On scattering, time reversal and information forms

Redheffer scattering theory provides a natural setting for the solution of various state-space estimation and control problems. In this short note we discuss the algorithms for filtering "in reverse" a process for which a forward model is given and the information form filter that is used when no priors are given on the model state. In the language of scattering theory the updates for both the backwards algorithm and the information form filter are shown to correspond to cascading rotated generator layers associated with a Hamiltonian two-point boundary value problem (TPBVP).