A Method for Solving an Inverse Problem with Unknown Parameters from Two Sets of Relative Measurements

VEGA, J.R.; FRONTINI, G.L.; GUGLIOTTA, L.M.; ELICABE, G.E.

LATIN AMERICAN APPLIED RESEARCH

Univ. Nac. del Sur

Lugar: Bahía Blanca (Argentina); Año: 2005 vol. 35 p. 149 - 154

0327-0793

This work deals with an ill-posed in-verse problem in which a distribution function, f(x), is estimated from two independent sets of non-negative relative measurements. Each measurement set is modeled through a Fredholm equation of the first kind, with unknown parameters in its kernel. While the first measurement model only includes a scalar unknown parameter, p0, the second model contains a vector of unknown parameters, p. The proposed method consists of the following steps: (i) to obtain a first estimate of f(x) and p0 from the first measurement; (ii) to estimate the vector p from the second measurement and the previous estimate of f(x); and (iii) to estimate an improved f(x) by simul-taneously using both measurements and the esti-mated parameters in a unique combined problem. The proposed algorithm is evaluated through a nu-merical example for simultaneously estimating the particle size distribution and the refractive index of a polymer latex, from combined measurements of elas-tic light scattering and turbidity.