Linear estimation of boundary value stochastic processes-- Part I: The role and construction of complementary models

This paper presents a substantial extension of the method of complementary models for minimum variance linear estimation introduced by Weinert and Desai in their important paper [1]. Specifically, the method of complementary models is extended to solve estimation problems for both discrete and continuous parameter linear boundary value stochastic processes in one and higher dimensions. A major contribution of this paper is an application of Green's identity in deriving a differential operator representation of the estimator. To clarify the development and to illustrate the range of applications of our approach, two brief examples are provided: one is a 1-D discrete two-point boundary value process and the other is a 2-D process governed by Poisson's equation on the unit disk.