Linear estimation of boundary value processes

In this paper we discuss the problem of estimating boundary value processes in one or several dimensions. The estimator dynamics are described, and by using operator transformations for these dynamics, several implementations are obtained which either diagonalize or triangularize the linear least-squares estimator. These implementations enable us to compute the estimate of the process by using two-filter type of smoothing formulas, or more general smoothing formulas similar to those used for solving the smoothing problem for 1-D causal processes.