Maximum-likelihood recursive nonlinear filtering

The basic model for the general nonlinear filtering problem consists of a nonlinear plant driven by noise followed by nonlinear observation with additive noise. The object is to estimate, at each instant, the current state of the plant, given thea priori information and the history of the observations up to the current time. The estimation procedure studied here is that of computing, at each instant, the most probable trajectory given the data at that time, and taking its final value. The purpose of the present paper is to clarify some earlier studies of this procedure.