Tree parameter estimation from interferometric radar responses

This paper describes the application of a high fidelity radar scattering model in an inversion process based on a stochastic global search method. Basically, a recently developed coherent scattering model that preserves the structural features of tree canopies using fractal models is employed to generate simplified empirical models (for different tree species) that can predict the polarimetric and interferometric radar response of a forest stand efficiently and accurately. The premise for the successful development of such empirical models stems from the fact that the model outputs are averaged quantities, such as backscattering coefficients or the mean height of the scattering phase center, and therefore are expected to be very gentle functions of model inputs. For the development of the empirical model used in this study, first a sensitivity analysis is conducted in order to determine the significant parameters, the number of which determines the dimensionality of the input vector space. A red pine stand is chosen and six parameters are selected as the input parameters. Each selected parameter is allowed to have about 30% variation with respect to a centroid. Using the Monte Carlo simulation results obtained from fractal-based coherent scattering model (FCSM), a database is constructed by varying the individual parameters over a prescribed range of the input vector space around the centroid. The parameters at the centroid are obtained from the ground truth data of a red pine test stand in Raco, Michigan. For the inversion process, first a least-square estimator is used and is shown to work properly when the number of measured channels is equal to or larger than the dimension of the input vector space. But since this may not be the case in general situations, a genetic algorithm is developed and employed as a search routine for the nonlinear optimization problem