Scattering theory and linear least squares estimation: Part II: Discrete-time problems

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 are noted.