Scattering framework for backwards partitioned estimators

A comprehensive framework for the study of backwards partitioned estimation problems is developed. An earlier work on providing a scattering framework for least-squares state-space estimation theory is extended to a more generalized case so as to handle a generalized backwards partitioning filter, by considering a fictitious initial layer between the actual initial layer and the primary one. The resulting algorithms are shown to be related to many other estimation algorithms, for example, a generalized two-filter smoothing algorithm, the Weinert-Desai smoothing algorithm, and generalized Chandrasekhar algorithms that are applicable to time-varying models as well as time-invariant ones for the filtering and smoothing problems.