General order moments in set theoretic estimation

A description is given of how information pertaining to an arbitrary absolute moment of the noise process can be used in a general set-theoretic estimation framework. It is shown that for each such piece of a priori information, a set can be constructed in the solution space by constraining the corresponding sample statistics of the estimation residual to lie within some acceptable distance from the expected value. The geometrical and topological properties of these sets are investigated. The benefits of the simultaneous use of several such sets with regard to the synthesis of better set-theoretic estimates are discussed. Applications to signal restoration/reconstruction, speech prediction, spectral estimation, and radar signal processing are discussed