Abstract
In recent years the inference of unknown parameters in differential equation has attracted considerable attention in the field of modern system theory. In particular, a need for approximate solution of conditionally wellposed problem with inaccurate data gave rise to an innovation with a regularization in the least square 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; Ueno 1981 a, b) invariant imbedding and quasi 1inearization have been applied to the inversion of diffuse reflection problems.In the present paper, making an extention of the above approach to the system identification of a distributed parameter in the nonlinear integro-differential equation, the estimation of unknown optical thickness in the homogeneous scattering in accordance with the Rayleigh's law has been, in the least-squares sense, performed. Finally, the result of the numerical experiment Cor the estimation of surface albedo in the isotropic case shown.
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