does not depend on the choice of a particular estimation method. We illustrate this methodology for P-band measurements with three synthetic examples chosen for their variability of polarimetric responses. For these examples, it is shown that there can exist a large set of transmit polarizations for which the loss of precision described by the CRB is small (smaller than a factor 2) although there also exist transmit polarizations for which the loss can be large (about a factor 100). This loss of precision is compared with the large dependency of the precision to the vegetation height estimation that can be observed with the vegetation height (more than a factor 100 in the precision described by the CRB) when all the other parameters of the vegetation, ground, and radar system are constant.

Invariant Contrast Parameters of PolInSAR Homogenous RVoG Model

It has been shown that the Cramer-Rao bound (CRB) can be helpful to characterize vegetation and ground height estimations based on the homogenous random volume over ground (RVoG) model and polarimetric interferometric SAR techniques. However, this model is a function of 20 unknown parameters, which makes the performance analysis a tedious task. We show that the group invariance property of the RVoG model can greatly reduce the complexity of the analysis since the CRB of the vegetation and ground heights only depends on four unknown parameters instead of 20. Furthermore, for the considered situations analyzed in this letter, only three of these four parameters have a nonnegligible influence and can be interpreted as contrast parameters.

Temporal decorrelation analysis at P band over tropical forest

The TropiSAR campaign was conducted in French Guiana in the summer 2009 in the framework of the Phase A studies pertaining to the BIOMASS mission, one of the three for Earth Explorer candidates. Its main objectives were the evaluation of P-Band radar imaging over tropical forests for biomass and forest height estimation. Over two main forest sites, Paracou and Nouragues, a temporal decorrelation analysis is done in order to evaluate the performance of the PolInSAR technique in a single-satellite configuration. The interferometric coherence is observed to stay high after 22 days over the Paracou site, while presenting larger decorrelation over the Nouragues area, a more rugged area.

Analysis of PolInSAR precision for forest and ground parameters estimation in tropical context

The analysis presented in this paper is focused on the TropiSAR PolInSAR, acquired over a dense tropical forest area. Under canopy Ground height estimation based on PolInSAR analysis is explored and shown to be in good agreement with the LIDAR data. The simple estimation based on HH phase center is observed to overestimate the ground height by about 10m and presents a larger standard deviation than the Polin-SAR approach. The single baseline approach for vegetation height estimation performs well when the altitude of ambiguity is favourable with a RMS error ranging from 3 to 5 m, depending on the topography. In order to analyse the effect of topography, we have investigated the relative contribution of the ground and volume layers, obtained based on the Tabb maximum likelihood approach. As expected the topography is mostly affecting the ground contribution, both in term of backscatter variation and of scattering mechanisms. These in turn will influence the estimation performances as given by the Cramer Rao Lower Bound analysis.