An innovations approach to least-squares estimation--Part II: Linear smoothing in additive white noise

Abstract

The innovations method of Part I is used to obtain, in a simple way, a general formula for the smoothed (or noncausal) estimation of a second-order process in white noise. The smoothing solution is shown to be completely determined by the results for the (causal) filtering problem. When the signal is a lumped process, differential equations for the smoothed estimate can easily be derived from the general formula. In several cases, both the derivations and the forms of the solution are significantly simpler than those given in the literature.