Parametric Identification of Multiple Scattering Systems Via the Quasilinearization

Abstract

In recent years the inference of unknown parameters in differential equations has attracted considerable attention in the field of modern system theory. In particular, a need for approximate solution of conditionally well-posed problem with inaccurate data gave rise to an innovation with a recrularization in the least squares sense, i.e., the reduction to the minimization of performance (quadratic) functionals (cf. Bellman, and Kalaba 1965). In a series of preceding papers (cf. Bellman, Kagiwada, Kalaba and Ueno 1965, 1967; Bellman, Fymat, Ueno and Vasudevan 1974), invariant imbedding and quasilinearization have been applied to the inversion of diffuse reflection problems. In the present paper, making an extension of the above approach to the system identication of multiple scattering slab bounded by the diffuse reflector, the estimation of unknown parameters in the nonlinear integro-differential equation is performed in the least squares sense. Finally, the results of numerical computation for the estimation of optical thickness and underlying surface albedo are shown.