Abstract

VEGA, J. R.; FRONTINI, G. L.; GUGLIOTTA, L. M.  and  ELICABE, G. E.. A method solving an inverse problem with unknown parameters from two sets of relative measurements. Lat. Am. appl. res. [online]. 2005, vol.35, n.2, pp.149-154. ISSN 0327-0793.

This work deals with an ill-posed inverse 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 simultaneously using both measurements and the estimated parameters in a unique combined problem. The proposed algorithm is evaluated through a numerical example for simultaneously estimating the particle size distribution and the refractive index of a polymer latex, from combined measurements of elastic light scattering and turbidity.

Keywords : Inverse Problem; Parameter Estimation; Combined Measurements; ELS; Turbidity.

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