Theoretical Performance Bounds on the Estimation of Forest Structure Parameters From Multibaseline SAR Data

Kurzfassung

Given their central role in the carbon budget, the SAR remote sensing of forests has become during the last two decades a “hot” research topic. A powerful way to analyze forest scattering consists in the coherent combination of multibaseline (MB) SAR data, possibly also polarimetric. For instance, SAR Tomography is a powerful technique whose natural output is the 3-D imaging in the range-azimuth-height space, thus allowing the resolution of multiple scatterers in height in the same cell. As a consequence, the extraction of a high amount of information is made possible, e.g. forest height and biomass, radar reflectivities, sub-canopy topography, soil humidity, volume extinction [1]. In the last years, many tomographic algorithms have been conceived for the estimation of forest structure parameters in both parametric and non parametric frameworks and their performance have been judged against the available in-situ measurements [2-5]. However, not so many efforts have been spent in the analytical derivation of theoretical performance bounds, despite their primary importance. In fact, such tools provide a benchmark against which it is possible to compare the performance of any estimator. Not only, but they alert to the physical impossibility of finding an estimator whose performance is lower than the bounds. This work offers a contribution to tackle the performance bounding problem by resorting to the Cramér-Rao bound (CRB) theory. The CRB is a result of the information theory which provides a lower bound on the variance of any unbiased estimator of an unknown parameter. Given also its relative easiness of calculation, the CRB is widely used in the statistical signal processing to judge the efficiency of the parameter estimators. In the specific MB SAR field, it could also be a very useful instrument to characterize the potentials of acquisition configurations and possibly as a guideline in designing acquisition patterns (mission planning) and systems. An interesting extension of the CRB is represented by the Hybrid CRB (HCRB), in which the presence of random phase offsets between different acquisitions (e.g. due to non perfect baseline estimation and/or propagation effects through the atmosphere) can be taken into account. In particular, in this work the CRB and HCRB derivations are focused to the analysis of forest areas by assuming a two-layer model for the MB data vector, i.e. a ground layer and a canopy layer, with different characteristics of their vertical structure. Starting from the very general formulations of MB bounds in [6] and [7], ready-to-use CRB and HCRB formulas are given for forest scenarios. Moreover, the obtained precision limits on the parameters of interest are calculated numerically for some realistic acquisition patterns and for different observed scenarios. The presence of temporal decorrelation is considered in the model, which is recognized to be one of the main application barriers of MB repeat-pass forest observations, especially from space [8]. References [1] A. Reigber, A.Moreira, “First Demonstration of Airborne SAR Tomography Using Multibaseline L-Band Data,” IEEE Trans. on Geoscience and Remote Sensing, vol. 38, 2000. [2] F. Lombardini, M. Pardini, “Experiments of Tomography-Based SAR Techniques with P-Band Polarimetric Data”, Proc. of the 2009 ESA PolInSAR Workshop. [3] M. Nannini, R. Scheiber, et al., “Estimation of the Minimum Number of Tracks for SAR Tomography,” IEEE Trans. on Geoscience and Remote Sensing, vol. 47, 2009. [4] M. Neumann, L. Ferro-Famil, et al., “Estimation of Forest Structure, Ground, and Canopy Layer Characteristics From Multibaseline Polarimetric Interferometric Data,” IEEE Trans. on Geoscience and Remote Sensing, vol. 48, 2010. [5] S. Tebaldini, “Single and Multipolarimetric SAR Tomography of Forested Areas: A Parametric Approach,” IEEE Trans. on Geoscience and Remote Sensing, vol. 48, 2010. [6] F. Gini, F. Lombardini, M. Montanari, “Layover Solution in Multibaseline SAR Interferometry,” IEEE Trans. on Aerospace and Electronic Systems, vol. 38, 2002. [7] M. Pardini, F. Lombardini, F. Gini, “The Hybrid Cramér-Rao Bound for Broadside DOA Estimation of Extended Sources in Presence of Array Errors,” IEEE Trans. on Signal Processing, vol. 56, pp. 1726–1730, Apr 2008. [8] F. Lombardini, F. Cai, M. Pardini, “Parametric Differential SAR Tomography of decorrelating Volume Scatterers,” Proc. of the 2009 European Radar Conference (EURAD).