Abstract
A certain “star-product” formalism in scattering theory as developed by Redheffer is shown to also be naturally applicable to discrete-time linear least-squares estimation problems. The formalism seems to provide a nice way of handling some of the well-known algebraic complications of the discrete-time case, e.g. the distinctions between time and measurement updates, predicted and filtered estimates, etc.Several other applications of the scattering framework are presented, including doubling formulas for the error covariance, a change of initial conditions formula, equations for a backwards Markov state model and a new derivation of the Chandrasekhar-type equations for the constant parameter case. The differences between the discrete-time and continuous- time cases are noted.
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