A general framework for the incorporation of uncertainty in set theoretic estimation

Abstract

In digital signal processing, the two main sources of uncertainty encountered in estimation problems are model uncertainty and noise. In many instances, probabilistic information is available to partially describe these sources of uncertainty. It is shown how such information can be exploited in a broad class of set theoretic estimation problems relevant to digital signal processing. A general framework is developed to construct sets in the solution space by constraining the estimation residual based on the known component of the model to be consistent with those known properties of a so-called uncertainty process consisting of the contribution of the unknown component of the model and the noise. Specific digital signal processing applications are discussed.<>