Filtering and fixed-point smoothing from an innovation approach in systems with uncertainty

Abstract

In this paper the least mean-squared error linear filtering and fixed- point smoothing problems in systems with uncertain observations are treated, assuming that the state-space model is not available. It is supposed that the variables describing the uncertainty are independent and the covariance matrix of the signal is known and presents a factorization in a semidegenerate kernel form. By applying an innovation approach, recursive algorithms for the filtering and fixed-point smoothing estimates are obtained; also, formulas for the error covariance matrices of the proposed estimators are presented.