Geometric Approach to the Singular Filtering Problem

摘要

The least-squares filtering problem for a stationary Gaussian process when the observation is not fully corrupted by white noise, the so-called singular case is studied. An optimal estimator is constructed consisting of an integrating part, which is, as in the regular case, computed from a spectral factorization or an equivalent matrix problem, and a differentiating part whose parameters are computed from a single matrix equation. This improves on older results which either work under restrictive assumptions, or describe the solution only as the result of a nested algorithm.