Recursive filtering and smoothing for discrete index gaussian reciprocal processes

We study minimum mean square error (MMSE) estimation problems for discrete index Gaussian reciprocal processes (Grp´s) (or boundary valued processes) with Dirichlet boundary conditions. Our contributions are: 1) deriving first order white noise driven representations from second order correlated noise driven representations; 2) deriving Kalman like recursive filtering equations for discrete index Grp´s; and 3) deriving recursive smoothing equations for discrete index Grp´s. Unlike previous work, our approach uses forward and backwards recursive representations for the Grp and leads to lower dimensional recursive filters and smoothers.