Subspace Sequence Estimation

Recent work in the theory of subspace filtering and estimation, for example the Multistage Wiener Filter (MWF) of Goldstein et. al., has focused primarily on the case of finite dimension filtering. While this is the more practical case, as it can be implemented in a general purpose computer, it has left open the theoretical question of the behavior of subspace filters in the infinite dimension case. In this work we begin develop a causal infinite dimensional filter that operates in a subspace similar to that of the MWF and whose performance approaches that of the causal Wiener Filter using this subspace.