The use of noise properties in set theoretic estimation

In most digital signal processing problems, the goal is to estimate an object from noise corrupted observations of a physical system. The authors describe how a wide range of probabilistic information pertaining to the noise process can be used in a general set theoretic estimation framework. The basic principle is to constrain the sample statistics of the estimation residual to be consistent with those probabilistic properties of the noise which are available and to construct sets accordingly in the solution space. Adding these sets to the collection of sets describing the solution will yield a smaller feasibility set and, hence, more reliable estimates. Pieces of information relative to quantities such as range, moments, absolute moments, and second and higher order probabilistic attributes are considered, and properties of the corresponding sets are established. Simulations are provided to illustrate the theoretical developments