Linear estimation of boundary value stochastic processes--Part II: 1-D smoothing problems

This paper addresses the fixed-interval smoothing problem for linear two-point boundary value stochastic processes of the type introduced by Krener [5]. As these models are not Markovian, Kalman filtering and associated smoothing algorithms are not applicable. The smoothing problem for this class of noncausal processes is solved here by an application of the estimator solution which is developed in Part I of this paper [3] via the method of complementary models. For an th-order model, this approach yields the smoother as a 2 th-order two-point boundary value problem. It is shown that this smoother can be realized in a stable two-filter form which is remarkably similar to two-filter smoothers for causal processes. In addition, expressions for the smoothing error and smoothing error covariance are developed. These equations are employed to perform a covariance analysis of estimating the temperature and heat flow in a cooling fin.