An innovations approach to least-squares estimation--Part III: Nonlinear estimation in white Gaussian noise

Abstract
In Parts I and II of this paper, we presented the innovations approach to linear least-squares estimation in additive white noise. In the present paper, we show how to extend this technique to the nonlinear estimation (filtering and smoothing) of non-Gaussian signals in additive white Gaussian noise. The use of the innovations allows us to obtain formulas and simple derivations that are remarkably similar to those used for the linear case thereby distinguishing clearly the essential points at which the nonlinear problem differs from the linear one.