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Redheffer scattering theory is reviewed in a generalized setting as a method to derive recursive solutions of linear two-point boundary value problems (TPBVP) over arbitrarily varying intervals. The results can be used to derive a complete solution for the problem of limited-memory (or sliding-window) estimation, when a usual state-space model for the signal is available. Recursive limited-memory filters are derived for both continuous and discrete time signals.
Bruckstein⋆ et al. (Wed,) studied this question.